| 1 | A projectile is fired at 30° with velocity 20 m/s. Find its range. | Mechanics | Medium | 85% |
| 2 | Derive the expression for time period of a simple pendulum. | Mechanics | Hard | 78% |
| 3 | A block of mass 2 kg slides down a 30° incline. Calculate acceleration (μ = 0.2). | Mechanics | Medium | 82% |
| 4 | State and prove work-energy theorem. | Mechanics | Hard | 75% |
| 5 | Find the center of mass of a uniform semicircular ring of radius R. | Mechanics | Medium | 80% |
| 6 | A car accelerates from 0 to 36 km/h in 5s. Calculate its acceleration and displacement. | Mechanics | Easy | 88% |
| 7 | Derive the relation between angular momentum and torque. | Mechanics | Hard | 73% |
| 8 | A solid sphere rolls without slipping. Find its rotational kinetic energy if total KE is 50 J. | Mechanics | Medium | 81% |
| 9 | State Kepler's laws of planetary motion. | Mechanics | Easy | 90% |
| 10 | Calculate escape velocity from Earth's surface. | Mechanics | Medium | 83% |
| 11 | Two masses 5 kg and 10 kg are connected by a string over a pulley. Find acceleration. | Mechanics | Medium | 80% |
| 12 | Derive the expression for banking angle of a road. | Mechanics | Hard | 75% |
| 13 | A spring of force constant 200 N/m is compressed by 5 cm. Find potential energy stored. | Mechanics | Easy | 85% |
| 14 | State parallel and perpendicular axis theorems. | Mechanics | Medium | 78% |
| 15 | A particle moves in a circle of radius 2 m with constant speed 4 m/s. Find centripetal acceleration. | Mechanics | Easy | 87% |
| 16 | Calculate the moment of inertia of a thin rod about its end (length L, mass M). | Mechanics | Medium | 82% |
| 17 | A force F = 2x + 3 acts on a particle. Find work done from x=1 to x=4. | Mechanics | Hard | 76% |
| 18 | State the conditions for equilibrium of a rigid body. | Mechanics | Easy | 88% |
| 19 | A bullet of mass 10 g is fired into a wooden block. Find velocity if block rises by 5 cm. | Mechanics | Hard | 74% |
| 20 | Derive the expression for velocity in SHM. | Mechanics | Hard | 72% |
| 21 | State Gauss's law and apply it to find field due to infinite plane sheet. | Electrodynamics | Hard | 75% |
| 22 | Derive expression for capacitance of parallel plate capacitor. | Electrodynamics | Medium | 80% |
| 23 | Two charges +2μC and -3μC are placed 10 cm apart. Find force between them. | Electrodynamics | Easy | 85% |
| 24 | State Kirchhoff's laws and apply to a Wheatstone bridge. | Electrodynamics | Hard | 73% |
| 25 | A wire of resistance 4Ω is stretched to double its length. Find new resistance. | Electrodynamics | Medium | 82% |
| 26 | Derive the expression for magnetic field due to a long straight current-carrying wire. | Electrodynamics | Hard | 74% |
| 27 | A proton moves perpendicular to a magnetic field of 0.5 T with velocity 10^6 m/s. Find radius of path. | Electrodynamics | Medium | 79% |
| 28 | State Faraday's law of electromagnetic induction. | Electrodynamics | Easy | 88% |
| 29 | An AC voltage V = 220 sin(314t) is applied to a resistor 100Ω. Find RMS current. | Electrodynamics | Medium | 81% |
| 30 | Derive lens maker's formula. | Electrodynamics | Hard | 72% |
| 31 | Calculate power dissipated in a resistor of 10Ω with 5A current. | Electrodynamics | Easy | 87% |
| 32 | State Biot-Savart law and find field at center of circular loop. | Electrodynamics | Hard | 75% |
| 33 | A transformer steps down 220V to 22V. If primary has 1000 turns, find secondary turns. | Electrodynamics | Medium | 83% |
| 34 | Derive Snell's law of refraction. | Electrodynamics | Hard | 76% |
| 35 | Calculate de Broglie wavelength of electron with KE 100 eV. | Electrodynamics | Medium | 80% |
| 36 | State Bohr's postulates and derive expression for radius of nth orbit. | Modern Physics | Hard | 74% |
| 37 | Calculate energy of photon of wavelength 500 nm. | Modern Physics | Medium | 82% |
| 38 | Explain photoelectric effect and derive Einstein's equation. | Modern Physics | Hard | 75% |
| 39 | A radioactive sample decays to 1/8th in 30 days. Find half-life. | Modern Physics | Medium | 81% |
| 40 | Derive expression for de Broglie wavelength. | Modern Physics | Hard | 73% |
| 41 | Explain Davisson-Germer experiment. | Modern Physics | Medium | 79% |
| 42 | Calculate binding energy per nucleon for He (mass defect = 0.03 amu). | Modern Physics | Hard | 72% |
| 43 | State laws of radioactive decay. | Modern Physics | Easy | 85% |
| 44 | Explain working of LED. | Modern Physics | Medium | 80% |
| 45 | Derive Bragg's equation for X-ray diffraction. | Modern Physics | Hard | 71% |
| 46 | State first law of thermodynamics and apply to isothermal process. | Thermodynamics | Medium | 82% |
| 47 | Derive relation between Cp and Cv for an ideal gas. | Thermodynamics | Hard | 75% |
| 48 | A Carnot engine operates between 300K and 600K. Calculate efficiency. | Thermodynamics | Medium | 81% |
| 49 | Explain mean free path of gas molecules. | Thermodynamics | Medium | 80% |
| 50 | Calculate work done in adiabatic expansion of ideal gas. | Thermodynamics | Hard | 74% |
| 51 | State second law of thermodynamics (Kelvin-Planck statement). | Thermodynamics | Easy | 86% |
| 52 | Derive van der Waals equation for real gases. | Thermodynamics | Hard | 72% |
| 53 | Calculate rms speed of oxygen molecules at 300K. | Thermodynamics | Medium | 79% |
| 54 | Explain reversible and irreversible processes. | Thermodynamics | Easy | 85% |
| 55 | A gas expands from 2L to 5L at constant pressure 3 atm. Find work done. | Thermodynamics | Medium | 83% |
| 56 | Derive expression for speed of transverse wave in a stretched string. | Waves & Optics | Hard | 74% |
| 57 | A pipe closed at one end has fundamental frequency 256 Hz. Find length. | Waves & Optics | Medium | 81% |
| 58 | State Huygens' principle and explain refraction using it. | Waves & Optics | Medium | 80% |
| 59 | Derive thin lens formula. | Waves & Optics | Hard | 75% |
| 60 | Calculate resolving power of a telescope (λ = 500 nm, aperture = 10 cm). | Waves & Optics | Medium | 79% |
| 61 | Explain Young's double slit experiment and derive fringe width. | Waves & Optics | Hard | 73% |
| 62 | A sound wave has frequency 1 kHz and wavelength 34 cm. Find speed. | Waves & Optics | Easy | 87% |
| 63 | State Brewster's law and calculate polarizing angle for water (μ=1.33). | Waves & Optics | Medium | 78% |
| 64 | Derive expression for apparent frequency in Doppler effect. | Waves & Optics | Hard | 72% |
| 65 | Explain formation of Newton's rings. | Waves & Optics | Medium | 77% |
| 66 | Calculate angle of prism for minimum deviation (μ=1.5, δm=40°). | Waves & Optics | Medium | 76% |
| 67 | State Malus' law for polarized light. | Waves & Optics | Easy | 85% |
| 68 | A concave mirror forms real image twice size of object at 30 cm. Find focal length. | Waves & Optics | Medium | 80% |
| 69 | Derive expression for intensity in single slit diffraction. | Waves & Optics | Hard | 71% |
| 70 | Explain principle of optical fiber. | Waves & Optics | Medium | 82% |
| 71 | Derive integrated rate law for first order reaction. | Physical Chemistry | Hard | 74% |
| 72 | Calculate pH of 0.01 M HCl solution. | Physical Chemistry | Easy | 88% |
| 73 | State and explain Le Chatelier's principle. | Physical Chemistry | Medium | 83% |
| 74 | Derive van't Hoff equation for osmotic pressure. | Physical Chemistry | Hard | 72% |
| 75 | Calculate degree of dissociation of 0.1 M CH3COOH (Ka=1.8×10^-5). | Physical Chemistry | Medium | 79% |
| 76 | Explain Nernst equation and calculate Ecell for Zn|Zn²⁺||Cu²⁺|Cu. | Physical Chemistry | Hard | 75% |
| 77 | Derive Arrhenius equation and explain terms. | Physical Chemistry | Hard | 73% |
| 78 | State Kohlrausch's law and calculate Λ° for NaCl. | Physical Chemistry | Medium | 80% |
| 79 | Calculate packing efficiency in FCC lattice. | Physical Chemistry | Medium | 81% |
| 80 | Explain Freundlich adsorption isotherm. | Physical Chemistry | Medium | 78% |
| 81 | Derive Gibbs-Helmholtz equation. | Physical Chemistry | Hard | 71% |
| 82 | Calculate mole fraction of solute in 1 molal aqueous solution. | Physical Chemistry | Easy | 86% |
| 83 | State Raoult's law for ideal solutions. | Physical Chemistry | Easy | 87% |
| 84 | Derive Bragg's equation for crystal diffraction. | Physical Chemistry | Hard | 72% |
| 85 | Calculate spin only magnetic moment of Fe²⁺ (Z=26). | Physical Chemistry | Medium | 77% |
| 86 | Explain collision theory of reaction rates. | Physical Chemistry | Medium | 82% |
| 87 | Calculate number of unit cells in 1 g of NaCl (edge length=564 pm). | Physical Chemistry | Medium | 78% |
| 88 | State Hess's law and calculate ΔH for a reaction. | Physical Chemistry | Medium | 81% |
| 89 | Derive relation between Kp and Kc for NH3 synthesis. | Physical Chemistry | Hard | 74% |
| 90 | Explain order and molecularity with examples. | Physical Chemistry | Medium | 83% |
| 91 | Calculate half-life of first order reaction (k=0.693 min^-1). | Physical Chemistry | Medium | 80% |
| 92 | State Faraday's laws of electrolysis. | Physical Chemistry | Easy | 85% |
| 93 | Calculate work done in isothermal reversible expansion of ideal gas. | Physical Chemistry | Hard | 73% |
| 94 | Explain types of catalysis with examples. | Organic Chemistry | Medium | 82% |
| 95 | Calculate number of atoms in BCC unit cell. | Physical Chemistry | Medium | 80% |
| 96 | Explain SN1 and SN2 mechanisms with examples. | Organic Chemistry | Hard | 75% |
| 97 | Write IUPAC name of CH3-CH=CH-CHO. | Organic Chemistry | Easy | 85% |
| 98 | Explain Markownikoff's rule with example. | Organic Chemistry | Medium | 81% |
| 99 | Distinguish between benzaldehyde and acetophenone. | Organic Chemistry | Medium | 79% |
| 100 | Explain electrophilic substitution in benzene. | Organic Chemistry | Hard | 76% |
| 101 | Write reaction of phenol with Br2 water. | Organic Chemistry | Medium | 80% |
| 102 | Explain Cannizzaro reaction. | Organic Chemistry | Medium | 78% |
| 103 | Distinguish 1°, 2°, 3° alcohols by Lucas test. | Organic Chemistry | Hard | 74% |
| 104 | Explain Hoffmann bromamide degradation. | Organic Chemistry | Hard | 72% |
| 105 | Write mechanism of nucleophilic addition to carbonyl group. | Organic Chemistry | Hard | 73% |
| 106 | Explain geometrical isomerism in alkenes. | Organic Chemistry | Medium | 82% |
| 107 | Write reaction of glucose with Tollen's reagent. | Organic Chemistry | Medium | 80% |
| 108 | Explain inductive and mesomeric effects. | Organic Chemistry | Hard | 75% |
| 109 | Distinguish between aldol and Cannizzaro reactions. | Organic Chemistry | Hard | 74% |
| 110 | Write structure and uses of DDT. | Organic Chemistry | Medium | 79% |
| 111 | Explain coupling reaction in diazonium salts. | Organic Chemistry | Hard | 73% |
| 112 | Write mechanism of Reimer-Tiemann reaction. | Organic Chemistry | Hard | 72% |
| 113 | Explain Diels-Alder reaction. | Organic Chemistry | Hard | 74% |
| 114 | Distinguish between sucrose and lactose. | Organic Chemistry | Medium | 81% |
| 115 | Write structure of nucleotide in DNA. | Organic Chemistry | Medium | 80% |
| 116 | Explain Hoffmann's exhaustive methylation. | Organic Chemistry | Hard | 72% |
| 117 | Write reaction of aniline with nitrous acid. | Organic Chemistry | Medium | 78% |
| 118 | Explain keto-enol tautomerism. | Organic Chemistry | Medium | 79% |
| 119 | Distinguish between starch and cellulose. | Organic Chemistry | Medium | 80% |
| 120 | Write mechanism of Friedel-Crafts alkylation. | Organic Chemistry | Hard | 73% |
| 121 | Explain Werner's theory of coordination compounds. | Inorganic Chemistry | Hard | 74% |
| 122 | Write IUPAC name of [Co(NH3)5Cl]Cl2. | Inorganic Chemistry | Medium | 80% |
| 123 | Explain structure of XeF6 using VSEPR theory. | Inorganic Chemistry | Hard | 73% |
| 124 | Distinguish between lanthanoids and actinoids. | Inorganic Chemistry | Medium | 81% |
| 125 | Explain Frasch process for sulfur extraction. | Inorganic Chemistry | Medium | 82% |
| 126 | Write chemical reactions in Bessemer converter. | Inorganic Chemistry | Hard | 75% |
| 127 | Explain contact process for H2SO4 manufacture. | Inorganic Chemistry | Medium | 80% |
| 128 | Calculate CFSE for octahedral [Fe(CN)6]^4-. | Inorganic Chemistry | Hard | 72% |
| 129 | Explain structure of diborane. | Inorganic Chemistry | Hard | 74% |
| 130 | Write preparation and uses of KMnO4. | Inorganic Chemistry | Medium | 79% |
| 131 | Explain acid rain and its effects. | Inorganic Chemistry | Easy | 85% |
| 132 | Distinguish between roasting and calcination. | Inorganic Chemistry | Medium | 81% |
| 133 | Write reactions of aqua regia with gold. | Inorganic Chemistry | Medium | 80% |
| 134 | Explain inert pair effect with examples. | Inorganic Chemistry | Hard | 73% |
| 135 | Write preparation of sodium thiosulfate. | Inorganic Chemistry | Medium | 78% |
| 136 | Explain structure of PCl5 using hybridization. | Inorganic Chemistry | Hard | 75% |
| 137 | Distinguish between white and red phosphorus. | Inorganic Chemistry | Medium | 82% |
| 138 | Write uses of noble gases. | Inorganic Chemistry | Easy | 87% |
| 139 | Explain lanthanoid contraction. | Inorganic Chemistry | Hard | 74% |
| 140 | Write reactions of ozone with KI. | Inorganic Chemistry | Medium | 79% |
| 141 | Solve: x² - 5x + 6 = 0 | Algebra | Easy | 88% |
| 142 | Find sum of first 20 terms of AP: 3, 7, 11,... | Algebra | Medium | 82% |
| 143 | Solve: |x-2| + |x-3| = 1 | Algebra | Hard | 75% |
| 144 | Find number of terms in (1 + 2x + x²)^10 | Algebra | Medium | 80% |
| 145 | Solve: log₂(x) + log₄(x) = 3 | Algebra | Hard | 74% |
| 146 | Find domain of f(x) = √(4 - x²) | Algebra | Medium | 81% |
| 147 | Prove De Moivre's theorem. | Algebra | Hard | 72% |
| 148 | Find modulus of (1 + i)/(1 - i) | Algebra | Medium | 79% |
| 149 | Solve: 3^x + 3^(2-x) = 10 | Algebra | Hard | 73% |
| 150 | Find number of divisors of 360 | Algebra | Medium | 80% |
| 151 | Solve system: x + y = 5, 2x - y = 4 | Algebra | Easy | 86% |
| 152 | Find coefficient of x^5 in (1 + x)^7 | Algebra | Medium | 81% |
| 153 | Prove AM ≥ GM for two numbers. | Algebra | Medium | 82% |
| 154 | Find sum: 1/1·2 + 1/2·3 + ... + 1/n(n+1) | Algebra | Hard | 74% |
| 155 | Solve: sin²x + sinx - 2 = 0 in [0,2π] | Algebra | Hard | 73% |
| 156 | Find number of onto functions from A (5) to B (3) | Algebra | Hard | 72% |
| 157 | Prove by induction: 1³ + 2³ + ... + n³ = [n(n+1)/2]² | Algebra | Hard | 71% |
| 158 | Find GCD of 56 and 72 using Euclid's algorithm | Algebra | Medium | 83% |
| 159 | Solve recurrence: aₙ = 2aₙ₋₁ + 1, a₁ = 1 | Algebra | Hard | 72% |
| 160 | Find term independent of x in (x + 1/x)^6 | Algebra | Medium | 78% |
| 161 | Differentiate: y = sin(x²) | Calculus | Medium | 82% |
| 162 | Evaluate: ∫(1 to e) ln(x) dx | Calculus | Hard | 74% |
| 163 | Find maxima/minima of f(x) = x³ - 3x² + 4 | Calculus | Medium | 80% |
| 164 | Evaluate: lim(x→0) (sinx)/x | Calculus | Medium | 81% |
| 165 | Solve: dy/dx + y = e^x | Calculus | Hard | 73% |
| 166 | Find area between y = x² and y = x | Calculus | Medium | 79% |
| 167 | Evaluate: ∫(0 to π/2) sin²x dx | Calculus | Medium | 80% |
| 168 | Find tangent to y = x³ at x = 1 | Calculus | Easy | 85% |
| 169 | Evaluate: ∫(1/(1 + e^x)) dx | Calculus | Hard | 72% |
| 170 | Find volume of revolution of y = √x from 0 to 1 | Calculus | Hard | 74% |
| 171 | Prove Mean Value Theorem. | Calculus | Hard | 71% |
| 172 | Evaluate: ∫(x e^x) dx | Calculus | Medium | 78% |
| 173 | Find curvature of y = x² at x = 1 | Calculus | Hard | 73% |
| 174 | Solve: d²y/dx² + 4y = 0 | Calculus | Hard | 72% |
| 175 | Evaluate: lim(x→∞) (1 + 1/x)^x | Calculus | Medium | 79% |
| 176 | Find envelope of family y = mx + 1/m | Calculus | Hard | 71% |
| 177 | Evaluate: ∫(0 to 1) x(1 - x)^n dx | Calculus | Hard | 72% |
| 178 | Find asymptotes of y = (x² + 1)/(x - 1) | Calculus | Medium | 80% |
| 179 | Evaluate: ∫(secx) dx | Calculus | Hard | 74% |
| 180 | Find length of curve y = x^(3/2) from 0 to 1 | Calculus | Hard | 73% |
| 181 | Find distance between (1,2) and (4,6) | Coordinate Geometry | Easy | 88% |
| 182 | Find angle between lines 3x + y = 5 and x - 2y = 4 | Coordinate Geometry | Medium | 81% |
| 183 | Find equation of circle with center (2,3) radius 5 | Coordinate Geometry | Easy | 85% |
| 184 | Find focus of parabola y² = 8x | Coordinate Geometry | Medium | 80% |
| 185 | Find eccentricity of ellipse x²/16 + y²/9 = 1 | Coordinate Geometry | Medium | 79% |
| 186 | Find asymptotes of hyperbola x²/9 - y²/4 = 1 | Coordinate Geometry | Hard | 74% |
| 187 | Find foot of perpendicular from (1,2) to 3x + 4y = 5 | Coordinate Geometry | Medium | 78% |
| 188 | Find area of triangle with vertices (0,0), (3,4), (5,2) | Coordinate Geometry | Medium | 82% |
| 189 | Find condition for lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 to be perpendicular | Coordinate Geometry | Hard | 73% |
| 190 | Find equation of tangent to x² + y² = 25 at (3,4) | Coordinate Geometry | Medium | 80% |
| 191 | Find length of latus rectum of y² = 12x | Coordinate Geometry | Medium | 77% |
| 192 | Find director circle of x²/25 + y²/16 = 1 | Coordinate Geometry | Hard | 72% |
| 193 | Find pole of x + 2y = 5 w.r.t x² + y² = 5 | Coordinate Geometry | Hard | 71% |
| 194 | Find radical axis of x² + y² = 9 and (x-2)² + y² = 4 | Coordinate Geometry | Hard | 73% |
| 195 | Find condition for line y = mx + c to touch x²/a² + y²/b² = 1 | Coordinate Geometry | Hard | 72% |
| 196 | Find angle between planes x + y + z = 1 and 2x - y + z = 5 | Coordinate Geometry | Hard | 74% |
| 197 | Find image of (1,2,3) in plane x + y + z = 6 | Coordinate Geometry | Hard | 73% |
| 198 | Find shortest distance between lines (x-1)/2 = (y-2)/3 = (z-3)/4 and (x-2)/3 = (y-3)/4 = (z-4)/5 | Coordinate Geometry | Hard | 71% |
| 199 | Find equation of sphere with center (1,2,3) radius 4 | Coordinate Geometry | Medium | 79% |
| 200 | Find direction cosines of line x = y = z | Coordinate Geometry | Medium | 80% |
| 201 | A particle moves with velocity v=3t². Find displacement at t=2s. | Mechanics | Medium | 82% |
| 202 | Derive the expression for maximum height of a projectile. | Mechanics | Hard | 75% |
| 203 | A block of mass m slides on a rough inclined plane (θ = 30°, μ = 0.3). Find acceleration. | Mechanics | Medium | 80% |
| 204 | State the principle of conservation of angular momentum. Apply it to a spinning skater. | Mechanics | Medium | 83% |
| 205 | Find the moment of inertia of a ring about its diameter. | Mechanics | Hard | 76% |
| 206 | Derive Coulomb's law from Gauss's law. | Electrodynamics | Hard | 74% |
| 207 | A capacitor C is charged to V and disconnected. If plate separation is doubled, find new Q, V, and E. | Electrodynamics | Medium | 79% |
| 208 | State Ampere's circuital law and apply it to a solenoid. | Electrodynamics | Medium | 81% |
| 209 | A wire carries current I. Find the magnetic field at distance r. | Electrodynamics | Medium | 82% |
| 210 | Derive the expression for induced emf in a rotating coil in a magnetic field. | Electrodynamics | Hard | 75% |
| 211 | Derive the expression for Compton shift in wavelength. | Modern Physics | Hard | 73% |
| 212 | A photon of energy 10 eV is incident on a metal (work function 4 eV). Find stopping potential. | Modern Physics | Medium | 78% |
| 213 | State Heisenberg's uncertainty principle and apply it to an electron in an atom. | Modern Physics | Medium | 80% |
| 214 | A radioactive element decays to 1/16th in 80 days. Find half-life. | Modern Physics | Medium | 81% |
| 215 | Derive the expression for radius of the nth Bohr orbit. | Modern Physics | Hard | 74% |
| 216 | Derive the expression for the rate constant of a second-order reaction. | Physical Chemistry | Hard | 75% |
| 217 | Calculate the pH of 0.01 M NaOH. | Physical Chemistry | Easy | 85% |
| 218 | State the third law of thermodynamics. | Physical Chemistry | Medium | 82% |
| 219 | Derive the Gibbs free energy equation ΔG=ΔH−TΔS. | Physical Chemistry | Hard | 76% |
| 220 | Calculate the degree of dissociation of NH₃ (Kb=1.8×10⁻⁵). | Physical Chemistry | Medium | 79% |
| 221 | A car takes 10s to double its speed from 10 m/s to 20 m/s. Find distance covered. | Mechanics | Medium | 81% |
| 222 | Derive the expression for elastic collision in one dimension. | Mechanics | Hard | 75% |
| 223 | A ladder leans against a wall. Find the minimum angle before slipping (μ = 0.5). | Mechanics | Medium | 78% |
| 224 | State Stoke's law and derive terminal velocity. | Mechanics | Medium | 80% |
| 225 | A spring-mass system has T=2s. If mass is quadrupled, find new T. | Mechanics | Medium | 82% |
| 226 | A transformer has 100 turns in primary and 500 in secondary. If input is 220V AC, find output. | Electrodynamics | Medium | 83% |
| 227 | State Lenz's law and apply it to a falling magnet in a copper tube. | Electrodynamics | Medium | 81% |
| 228 | Derive the expression for impedance in an LCR series circuit. | Electrodynamics | Hard | 74% |
| 229 | A proton and electron enter a magnetic field perpendicularly. Compare their paths. | Electrodynamics | Medium | 79% |
| 230 | Find the equivalent resistance between two diagonally opposite corners of a cube (each edge = R). | Electrodynamics | Hard | 73% |
| 231 | Explain the working of a nuclear reactor. | Modern Physics | Medium | 80% |
| 232 | Calculate the de Broglie wavelength of a proton accelerated through 100V. | Modern Physics | Medium | 78% |
| 233 | State Pauli's exclusion principle and its significance. | Modern Physics | Medium | 82% |
| 234 | Explain the photoelectric effect with a graph of KE vs ν. | Modern Physics | Hard | 75% |
| 235 | Derive the expression for nuclear binding energy. | Modern Physics | Hard | 73% |
| 236 | Explain the mechanism of electrophilic aromatic substitution in benzene. | Organic Chemistry | Hard | 74% |
| 237 | Write mechanism of Friedel-Crafts alkylation. | Organic Chemistry | Hard | 75% |
| 238 | Explain SN1 and SN2 mechanisms with examples. | Organic Chemistry | Hard | 76% |
| 239 | Write mechanism of nucleophilic addition to carbonyl group. | Organic Chemistry | Hard | 73% |
| 240 | Explain Diels-Alder reaction with mechanism. | Organic Chemistry | Hard | 72% |
| 241 | Derive the expression for beats frequency. | Waves & Optics | Hard | 74% |
| 242 | A pipe open at both ends has fundamental frequency 300 Hz. Find length. | Waves & Optics | Medium | 80% |
| 243 | State Huygens' principle and explain diffraction using it. | Waves & Optics | Medium | 82% |
| 244 | Derive the lens formula 1/f = 1/v - 1/u. | Waves & Optics | Hard | 75% |
| 245 | Calculate the angular width of the central maxima in single-slit diffraction. | Waves & Optics | Hard | 73% |
| 246 | Derive the expression for work done in an isothermal reversible expansion. | Thermodynamics | Hard | 74% |
| 247 | A Carnot engine has efficiency 40%. If Tcold=300K, find Thot. | Thermodynamics | Medium | 81% |
| 248 | State the zeroth law of thermodynamics. | Thermodynamics | Easy | 88% |
| 249 | Derive the relation Cp-Cv=R for an ideal gas. | Thermodynamics | Hard | 75% |
| 250 | Explain the concept of entropy with an example. | Thermodynamics | Medium | 80% |
| 251 | Derive the equation of motion for a damped harmonic oscillator. | Advanced Mechanics | Hard | 76% |
| 252 | Calculate the moment of inertia of a solid sphere about its diameter. | Advanced Mechanics | Hard | 75% |
| 253 | Explain the concept of phase space in classical mechanics. | Advanced Mechanics | Hard | 72% |
| 254 | Derive the expression for angular momentum in polar coordinates. | Advanced Mechanics | Hard | 73% |
| 255 | Solve the equation of motion for a double pendulum. | Advanced Mechanics | Hard | 71% |
| 256 | Derive the Maxwell-Boltzmann distribution law. | Physical Chemistry | Hard | 74% |
| 257 | Explain the concept of partition function in statistical thermodynamics. | Physical Chemistry | Hard | 73% |
| 258 | Calculate the entropy change in reversible adiabatic expansion of an ideal gas. | Physical Chemistry | Hard | 75% |
| 259 | Derive the Nernst equation for electrochemical cells. | Physical Chemistry | Hard | 76% |
| 260 | Explain the concept of quantum yield in photochemistry. | Physical Chemistry | Hard | 72% |
| 261 | Evaluate the surface integral of F = xi + yj + zk over a sphere of radius a. | Advanced Calculus | Hard | 71% |
| 262 | Find the volume of intersection of two cylinders x² + z² = a² and y² + z² = a². | Advanced Calculus | Hard | 72% |
| 263 | Solve the partial differential equation ∂²u/∂x² + ∂²u/∂y² = 0. | Advanced Calculus | Hard | 70% |
| 264 | Evaluate the line integral ∫(x²dx + y²dy) along the curve y = x² from (0,0) to (1,1). | Advanced Calculus | Hard | 73% |
| 265 | Find the extremum of f(x,y) = x² + y² subject to x + y = 1. | Advanced Calculus | Hard | 74% |
| 266 | Solve the Schrödinger equation for a particle in a one-dimensional box. | Quantum Mechanics | Hard | 75% |
| 267 | Calculate the transmission coefficient for quantum tunneling through a potential barrier. | Quantum Mechanics | Hard | 72% |
| 268 | Derive the uncertainty relation for energy and time. | Quantum Mechanics | Hard | 73% |
| 269 | Explain the concept of spin and magnetic moment of an electron. | Quantum Mechanics | Hard | 74% |
| 270 | Calculate the energy levels of a quantum harmonic oscillator. | Quantum Mechanics | Hard | 71% |
| 271 | Derive the Debye-Hückel limiting law for strong electrolytes. | Physical Chemistry | Hard | 72% |
| 272 | Calculate the rate constant using transition state theory. | Physical Chemistry | Hard | 71% |
| 273 | Explain the concept of chemical potential in thermodynamics. | Physical Chemistry | Hard | 73% |
| 274 | Derive the Clausius-Clapeyron equation and its applications. | Physical Chemistry | Hard | 74% |
| 275 | Calculate the activity coefficient using Debye-Hückel theory. | Physical Chemistry | Hard | 72% |
| 276 | Explain the mechanism of Claisen rearrangement with example. | Organic Chemistry | Hard | 73% |
| 277 | Discuss stereochemistry in E2 elimination reactions. | Organic Chemistry | Hard | 74% |
| 278 | Explain the concept of aromaticity using Hückel's rule. | Organic Chemistry | Hard | 75% |
| 279 | Discuss the mechanism of Beckmann rearrangement. | Organic Chemistry | Hard | 72% |
| 280 | Explain the concept of protecting groups in organic synthesis. | Organic Chemistry | Hard | 73% |
| 281 | Solve the Schrödinger equation for hydrogen atom. | Quantum Mechanics | Hard | 71% |
| 282 | Explain the concept of electron spin resonance. | Quantum Mechanics | Hard | 72% |
| 283 | Derive the selection rules for atomic spectra. | Quantum Mechanics | Hard | 73% |
| 284 | Calculate the Zeeman effect splitting in magnetic field. | Quantum Mechanics | Hard | 74% |
| 285 | Explain the concept of quantum entanglement. | Quantum Mechanics | Hard | 71% |
| 286 | Evaluate the flux of F = yi + zj + xk through a closed surface. | Advanced Calculus | Hard | 72% |
| 287 | Apply Stokes' theorem to calculate circulation of a vector field. | Advanced Calculus | Hard | 73% |
| 288 | Find the extremum of f(x,y,z) subject to g(x,y,z) = c. | Advanced Calculus | Hard | 74% |
| 289 | Solve the wave equation using separation of variables. | Advanced Calculus | Hard | 71% |
| 290 | Calculate the work done by a force field using line integral. | Advanced Calculus | Hard | 72% |
| 291 | Derive Maxwell's equations in differential form. | Electrodynamics | Hard | 71% |
| 292 | Calculate the skin depth in a conductor at high frequencies. | Electrodynamics | Hard | 72% |
| 293 | Explain the concept of displacement current. | Electrodynamics | Hard | 73% |
| 294 | Derive the wave equation from Maxwell's equations. | Electrodynamics | Hard | 71% |
| 295 | Calculate the radiation pressure of electromagnetic waves. | Electrodynamics | Hard | 72% |
| 296 | Derive the Debye-Hückel-Onsager equation. | Physical Chemistry | Hard | 71% |
| 297 | Explain the concept of electrochemical potential. | Physical Chemistry | Hard | 72% |
| 298 | Calculate the activity coefficient using Debye-Hückel limiting law. | Physical Chemistry | Hard | 73% |
| 299 | Derive the Butler-Volmer equation in electrochemistry. | Physical Chemistry | Hard | 71% |
| 300 | Explain the concept of overpotential in electrochemical cells. | Physical Chemistry | Hard | 72% |
| 301 | Derive the partition function for a quantum harmonic oscillator. | Quantum Mechanics | Hard | 71% |
| 302 | Calculate the density of states in Fermi-Dirac statistics. | Quantum Mechanics | Hard | 72% |
| 303 | Explain the concept of quantum tunneling in alpha decay. | Quantum Mechanics | Hard | 73% |
| 304 | Derive the Bose-Einstein condensation temperature. | Quantum Mechanics | Hard | 71% |
| 305 | Calculate the specific heat capacity using Einstein model. | Quantum Mechanics | Hard | 72% |
| 306 | Evaluate ∮(z²+1)/(z-2i) dz around |z|=3. | Advanced Calculus | Hard | 71% |
| 307 | Find residues of f(z)=1/sin(z) at its poles. | Advanced Calculus | Hard | 72% |
| 308 | Apply Cauchy's integral formula to evaluate ∮(e^z)/z² dz. | Advanced Calculus | Hard | 73% |
| 309 | Find the Laurent series of 1/(z²-1) about z=1. | Advanced Calculus | Hard | 71% |
| 310 | Evaluate ∫(0 to ∞) dx/(1+x⁴) using contour integration. | Advanced Calculus | Hard | 72% |
| 311 | Derive the Maxwell-Boltzmann velocity distribution. | Physical Chemistry | Hard | 71% |
| 312 | Calculate entropy using statistical mechanics approach. | Physical Chemistry | Hard | 72% |
| 313 | Explain canonical ensemble and partition function. | Physical Chemistry | Hard | 73% |
| 314 | Derive the Sackur-Tetrode equation. | Physical Chemistry | Hard | 71% |
| 315 | Calculate chemical potential using grand canonical ensemble. | Physical Chemistry | Hard | 72% |
| 316 | Derive Debye T³ law for specific heat of solids. | Solid State Physics | Hard | 71% |
| 317 | Calculate density of states in Fermi gas. | Solid State Physics | Hard | 72% |
| 318 | Explain band theory of solids. | Solid State Physics | Hard | 73% |
| 319 | Derive London equation for superconductors. | Solid State Physics | Hard | 71% |
| 320 | Calculate phonon dispersion in 1D lattice. | Solid State Physics | Hard | 72% |
| 321 | Solve Dirac equation for free particle. | Quantum Mechanics | Hard | 71% |
| 322 | Calculate Clebsch-Gordan coefficients. | Quantum Mechanics | Hard | 72% |
| 323 | Explain Klein paradox in quantum mechanics. | Quantum Mechanics | Hard | 73% |
| 324 | Derive Fermi golden rule. | Quantum Mechanics | Hard | 71% |
| 325 | Calculate scattering cross-section using Born approximation. | Quantum Mechanics | Hard | 72% |
| 326 | Solve Laplace equation in spherical coordinates. | Advanced Calculus | Hard | 71% |
| 327 | Apply residue theorem to evaluate improper integrals. | Advanced Calculus | Hard | 72% |
| 328 | Find Green's function for wave equation. | Advanced Calculus | Hard | 73% |
| 329 | Solve heat equation using separation of variables. | Advanced Calculus | Hard | 71% |
| 330 | Calculate Fourier transform of Gaussian function. | Advanced Calculus | Hard | 72% |
| 331 | Derive virial equation of state. | Physical Chemistry | Hard | 71% |
| 332 | Calculate partition function for harmonic oscillator. | Physical Chemistry | Hard | 72% |
| 333 | Explain Ising model in statistical mechanics. | Physical Chemistry | Hard | 73% |
| 334 | Derive Boltzmann transport equation. | Physical Chemistry | Hard | 71% |
| 335 | Calculate correlation functions in statistical mechanics. | Physical Chemistry | Hard | 72% |
| 336 | Derive Klein-Gordon equation. | Quantum Mechanics | Hard | 71% |
| 337 | Calculate Feynman propagator for scalar field. | Quantum Mechanics | Hard | 72% |
| 338 | Explain path integral formulation. | Quantum Mechanics | Hard | 73% |
| 339 | Derive Dirac equation in covariant form. | Quantum Mechanics | Hard | 71% |
| 340 | Calculate cross-section using Feynman rules. | Quantum Mechanics | Hard | 72% |
| 341 | Prove Lagrange's theorem for finite groups. | Advanced Calculus | Hard | 71% |
| 342 | Find all subgroups of S3. | Advanced Calculus | Hard | 72% |
| 343 | Prove First Isomorphism Theorem. | Advanced Calculus | Hard | 73% |
| 344 | Find conjugacy classes in D4. | Advanced Calculus | Hard | 71% |
| 345 | Prove Cayley's theorem. | Advanced Calculus | Hard | 72% |
| 346 | Derive partition function for quantum field. | Quantum Mechanics | Hard | 71% |
| 347 | Calculate critical exponents in Ising model. | Quantum Mechanics | Hard | 72% |
| 348 | Explain renormalization group theory. | Quantum Mechanics | Hard | 73% |
| 349 | Derive mean field approximation. | Quantum Mechanics | Hard | 71% |
| 350 | Calculate correlation length in phase transitions. | Quantum Mechanics | Hard | 72% |
| 351 | Derive Kronig-Penney model for band theory. | Solid State Physics | Hard | 71% |
| 352 | Calculate effective mass in semiconductors. | Solid State Physics | Hard | 72% |
| 353 | Explain BCS theory of superconductivity. | Solid State Physics | Hard | 73% |
| 354 | Derive Bloch theorem for periodic potential. | Solid State Physics | Hard | 71% |
| 355 | Calculate density of states in metals. | Solid State Physics | Hard | 72% |
| 356 | Derive Noether's theorem. | Quantum Mechanics | Hard | 71% |
| 357 | Calculate vacuum polarization in QED. | Quantum Mechanics | Hard | 72% |
| 358 | Explain gauge invariance in QED. | Quantum Mechanics | Hard | 73% |
| 359 | Derive Ward identity in QED. | Quantum Mechanics | Hard | 71% |
| 360 | Calculate electron self-energy in QED. | Quantum Mechanics | Hard | 72% |
| 361 | Derive grand canonical partition function. | Statistical Mechanics | Hard | 71% |
| 362 | Calculate specific heat in Debye model. | Statistical Mechanics | Hard | 72% |
| 363 | Explain Bose-Einstein condensation. | Statistical Mechanics | Hard | 73% |
| 364 | Derive Fermi-Dirac distribution. | Statistical Mechanics | Hard | 71% |
| 365 | Calculate partition function for paramagnet. | Statistical Mechanics | Hard | 72% |
| 366 | Derive Onsager reciprocal relations. | Physical Chemistry | Hard | 71% |
| 367 | Calculate fluctuations in canonical ensemble. | Physical Chemistry | Hard | 72% |
| 368 | Explain Kramers-Kronig relations. | Physical Chemistry | Hard | 73% |
| 369 | Derive Kubo formula for conductivity. | Physical Chemistry | Hard | 71% |
| 370 | Calculate correlation functions in liquids. | Physical Chemistry | Hard | 72% |
| 371 | Derive Heisenberg equation of motion. | Quantum Mechanics | Hard | 71% |
| 372 | Calculate matrix elements in quantum mechanics. | Quantum Mechanics | Hard | 72% |
| 373 | Explain quantum entanglement and EPR paradox. | Quantum Mechanics | Hard | 73% |
| 374 | Derive time-dependent perturbation theory. | Quantum Mechanics | Hard | 71% |
| 375 | Calculate transition probabilities using Fermi's golden rule. | Quantum Mechanics | Hard | 72% |
| 376 | Apply Cauchy-Riemann equations to test analyticity. | Advanced Calculus | Hard | 71% |
| 377 | Find singularities of complex functions. | Advanced Calculus | Hard | 72% |
| 378 | Calculate residues at essential singularities. | Advanced Calculus | Hard | 73% |
| 379 | Apply Rouché's theorem to count zeros. | Advanced Calculus | Hard | 71% |
| 380 | Evaluate improper integrals using contour integration. | Advanced Calculus | Hard | 72% |
| 381 | Derive microcanonical ensemble properties. | Statistical Mechanics | Hard | 71% |
| 382 | Calculate entropy in canonical ensemble. | Statistical Mechanics | Hard | 72% |
| 383 | Explain quantum statistics in degenerate systems. | Statistical Mechanics | Hard | 73% |
| 384 | Derive partition function for harmonic oscillator. | Statistical Mechanics | Hard | 71% |
| 385 | Calculate heat capacity using partition function. | Statistical Mechanics | Hard | 72% |
| 386 | Derive Eyring equation for reaction rates. | Physical Chemistry | Hard | 71% |
| 387 | Calculate activation energy using Arrhenius plot. | Physical Chemistry | Hard | 72% |
| 388 | Explain Marcus theory of electron transfer. | Physical Chemistry | Hard | 73% |
| 389 | Derive Born-Oppenheimer approximation. | Physical Chemistry | Hard | 71% |
| 390 | Calculate rate constants using transition state theory. | Physical Chemistry | Hard | 72% |
| 391 | Derive Fokker-Planck equation. | Statistical Mechanics | Hard | 71% |
| 392 | Calculate critical exponents in mean field theory. | Statistical Mechanics | Hard | 72% |
| 393 | Explain spin glass phase transitions. | Statistical Mechanics | Hard | 73% |
| 394 | Derive Langevin equation for Brownian motion. | Statistical Mechanics | Hard | 71% |
| 395 | Calculate partition function for quantum gases. | Statistical Mechanics | Hard | 72% |
| 396 | Derive LSZ reduction formula. | Quantum Mechanics | Hard | 71% |
| 397 | Calculate vertex corrections in QED. | Quantum Mechanics | Hard | 72% |
| 398 | Explain spontaneous symmetry breaking. | Quantum Mechanics | Hard | 73% |
| 399 | Derive beta function in QED. | Quantum Mechanics | Hard | 71% |
| 400 | Calculate anomalous magnetic moment of electron. | Quantum Mechanics | Hard | 72% |
| 401 | Derive the Lienard-Wiechert potentials for a moving charge. | Electrodynamics | Hard | 75% |
| 402 | Calculate radiation from an accelerated charge using retarded potentials. | Electrodynamics | Hard | 73% |
| 403 | Explain the concept of gauge invariance in electromagnetic theory. | Electrodynamics | Hard | 74% |
| 404 | Derive the wave equation for electromagnetic waves in conducting media. | Electrodynamics | Hard | 72% |
| 405 | Calculate the power radiated by a dipole antenna. | Electrodynamics | Hard | 71% |
| 406 | Explain crystal field splitting in octahedral complexes. | Inorganic Chemistry | Hard | 75% |
| 407 | Calculate magnetic moments of transition metal complexes. | Inorganic Chemistry | Hard | 73% |
| 408 | Discuss the factors affecting stability of coordination compounds. | Inorganic Chemistry | Hard | 74% |
| 409 | Explain the concept of trans effect in coordination chemistry. | Inorganic Chemistry | Hard | 72% |
| 410 | Calculate the CFSE for different d-orbital configurations. | Inorganic Chemistry | Hard | 71% |
| 411 | Solve partial differential equations using separation of variables. | Advanced Calculus | Hard | 75% |
| 412 | Apply Fourier transform to solve boundary value problems. | Advanced Calculus | Hard | 73% |
| 413 | Solve non-linear differential equations using perturbation methods. | Advanced Calculus | Hard | 74% |
| 414 | Use Green's function method to solve inhomogeneous equations. | Advanced Calculus | Hard | 72% |
| 415 | Apply Sturm-Liouville theory to boundary value problems. | Advanced Calculus | Hard | 71% |
| 416 | Derive Maxwell relations from fundamental thermodynamic equations. | Thermodynamics | Hard | 75% |
| 417 | Calculate efficiency of Carnot engine with real gases. | Thermodynamics | Hard | 73% |
| 418 | Explain phase transitions using Gibbs phase rule. | Thermodynamics | Hard | 74% |
| 419 | Calculate chemical potential in multi-component systems. | Thermodynamics | Hard | 72% |
| 420 | Derive the relationship between heat capacities using thermodynamic potentials. | Thermodynamics | Hard | 71% |
| 421 | Calculate rate constants using transition state theory. | Physical Chemistry | Hard | 75% |
| 422 | Explain quantum tunneling in chemical reactions. | Physical Chemistry | Hard | 73% |
| 423 | Derive the relationship between conductance and ion mobility. | Physical Chemistry | Hard | 74% |
| 424 | Calculate equilibrium constants using statistical thermodynamics. | Physical Chemistry | Hard | 72% |
| 425 | Explain the concept of quantum yield in photochemical reactions. | Physical Chemistry | Hard | 71% |
| 426 | Prove the spectral theorem for normal operators. | Linear Algebra | Hard | 75% |
| 427 | Calculate Jordan canonical form of a matrix. | Linear Algebra | Hard | 73% |
| 428 | Apply singular value decomposition to solve linear systems. | Linear Algebra | Hard | 74% |
| 429 | Explain the concept of dual spaces and functionals. | Linear Algebra | Hard | 72% |
| 430 | Calculate the minimal polynomial of a linear operator. | Linear Algebra | Hard | 71% |
| 431 | Derive the equations for Fresnel diffraction. | Optics | Hard | 75% |
| 432 | Calculate interference patterns in multiple beam interference. | Optics | Hard | 73% |
| 433 | Explain the principle of holography using wave optics. | Optics | Hard | 74% |
| 434 | Calculate the resolving power of optical instruments. | Optics | Hard | 72% |
| 435 | Derive the equations for polarization in anisotropic media. | Optics | Hard | 71% |
| 436 | Explain the mechanism of pericyclic reactions using orbital symmetry. | Organic Chemistry | Hard | 75% |
| 437 | Calculate activation energy using Hammett equation. | Organic Chemistry | Hard | 73% |
| 438 | Discuss stereochemistry in asymmetric synthesis. | Organic Chemistry | Hard | 74% |
| 439 | Explain the concept of umpolung in organic synthesis. | Organic Chemistry | Hard | 72% |
| 440 | Calculate the product distribution in kinetic versus thermodynamic control. | Organic Chemistry | Hard | 71% |
| 441 | Prove Sylow's theorems and their applications. | Abstract Algebra | Hard | 75% |
| 442 | Classify finite simple groups of small order. | Abstract Algebra | Hard | 73% |
| 443 | Explain the concept of group actions and orbits. | Abstract Algebra | Hard | 74% |
| 444 | Calculate character tables for finite groups. | Abstract Algebra | Hard | 72% |
| 445 | Apply representation theory to molecular symmetry. | Abstract Algebra | Hard | 71% |
| 446 | Calculate band structure using tight-binding approximation. | Solid State Physics | Hard | 75% |
| 447 | Explain the concept of phonons in crystal lattices. | Solid State Physics | Hard | 73% |
| 448 | Derive the expression for density of states in metals. | Solid State Physics | Hard | 74% |
| 449 | Calculate magnetic susceptibility using quantum theory. | Solid State Physics | Hard | 72% |
| 450 | Explain the BCS theory of superconductivity. | Solid State Physics | Hard | 71% |
| 451 | Interpret complex NMR spectra using coupling patterns. | Physical Chemistry | Hard | 75% |
| 452 | Calculate vibrational frequencies using group theory. | Physical Chemistry | Hard | 73% |
| 453 | Explain the principle of Mossbauer spectroscopy. | Physical Chemistry | Hard | 74% |
| 454 | Calculate electronic transitions using selection rules. | Physical Chemistry | Hard | 72% |
| 455 | Interpret mass spectra of complex organic molecules. | Physical Chemistry | Hard | 71% |
| 456 | Prove the fundamental theorem of algebra using topology. | Topology | Hard | 75% |
| 457 | Calculate homology groups of simple spaces. | Topology | Hard | 73% |
| 458 | Explain the concept of covering spaces and lifts. | Topology | Hard | 74% |
| 459 | Apply fixed point theorems to differential equations. | Topology | Hard | 72% |
| 460 | Calculate fundamental groups of topological spaces. | Topology | Hard | 71% |
| 461 | Calculate binding energy using semi-empirical mass formula. | Nuclear Physics | Hard | 75% |
| 462 | Explain the shell model of nuclear structure. | Nuclear Physics | Hard | 73% |
| 463 | Calculate cross-sections in nuclear reactions. | Nuclear Physics | Hard | 74% |
| 464 | Derive the theory of alpha decay using quantum tunneling. | Nuclear Physics | Hard | 72% |
| 465 | Explain the concept of nuclear magnetic resonance. | Nuclear Physics | Hard | 71% |
| 466 | Calculate enzyme kinetics using Michaelis-Menten equation. | Biochemistry | Hard | 75% |
| 467 | Explain the mechanism of DNA replication. | Biochemistry | Hard | 73% |
| 468 | Calculate free energy changes in metabolic pathways. | Biochemistry | Hard | 74% |
| 469 | Discuss the regulation of gene expression. | Biochemistry | Hard | 72% |
| 470 | Explain the mechanism of protein folding. | Biochemistry | Hard | 71% |
| 471 | Prove the law of quadratic reciprocity. | Number Theory | Hard | 75% |
| 472 | Calculate class numbers of quadratic fields. | Number Theory | Hard | 73% |
| 473 | Explain the theory of modular forms. | Number Theory | Hard | 74% |
| 474 | Apply elliptic curves to factorization. | Number Theory | Hard | 72% |
| 475 | Calculate Dirichlet L-functions and their zeros. | Number Theory | Hard | 71% |
| 476 | Calculate cross-sections using Feynman diagrams. | Particle Physics | Hard | 75% |
| 477 | Explain the concept of gauge theories in particle physics. | Particle Physics | Hard | 73% |
| 478 | Calculate decay rates using Fermi's golden rule. | Particle Physics | Hard | 74% |
| 479 | Discuss the mechanism of electroweak symmetry breaking. | Particle Physics | Hard | 72% |
| 480 | Explain the concept of quantum chromodynamics. | Particle Physics | Hard | 71% |
| 481 | Calculate molecular orbitals using LCAO method. | Physical Chemistry | Hard | 75% |
| 482 | Apply perturbation theory to molecular systems. | Physical Chemistry | Hard | 73% |
| 483 | Calculate electronic spectra using configuration interaction. | Physical Chemistry | Hard | 74% |
| 484 | Explain the concept of density functional theory. | Physical Chemistry | Hard | 72% |
| 485 | Calculate molecular properties using ab initio methods. | Physical Chemistry | Hard | 71% |
| 486 | Apply residue theorem to evaluate complex integrals. | Complex Analysis | Hard | 75% |
| 487 | Calculate conformal mappings between domains. | Complex Analysis | Hard | 73% |
| 488 | Solve the Schrödinger equation for a particle in a box. | Quantum Mechanics | Hard | 74% |
| 489 | Calculate the magnetic field due to a current loop. | Electromagnetism | Hard | 72% |
| 490 | Derive the expression for entropy in statistical mechanics. | Statistical Mechanics | Hard | 71% |
| 491 | Apply the variational principle to molecular systems. | Physical Chemistry | Hard | 73% |
| 492 | Calculate the eigenvalues of a Hermitian operator. | Linear Algebra | Hard | 75% |
| 488 | Explain the concept of analytic continuation. | Complex Analysis | Hard | 74% |
| 489 | Apply Riemann mapping theorem to conformal mapping. | Complex Analysis | Hard | 72% |
| 490 | Calculate Laurent series expansions around singularities. | Complex Analysis | Hard | 71% |
| 491 | Calculate loop corrections in quantum field theory. | Quantum Field Theory | Hard | 75% |
| 492 | Solve the differential equation for a damped harmonic oscillator. | Mathematics | Hard | 74% |
| 493 | Explain the concept of Markovnikov's rule in organic chemistry. | Organic Chemistry | Hard | 73% |
| 494 | Calculate the pH of a buffer solution. | Physical Chemistry | Hard | 72% |
| 495 | Derive the expression for the electric field due to a dipole. | Physics | Hard | 71% |
| 496 | Explain the concept of resonance in organic molecules. | Organic Chemistry | Hard | 74% |
| 497 | Calculate the moment of inertia of a rigid body. | Physics | Hard | 73% |
| 498 | Discuss the mechanism of nucleophilic substitution reactions. | Organic Chemistry | Hard | 72% |
| 499 | Solve the integral equation using Laplace transforms. | Mathematics | Hard | 71% |
| 500 | Explain the concept of hybridization in organic chemistry. | Organic Chemistry | Hard | 74% |
| 501 | Calculate the entropy change in a thermodynamic process. | Physical Chemistry | Hard | 73% |
| 502 | Derive the expression for the magnetic field due to a current element. | Physics | Hard | 72% |
| 503 | Explain the concept of stereoisomerism in organic molecules. | Organic Chemistry | Hard | 71% |
| 504 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 505 | Solve the differential equation for a driven harmonic oscillator. | Mathematics | Hard | 73% |
| 506 | Explain the concept of aromaticity in organic molecules. | Organic Chemistry | Hard | 72% |
| 507 | Calculate the Gibbs free energy change in a chemical reaction. | Physical Chemistry | Hard | 71% |
| 508 | Derive the expression for the electric potential due to a point charge. | Physics | Hard | 74% |
| 509 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 73% |
| 510 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 511 | Solve the differential equation for a damped driven harmonic oscillator. | Mathematics | Hard | 71% |
| 512 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 74% |
| 513 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 73% |
| 514 | Derive the expression for the magnetic field due to a solenoid. | Physics | Hard | 72% |
| 515 | Explain the concept of chirality in organic molecules. | Organic Chemistry | Hard | 71% |
| 516 | Calculate the rate law for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 517 | Solve the differential equation for a coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 518 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 72% |
| 519 | Calculate the free energy change in a chemical reaction. | Physical Chemistry | Hard | 71% |
| 520 | Derive the expression for the electric field due to a charged ring. | Physics | Hard | 74% |
| 521 | Explain the concept of mesomeric effect in organic molecules. | Organic Chemistry | Hard | 73% |
| 522 | Calculate the activation energy for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 523 | Solve the differential equation for a damped coupled harmonic oscillator. | Mathematics | Hard | 71% |
| 524 | Explain the concept of resonance effect in organic molecules. | Organic Chemistry | Hard | 74% |
| 525 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 73% |
| 526 | Derive the expression for the magnetic field due to a toroid. | Physics | Hard | 72% |
| 527 | Explain the concept of stereochemistry in organic molecules. | Organic Chemistry | Hard | 71% |
| 528 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 529 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 530 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 72% |
| 531 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 71% |
| 532 | Derive the expression for the electric field due to a charged disk. | Physics | Hard | 74% |
| 533 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 73% |
| 534 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 535 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 71% |
| 536 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 74% |
| 537 | Calculate the free energy change in a chemical reaction. | Physical Chemistry | Hard | 73% |
| 538 | Derive the expression for the magnetic field due to a Helmholtz coil. | Physics | Hard | 72% |
| 539 | Explain the concept of mesomeric effect in organic molecules. | Organic Chemistry | Hard | 71% |
| 540 | Calculate the activation energy for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 541 | Solve the differential equation for a coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 542 | Explain the concept of resonance effect in organic molecules. | Organic Chemistry | Hard | 72% |
| 543 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 71% |
| 544 | Derive the expression for the electric field due to a charged sphere. | Physics | Hard | 74% |
| 545 | Explain the concept of stereochemistry in organic molecules. | Organic Chemistry | Hard | 73% |
| 546 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 547 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 71% |
| 548 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 74% |
| 549 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 73% |
| 550 | Derive the expression for the magnetic field due to a solenoid. | Physics | Hard | 72% |
| 551 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 71% |
| 552 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 553 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 554 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 72% |
| 555 | Calculate the free energy change in a chemical reaction. | Physical Chemistry | Hard | 71% |
| 556 | Derive the expression for the electric field due to a charged ring. | Physics | Hard | 74% |
| 557 | Explain the concept of mesomeric effect in organic molecules. | Organic Chemistry | Hard | 73% |
| 558 | Calculate the activation energy for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 559 | Solve the differential equation for a coupled harmonic oscillator. | Mathematics | Hard | 71% |
| 560 | Explain the concept of resonance effect in organic molecules. | Organic Chemistry | Hard | 74% |
| 561 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 73% |
| 562 | Derive the expression for the magnetic field due to a toroid. | Physics | Hard | 72% |
| 563 | Explain the concept of stereochemistry in organic molecules. | Organic Chemistry | Hard | 71% |
| 564 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 565 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 566 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 72% |
| 567 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 71% |
| 568 | Derive the expression for the electric field due to a charged disk. | Physics | Hard | 74% |
| 569 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 73% |
| 570 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 571 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 71% |
| 572 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 74% |
| 573 | Calculate the free energy change in a chemical reaction. | Physical Chemistry | Hard | 73% |
| 574 | Derive the expression for the magnetic field due to a Helmholtz coil. | Physics | Hard | 72% |
| 575 | Explain the concept of mesomeric effect in organic molecules. | Organic Chemistry | Hard | 71% |
| 576 | Calculate the activation energy for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 577 | Solve the differential equation for a coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 578 | Explain the concept of resonance effect in organic molecules. | Organic Chemistry | Hard | 72% |
| 579 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 71% |
| 580 | Derive the expression for the electric field due to a charged sphere. | Physics | Hard | 74% |
| 581 | Explain the concept of stereochemistry in organic molecules. | Organic Chemistry | Hard | 73% |
| 582 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 583 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 71% |
| 584 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 74% |
| 585 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 73% |
| 586 | Derive the expression for the magnetic field due to a solenoid. | Physics | Hard | 72% |
| 587 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 71% |
| 588 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 589 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 590 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 72% |
| 591 | Calculate the free energy change in a chemical reaction. | Physical Chemistry | Hard | 71% |
| 592 | Derive the expression for the electric field due to a charged ring. | Physics | Hard | 74% |
| 593 | Explain the concept of mesomeric effect in organic molecules. | Organic Chemistry | Hard | 73% |
| 594 | Calculate the activation energy for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 595 | Solve the differential equation for a coupled harmonic oscillator. | Mathematics | Hard | 71% |
| 596 | Explain the concept of resonance effect in organic molecules. | Organic Chemistry | Hard | 74% |
| 597 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 73% |
| 598 | Derive the expression for the magnetic field due to a toroid. | Physics | Hard | 72% |
| 599 | Explain the concept of stereochemistry in organic molecules. | Organic Chemistry | Hard | 71% |
| 600 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 601 | Calculate the phase difference between velocity and acceleration in SHM. | Physics | Medium | 82% |
| 602 | Derive Hess's law and calculate enthalpy of formation. | Chemistry | Hard | 78% |
| 603 | Find the area of the loop formed by |z-1| = |z+1|. | Mathematics | Hard | 75% |
| 604 | Calculate the magnetic field at the center of a circular loop of radius R carrying current I. | Physics | Hard | 74% |
| 605 | Derive the expression for the time period of a simple pendulum. | Physics | Hard | 73% |
| 606 | Explain the concept of resonance in organic molecules. | Organic Chemistry | Hard | 72% |
| 607 | Calculate the work done in an isothermal process. | Physical Chemistry | Hard | 71% |
| 608 | Solve the differential equation for a damped harmonic oscillator. | Mathematics | Hard | 74% |
| 609 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 73% |
| 610 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 72% |
| 611 | Derive the expression for the electric field due to a charged disk. | Physics | Hard | 71% |
| 612 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 74% |
| 613 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 73% |
| 614 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 72% |
| 615 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 71% |
| 616 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 617 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 618 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 72% |
| 619 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 71% |
| 620 | Derive the expression for the electric field due to a charged disk. | Physics | Hard | 74% |
| 621 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 73% |
| 622 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 623 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 71% |
| 624 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 74% |
| 625 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 73% |
| 626 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 72% |
| 627 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 71% |
| 628 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 74% |
| 629 | Derive the expression for the electric field due to a charged disk. | Physics | Hard | 73% |
| 630 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 72% |
| 631 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 71% |
| 632 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 74% |
| 633 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 73% |
| 634 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 635 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 71% |
| 636 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 74% |
| 637 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 73% |
| 638 | Derive the expression for the electric field due to a charged disk. | Physics | Hard | 72% |
| 639 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 71% |
| 640 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 641 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 642 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 72% |
| 643 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 71% |
| 644 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 74% |
| 645 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 73% |
| 646 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 72% |
| 647 | Derive the expression for the electric field due to a charged disk. | Physics | Hard | 71% |
| 648 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 74% |
| 649 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 73% |
| 650 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 72% |
| 651 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 71% |
| 652 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 653 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 654 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 72% |
| 655 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 71% |
| 656 | Derive the expression for the electric field due to a charged disk. | Physics | Hard | 74% |
| 657 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 73% |
| 658 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 659 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 71% |
| 660 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 74% |
| 661 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 73% |
| 662 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 72% |
| 663 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 71% |
| 664 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 74% |
| 665 | Derive the expression for the electric field due to a charged disk. | Physics | Hard | 73% |
| 666 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 72% |
| 667 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 71% |
| 668 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 74% |
| 669 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 73% |
| 670 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 671 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 71% |
| 672 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 74% |
| 673 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 73% |
| 674 | Derive the expression for the electric field due to a charged disk. | Physics | Hard | 72% |
| 675 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 71% |
| 676 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 677 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 678 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 72% |
| 679 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 71% |
| 680 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 74% |
| 681 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 73% |
| 682 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 72% |
| 683 | Derive the expression for the electric field due to a charged disk. | Physics | Hard | 71% |
| 684 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 74% |
| 685 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 73% |
| 686 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 72% |
| 687 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 71% |
| 688 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 689 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 690 | Calculate the eigenvalues of a Hermitian operator. | Linear Algebra | Hard | 75% |
| 691 | Explain the concept of analytic continuation. | Complex Analysis | Hard | 74% |
| 692 | Apply Riemann mapping theorem to conformal mapping. | Complex Analysis | Hard | 72% |
| 693 | Calculate Laurent series expansions around singularities. | Complex Analysis | Hard | 71% |
| 694 | Calculate loop corrections in quantum field theory. | Quantum Field Theory | Hard | 75% |
| 695 | Explain the mechanism of protein folding. | Biochemistry | Hard | 71% |
| 696 | Prove the law of quadratic reciprocity. | Number Theory | Hard | 75% |
| 697 | Calculate class numbers of quadratic fields. | Number Theory | Hard | 73% |
| 698 | Explain the theory of modular forms. | Number Theory | Hard | 74% |
| 699 | Apply elliptic curves to factorization. | Number Theory | Hard | 72% |
| 700 | Calculate Dirichlet L-functions and their zeros. | Number Theory | Hard | 71% |
| 701 | Calculate cross-sections using Feynman diagrams. | Particle Physics | Hard | 75% |
| 702 | Explain the concept of gauge theories in particle physics. | Particle Physics | Hard | 73% |
| 703 | Calculate decay rates using Fermi's golden rule. | Particle Physics | Hard | 74% |
| 704 | Solve the Schrödinger equation for a particle in a box. | Quantum Mechanics | Hard | 74% |
| 705 | Calculate the magnetic field due to a current loop. | Electromagnetism | Hard | 72% |
| 706 | Derive the expression for entropy in statistical mechanics. | Statistical Mechanics | Hard | 71% |
| 707 | Apply the variational principle to molecular systems. | Physical Chemistry | Hard | 73% |
| 708 | Calculate the eigenvalues of a Hermitian operator. | Linear Algebra | Hard | 75% |
| 709 | Explain the concept of analytic continuation. | Complex Analysis | Hard | 74% |
| 710 | Apply Riemann mapping theorem to conformal mapping. | Complex Analysis | Hard | 72% |
| 711 | Calculate Laurent series expansions around singularities. | Complex Analysis | Hard | 71% |
| 712 | Calculate loop corrections in quantum field theory. | Quantum Field Theory | Hard | 75% |
| 713 | Explain the mechanism of protein folding. | Biochemistry | Hard | 71% |
| 714 | Prove the law of quadratic reciprocity. | Number Theory | Hard | 75% |
| 715 | Calculate class numbers of quadratic fields. | Number Theory | Hard | 73% |
| 716 | Explain the theory of modular forms. | Number Theory | Hard | 74% |
| 717 | Apply elliptic curves to factorization. | Number Theory | Hard | 72% |
| 718 | Calculate Dirichlet L-functions and their zeros. | Number Theory | Hard | 71% |
| 719 | Calculate cross-sections using Feynman diagrams. | Particle Physics | Hard | 75% |
| 720 | Explain the concept of gauge theories in particle physics. | Particle Physics | Hard | 73% |
| 721 | Calculate decay rates using Fermi's golden rule. | Particle Physics | Hard | 74% |
| 722 | Solve the Schrödinger equation for a particle in a box. | Quantum Mechanics | Hard | 74% |
| 723 | Calculate the magnetic field due to a current loop. | Electromagnetism | Hard | 72% |
| 724 | Derive the expression for entropy in statistical mechanics. | Statistical Mechanics | Hard | 71% |
| 725 | Apply the variational principle to molecular systems. | Physical Chemistry | Hard | 73% |
| 726 | Calculate the eigenvalues of a Hermitian operator. | Linear Algebra | Hard | 75% |
| 727 | Explain the concept of analytic continuation. | Complex Analysis | Hard | 74% |
| 728 | Apply Riemann mapping theorem to conformal mapping. | Complex Analysis | Hard | 72% |
| 729 | Calculate Laurent series expansions around singularities. | Complex Analysis | Hard | 71% |
| 730 | Calculate loop corrections in quantum field theory. | Quantum Field Theory | Hard | 75% |
| 731 | Explain the mechanism of protein folding. | Biochemistry | Hard | 71% |
| 732 | Prove the law of quadratic reciprocity. | Number Theory | Hard | 75% |
| 733 | Calculate class numbers of quadratic fields. | Number Theory | Hard | 73% |
| 734 | Explain the theory of modular forms. | Number Theory | Hard | 74% |
| 735 | Apply elliptic curves to factorization. | Number Theory | Hard | 72% |
| 736 | Calculate Dirichlet L-functions and their zeros. | Number Theory | Hard | 71% |
| 737 | Calculate cross-sections using Feynman diagrams. | Particle Physics | Hard | 75% |
| 738 | Explain the concept of gauge theories in particle physics. | Particle Physics | Hard | 73% |
| 739 | Calculate decay rates using Fermi's golden rule. | Particle Physics | Hard | 74% |
| 740 | Solve the Schrödinger equation for a particle in a box. | Quantum Mechanics | Hard | 74% |
| 741 | Calculate the magnetic field due to a current loop. | Electromagnetism | Hard | 72% |
| 742 | Derive the expression for entropy in statistical mechanics. | Statistical Mechanics | Hard | 71% |
| 743 | Apply the variational principle to molecular systems. | Physical Chemistry | Hard | 73% |
| 744 | Calculate the eigenvalues of a Hermitian operator. | Linear Algebra | Hard | 75% |
| 745 | Explain the concept of analytic continuation. | Complex Analysis | Hard | 74% |
| 746 | Apply Riemann mapping theorem to conformal mapping. | Complex Analysis | Hard | 72% |
| 747 | Calculate Laurent series expansions around singularities. | Complex Analysis | Hard | 71% |
| 748 | Calculate loop corrections in quantum field theory. | Quantum Field Theory | Hard | 75% |
| 749 | Explain the mechanism of protein folding. | Biochemistry | Hard | 71% |
| 750 | Prove the law of quadratic reciprocity. | Number Theory | Hard | 75% |
| 751 | Calculate class numbers of quadratic fields. | Number Theory | Hard | 73% |
| 752 | Explain the theory of modular forms. | Number Theory | Hard | 74% |
| 753 | Apply elliptic curves to factorization. | Number Theory | Hard | 72% |
| 754 | Calculate Dirichlet L-functions and their zeros. | Number Theory | Hard | 71% |
| 755 | Calculate cross-sections using Feynman diagrams. | Particle Physics | Hard | 75% |
| 756 | Explain the concept of gauge theories in particle physics. | Particle Physics | Hard | 73% |
| 757 | Calculate decay rates using Fermi's golden rule. | Particle Physics | Hard | 74% |
| 758 | Solve the Schrödinger equation for a particle in a box. | Quantum Mechanics | Hard | 74% |
| 759 | Calculate the magnetic field due to a current loop. | Electromagnetism | Hard | 72% |
| 760 | Derive the expression for entropy in statistical mechanics. | Statistical Mechanics | Hard | 71% |
| 761 | Apply the variational principle to molecular systems. | Physical Chemistry | Hard | 73% |
| 762 | Calculate the eigenvalues of a Hermitian operator. | Linear Algebra | Hard | 75% |
| 763 | Explain the concept of analytic continuation. | Complex Analysis | Hard | 74% |
| 764 | Apply Riemann mapping theorem to conformal mapping. | Complex Analysis | Hard | 72% |
| 765 | Calculate Laurent series expansions around singularities. | Complex Analysis | Hard | 71% |
| 766 | Calculate loop corrections in quantum field theory. | Quantum Field Theory | Hard | 75% |
| 767 | Explain the mechanism of protein folding. | Biochemistry | Hard | 71% |
| 768 | Prove the law of quadratic reciprocity. | Number Theory | Hard | 75% |
| 769 | Calculate class numbers of quadratic fields. | Number Theory | Hard | 73% |
| 770 | Explain the theory of modular forms. | Number Theory | Hard | 74% |
| 771 | Apply elliptic curves to factorization. | Number Theory | Hard | 72% |
| 772 | Calculate Dirichlet L-functions and their zeros. | Number Theory | Hard | 71% |
| 773 | Calculate cross-sections using Feynman diagrams. | Particle Physics | Hard | 75% |
| 774 | Explain the concept of gauge theories in particle physics. | Particle Physics | Hard | 73% |
| 775 | Calculate decay rates using Fermi's golden rule. | Particle Physics | Hard |
| 776 | Solve the wave equation for a vibrating string. | Classical Mechanics | Hard | 74% |
| 777 | Calculate the moment of inertia for a rigid body. | Classical Mechanics | Hard | 73% |
| 778 | Explain the concept of angular momentum conservation. | Classical Mechanics | Hard | 75% |
| 779 | Calculate the center of mass for a system of particles. | Classical Mechanics | Hard | 72% |
| 780 | Derive the equations of motion for a simple pendulum. | Classical Mechanics | Hard | 74% |
| 781 | Calculate the potential energy of a spring-mass system. | Classical Mechanics | Hard | 73% |
| 782 | Explain the concept of work-energy theorem. | Classical Mechanics | Hard | 75% |
| 783 | Calculate the torque acting on a rotating object. | Classical Mechanics | Hard | 72% |
| 784 | Derive the equations for projectile motion. | Classical Mechanics | Hard | 74% |
| 785 | Explain the concept of rotational kinetic energy. | Classical Mechanics | Hard | 73% |
| 786 | Calculate the angular velocity of a rotating disk. | Classical Mechanics | Hard | 75% |
| 787 | Derive the equations for circular motion. | Classical Mechanics | Hard | 72% |
| 788 | Calculate the kinetic energy of a rolling object. | Classical Mechanics | Hard | 74% |
| 789 | Explain the concept of conservation of mechanical energy. | Classical Mechanics | Hard | 73% |
| 790 | Calculate the gravitational potential energy of a system. | Classical Mechanics | Hard | 75% |
| 791 | Derive the equations for simple harmonic motion. | Classical Mechanics | Hard | 72% |
| 792 | Calculate the period of a physical pendulum. | Classical Mechanics | Hard | 74% |
| 793 | Explain the concept of damped oscillations. | Classical Mechanics | Hard | 73% |
| 794 | Calculate the energy of a forced oscillator. | Classical Mechanics | Hard | 75% |
| 795 | Derive the equations for coupled oscillations. | Classical Mechanics | Hard | 72% |
| 796 | Calculate the normal modes of a vibrating system. | Classical Mechanics | Hard | 74% |
| 797 | Explain the concept of resonance in mechanical systems. | Classical Mechanics | Hard | 73% |
| 798 | Calculate the energy of a standing wave. | Classical Mechanics | Hard | 75% |
| 799 | Derive the equations for wave propagation in a string. | Classical Mechanics | Hard | 72% |
| 800 | Calculate the speed of sound in a medium. | Classical Mechanics | Hard | 74% |
| 801 | Explain the concept of Doppler effect in sound waves. | Classical Mechanics | Hard | 73% |
| 802 | Calculate the intensity of a sound wave. | Classical Mechanics | Hard | 75% |
| 803 | Derive the equations for interference of sound waves. | Classical Mechanics | Hard | 72% |
| 804 | Calculate the beat frequency of two sound waves. | Classical Mechanics | Hard | 74% |
| 805 | Explain the concept of standing waves in air columns. | Classical Mechanics | Hard | 73% |
| 806 | Calculate the fundamental frequency of a vibrating string. | Classical Mechanics | Hard | 75% |
| 807 | Derive the equations for harmonics in a vibrating string. | Classical Mechanics | Hard | 72% |
| 808 | Calculate the energy of a vibrating membrane. | Classical Mechanics | Hard | 74% |
| 809 | Explain the concept of wave-particle duality. | Quantum Mechanics | Hard | 73% |
| 810 | Calculate the de Broglie wavelength of a particle. | Quantum Mechanics | Hard | 75% |
| 811 | Derive the equations for Heisenberg's uncertainty principle. | Quantum Mechanics | Hard | 72% |
| 812 | Calculate the probability density of a quantum particle. | Quantum Mechanics | Hard | 74% |
| 813 | Explain the concept of quantum tunneling. | Quantum Mechanics | Hard | 73% |
| 814 | Calculate the transmission coefficient for a potential barrier. | Quantum Mechanics | Hard | 75% |
| 815 | Derive the equations for the time-independent Schrödinger equation. | Quantum Mechanics | Hard | 72% |
| 816 | Calculate the energy levels of a harmonic oscillator. | Quantum Mechanics | Hard | 74% |
| 817 | Explain the concept of quantum superposition. | Quantum Mechanics | Hard | 73% |
| 818 | Calculate the expectation value of a quantum operator. | Quantum Mechanics | Hard | 75% |
| 819 | Derive the equations for the time-dependent Schrödinger equation. | Quantum Mechanics | Hard | 72% |
| 820 | Calculate the wave function of a free particle. | Quantum Mechanics | Hard | 74% |
| 821 | Explain the concept of quantum entanglement. | Quantum Mechanics | Hard | 73% |
| 822 | Calculate the spin states of an electron. | Quantum Mechanics | Hard | 75% |
| 823 | Derive the equations for Pauli exclusion principle. | Quantum Mechanics | Hard | 72% |
| 824 | Calculate the energy levels of a hydrogen atom. | Quantum Mechanics | Hard | 74% |
| 825 | Explain the concept of quantum decoherence. | Quantum Mechanics | Hard | 73% |
| 826 | Calculate the transition probabilities between quantum states. | Quantum Mechanics | Hard | 75% |
| 827 | Derive the equations for Fermi's golden rule. | Quantum Mechanics | Hard | 72% |
| 828 | Calculate the scattering cross-section of a particle. | Quantum Mechanics | Hard | 74% |
| 829 | Explain the concept of quantum field theory. | Quantum Mechanics | Hard | 73% |
| 830 | Calculate the Feynman diagrams for particle interactions. | Quantum Mechanics | Hard | 75% |
| 831 | Derive the equations for quantum electrodynamics. | Quantum Mechanics | Hard | 72% |
| 832 | Calculate the energy levels of a particle in a box. | Quantum Mechanics | Hard | 74% |
| 833 | Explain the concept of quantum chromodynamics. | Quantum Mechanics | Hard | 73% |
| 834 | Calculate the quark content of a hadron. | Quantum Mechanics | Hard | 75% |
| 835 | Derive the equations for the standard model of particle physics. | Quantum Mechanics | Hard | 72% |
| 836 | Calculate the mass of a Higgs boson. | Quantum Mechanics | Hard | 74% |
| 837 | Explain the concept of supersymmetry in particle physics. | Quantum Mechanics | Hard | 73% |
| 838 | Calculate the decay rates of unstable particles. | Quantum Mechanics | Hard | 75% |
| 839 | Derive the equations for the weak interaction. | Quantum Mechanics | Hard | 72% |
| 840 | Calculate the neutrino oscillation probabilities. | Quantum Mechanics | Hard | 74% |
| 841 | Explain the concept of dark matter in cosmology. | Quantum Mechanics | Hard | 73% |
| 842 | Calculate the energy density of the universe. | Quantum Mechanics | Hard | 75% |
| 843 | Derive the equations for the Big Bang theory. | Quantum Mechanics | Hard | 72% |
| 844 | Calculate the Hubble constant from redshift data. | Quantum Mechanics | Hard | 74% |
| 845 | Explain the concept of cosmic microwave background radiation. | Quantum Mechanics | Hard | 73% |
| 846 | Calculate the age of the universe. | Quantum Mechanics | Hard | 75% |
| 847 | Derive the equations for the expansion of the universe. | Quantum Mechanics | Hard | 72% |
| 848 | Calculate the critical density of the universe. | Quantum Mechanics | Hard | 74% |
| 849 | Explain the concept of dark energy in cosmology. | Quantum Mechanics | Hard | 73% |
| 850 | Calculate the acceleration of the universe's expansion. | Quantum Mechanics | Hard | 75% |
| 851 | Derive the equations for the inflationary universe model. | Quantum Mechanics | Hard | 72% |
| 852 | Calculate the density fluctuations in the early universe. | Quantum Mechanics | Hard | 74% |
| 853 | Explain the concept of baryogenesis in cosmology. | Quantum Mechanics | Hard | 73% |
| 854 | Calculate the matter-antimatter asymmetry in the universe. | Quantum Mechanics | Hard | 75% |
| 855 | Derive the equations for nucleosynthesis in the early universe. | Quantum Mechanics | Hard | 72% |
| 856 | Calculate the abundance of light elements in the universe. | Quantum Mechanics | Hard | 74% |
| 857 | Explain the concept of galaxy formation in cosmology. | Quantum Mechanics | Hard | 73% |
| 858 | Calculate the rotation curves of galaxies. | Quantum Mechanics | Hard | 75% |
| 859 | Derive the equations for the Tully-Fisher relation. | Quantum Mechanics | Hard | 72% |
| 860 | Calculate the mass-to-light ratio of galaxies. | Quantum Mechanics | Hard | 74 |
| 861 | Solve the differential equation for damped harmonic motion. | Physics | Hard | 73% |
| 862 | Calculate the moment of inertia for a solid sphere. | Physics | Hard | 74% |
| 863 | Derive the expression for critical damping coefficient. | Physics | Hard | 72% |
| 864 | Calculate the magnetic field inside a solenoid. | Physics | Hard | 75% |
| 865 | Explain the principle of superposition in wave mechanics. | Physics | Hard | 74% |
| 866 | Calculate the de Broglie wavelength of an electron. | Physics | Hard | 73% |
| 867 | Solve the Schrödinger equation for a potential well. | Physics | Hard | 75% |
| 868 | Calculate the binding energy of a nucleus. | Physics | Hard | 72% |
| 869 | Explain the concept of quantum tunneling. | Physics | Hard | 74% |
| 870 | Calculate the half-life of a radioactive element. | Physics | Hard | 73% |
| 871 | Solve the differential equation for simple harmonic motion. | Physics | Hard | 75% |
| 872 | Calculate the escape velocity from a planet's surface. | Physics | Hard | 74% |
| 873 | Derive the expression for centripetal acceleration. | Physics | Hard | 73% |
| 874 | Calculate the work done in an isothermal process. | Physics | Hard | 72% |
| 875 | Explain the concept of Carnot cycle efficiency. | Physics | Hard | 75% |
| 876 | Calculate the efficiency of a heat engine. | Physics | Hard | 74% |
| 877 | Solve the differential equation for forced oscillations. | Physics | Hard | 73% |
| 878 | Calculate the torque on a current loop in a magnetic field. | Physics | Hard | 75% |
| 879 | Explain the concept of electromagnetic induction. | Physics | Hard | 74% |
| 880 | Calculate the magnetic moment of a current loop. | Physics | Hard | 73% |
| 881 | Solve the differential equation for RC circuits. | Physics | Hard | 75% |
| 882 | Calculate the time constant of an RC circuit. | Physics | Hard | 74% |
| 883 | Explain the concept of Lenz's law. | Physics | Hard | 73% |
| 884 | Calculate the self-inductance of a solenoid. | Physics | Hard | 75% |
| 885 | Solve the differential equation for RL circuits. | Physics | Hard | 74% |
| 886 | Calculate the time constant of an RL circuit. | Physics | Hard | 73% |
| 887 | Explain the concept of mutual inductance. | Physics | Hard | 75% |
| 888 | Calculate the energy stored in a magnetic field. | Physics | Hard | 74% |
| 889 | Solve the differential equation for LC circuits. | Physics | Hard | 73% |
| 890 | Calculate the resonant frequency of an LC circuit. | Physics | Hard | 75% |
| 891 | Explain the concept of impedance in AC circuits. | Physics | Hard | 74% |
| 892 | Calculate the power factor in an AC circuit. | Physics | Hard | 73% |
| 893 | Solve the differential equation for RLC circuits. | Physics | Hard | 75% |
| 894 | Calculate the quality factor of an RLC circuit. | Physics | Hard | 74% |
| 895 | Explain the concept of skin effect in conductors. | Physics | Hard | 73% |
| 896 | Calculate the energy density of an electromagnetic wave. | Physics | Hard | 75% |
| 897 | Solve the wave equation for a standing wave. | Physics | Hard | 74% |
| 898 | Calculate the speed of sound in a gas. | Physics | Hard | 73% |
| 899 | Explain the concept of Doppler effect in sound waves. | Physics | Hard | 75% |
| 900 | Calculate the intensity level of a sound wave. | Physics | Hard | 74% |
| 901 | Solve the wave equation for a traveling wave. | Physics | Hard | 73% |
| 902 | Calculate the wavelength of a standing wave in a string. | Physics | Hard | 75% |
| 903 | Explain the concept of interference in sound waves. | Physics | Hard | 74% |
| 904 | Calculate the beat frequency of two sound waves. | Physics | Hard | 73% |
| 905 | Solve the wave equation for a transverse wave. | Physics | Hard | 75% |
| 906 | Calculate the speed of a wave on a string. | Physics | Hard | 74% |
| 907 | Explain the concept of polarization of light. | Physics | Hard | 73% |
| 908 | Calculate the Brewster's angle for light reflection. | Physics | Hard | 75% |
| 909 | Solve the wave equation for a longitudinal wave. | Physics | Hard | 74% |
| 910 | Calculate the refractive index of a medium. | Physics | Hard | 73% |
| 911 | Explain the concept of total internal reflection. | Physics | Hard | 75% |
| 912 | Calculate the critical angle for total internal reflection. | Physics | Hard | 74% |
| 913 | Solve the wave equation for a plane wave. | Physics | Hard | 73% |
| 914 | Calculate the intensity of a light wave. | Physics | Hard | 75% |
| 915 | Explain the concept of diffraction of light. | Physics | Hard | 74% |
| 916 | Calculate the angular width of a diffraction pattern. | Physics | Hard | 73% |
| 917 | Solve the wave equation for a spherical wave. | Physics | Hard | 75% |
| 918 | Calculate the resolving power of a diffraction grating. | Physics | Hard | 74% |
| 919 | Explain the concept of interference in light waves. | Physics | Hard | 73% |
| 920 | Calculate the fringe width in a double-slit experiment. | Physics | Hard | 75% |
| 921 | Solve the wave equation for a cylindrical wave. | Physics | Hard | 74% |
| 922 | Calculate the focal length of a thin lens. | Physics | Hard | 73% |
| 923 | Explain the concept of chromatic aberration in lenses. | Physics | Hard | 75% |
| 924 | Calculate the magnification produced by a lens. | Physics | Hard | 74% |
| 925 | Solve the lens maker's equation for a thin lens. | Physics | Hard | 73% |
| 926 | Calculate the power of a lens. | Physics | Hard | 75% |
| 927 | Explain the concept of spherical aberration in lenses. | Physics | Hard | 74% |
| 928 | Calculate the depth of field for a lens system. | Physics | Hard | 73% |
| 929 | Solve the mirror equation for a spherical mirror. | Physics | Hard | 75% |
| 930 | Calculate the magnification produced by a mirror. | Physics | Hard | 74% |
| 931 | Explain the concept of aberration in mirrors. | Physics | Hard | 73% |
| 932 | Calculate the focal length of a concave mirror. | Physics | Hard | 75% |
| 933 | Solve the mirror equation for a convex mirror. | Physics | Hard | 74% |
| 934 | Calculate the radius of curvature of a mirror. | Physics | Hard | 73% |
| 935 | Explain the concept of optical activity in materials. | Physics | Hard | 75% |
| 936 | Calculate the specific rotation of an optically active substance. | Physics | Hard | 74% |
| 937 | Solve the wave equation for a circularly polarized wave. | Physics | Hard | 73% |
| 938 | Calculate the intensity of a circularly polarized light wave. | Physics | Hard | 75% |
| 939 | Explain the concept of chemical kinetics and rate laws. | Chemistry | Hard | 74% |
| 940 | Solve the differential equation for a damped harmonic oscillator. | Mathematics | Hard | 73% |
| 941 | Derive the expression for the rate constant using Arrhenius equation. | Chemistry | Hard | 72% |
| 942 | Calculate the eigenvalues of a given matrix. | Mathematics | Hard | 71% |
| 943 | Explain the mechanism of nucleophilic substitution reactions. | Chemistry | Hard | 74% |
| 944 | Solve the system of linear equations using matrix methods. | Mathematics | Hard | 73% |
| 945 | Calculate the pH of a buffer solution. | Chemistry | Hard | 72% |
| 946 | Find the inverse of a given matrix. | Mathematics | Hard | 71% |
| 947 | Explain the concept of chemical equilibrium and Le Chatelier's principle. | Chemistry | Hard | 74% |
| 948 | Solve the differential equation for a simple harmonic oscillator. | Mathematics | Hard | 73% |
| 949 | Calculate the solubility product constant for a given salt. | Chemistry | Hard | 72% |
| 950 | Find the determinant of a given matrix. | Mathematics | Hard | 71% |
| 951 | Explain the mechanism of electrophilic addition reactions. | Chemistry | Hard | 74% |
| 952 | Solve the system of linear equations using Cramer's rule. | Mathematics | Hard | 73% |
| 953 | Calculate the standard enthalpy of formation for a given compound. | Chemistry | Hard | 72% |
| 954 | Find the rank of a given matrix. | Mathematics | Hard | 71% |
| 955 | Explain the concept of chemical bonding and molecular orbitals. | Chemistry | Hard | 74% |
| 956 | Solve the differential equation for a forced harmonic oscillator. | Mathematics | Hard | 73% |
| 957 | Calculate the equilibrium constant for a given reaction. | Chemistry | Hard | 72% |
| 958 | Find the trace of a given matrix. | Mathematics | Hard | 71% |
| 959 | Explain the mechanism of elimination reactions. | Chemistry | Hard | 74% |
| 960 | Solve the system of linear equations using Gauss-Jordan elimination. | Mathematics | Hard | 73% |
| 961 | Calculate the standard entropy change for a given reaction. | Chemistry | Hard | 72% |
| 962 | Find the eigenvalues and eigenvectors of a given matrix. | Mathematics | Hard | 71% |
| 963 | Explain the concept of chemical thermodynamics and Gibbs free energy. | Chemistry | Hard | 74% |
| 964 | Solve the differential equation for a damped driven harmonic oscillator. | Mathematics | Hard | 73% |
| 965 | Calculate the standard free energy change for a given reaction. | Chemistry | Hard | 72% |
| 966 | Find the inverse of a given matrix using adjoint method. | Mathematics | Hard | 71% |
| 967 | Explain the mechanism of addition reactions. | Chemistry | Hard | 74% |
| 968 | Solve the system of linear equations using LU decomposition. | Mathematics | Hard | 73% |
| 969 | Calculate the standard enthalpy change for a given reaction. | Chemistry | Hard | 72% |
| 970 | Find the determinant of a given matrix using Laplace expansion. | Mathematics | Hard | 71% |
| 971 | Explain the concept of chemical kinetics and reaction mechanisms. | Chemistry | Hard | 74% |
| 972 | Solve the differential equation for a coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 973 | Calculate the standard entropy of formation for a given compound. | Chemistry | Hard | 72% |
| 974 | Find the eigenvalues of a given matrix using characteristic polynomial. | Mathematics | Hard | 71% |
| 975 | Explain the mechanism of substitution reactions. | Chemistry | Hard | 74% |
| 976 | Solve the system of linear equations using Cholesky decomposition. | Mathematics | Hard | 73% |
| 977 | Calculate the standard free energy of formation for a given compound. | Chemistry | Hard | 72% |
| 978 | Find the inverse of a given matrix using Gauss-Jordan elimination. | Mathematics | Hard | 71% |
| 979 | Explain the concept of chemical equilibrium and equilibrium constant. | Chemistry | Hard | 74% |
| 980 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 981 | Calculate the standard enthalpy of reaction for a given reaction. | Chemistry | Hard | 72% |
| 982 | Find the determinant of a given matrix using cofactor expansion. | Mathematics | Hard | 71% |
| 983 | Explain the mechanism of rearrangement reactions. | Chemistry | Hard | 74% |
| 984 | Solve the system of linear equations using QR decomposition. | Mathematics | Hard | 73% |
| 985 | Calculate the standard entropy of reaction for a given reaction. | Chemistry | Hard | 72% |
| 986 | Find the eigenvalues of a given matrix using power method. | Mathematics | Hard | 71% |
| 987 | Explain the concept of chemical kinetics and rate determining step. | Chemistry | Hard | 74% |
| 988 | Solve the differential equation for a damped coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 989 | Calculate the standard free energy of reaction for a given reaction. | Chemistry | Hard | 72% |
| 990 | Find the inverse of a given matrix using LU decomposition. | Mathematics | Hard | 71% |
| 991 | Explain the mechanism of addition-elimination reactions. | Chemistry | Hard | 74% |
| 992 | Solve the system of linear equations using singular value decomposition. | Mathematics | Hard | 73% |
| 993 | Calculate the standard enthalpy of formation for a given compound. | Chemistry | Hard | 72% |
| 994 | Find the determinant of a given matrix using row reduction. | Mathematics | Hard | 71% |
| 995 | Explain the concept of chemical thermodynamics and enthalpy. | Chemistry | Hard | 74% |
| 996 | Solve the differential equation for a driven damped harmonic oscillator. | Mathematics | Hard | 73% |
| 997 | Calculate the standard entropy of formation for a given compound. | Chemistry | Hard | 72% |
| 998 | Find the eigenvalues of a given matrix using Jacobi method. | Mathematics | Hard | 71% |
| 999 | Explain the mechanism of elimination-addition reactions. | Chemistry | Hard | 74% |
| 1000 | Solve the system of linear equations using eigenvalue decomposition. | Mathematics | Hard | 73% |
| 1001 | Calculate the standard free energy of formation for a given compound. | Chemistry | Hard | 72% |
| 1002 | Find the determinant of a given matrix using cofactor expansion. | Mathematics | Hard | 71% |
| 1003 | Explain the concept of chemical kinetics and reaction rate. | Chemistry | Hard | 74% |
| 1004 | Solve the differential equation for a damped driven coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 1005 | Calculate the standard enthalpy of reaction for a given reaction. | Chemistry | Hard | 72% |
| 1006 | Find the eigenvalues of a given matrix using QR algorithm. | Mathematics | Hard | 71% |
| 1007 | Explain the mechanism of substitution-elimination reactions. | Chemistry | Hard | 74% |
| 1008 | Solve the system of linear equations using Cholesky decomposition. | Mathematics | Hard | 73% |
| 1009 | Calculate the standard entropy of reaction for a given reaction. | Chemistry | Hard | 72% |
| 1010 | Find the inverse of a given matrix using adjoint method. | Mathematics | Hard | 71% |
| 1011 | Explain the concept of chemical equilibrium and equilibrium constant. | Chemistry | Hard | 74% |
| 1012 | Solve the differential equation for a driven coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 1013 | Calculate the standard free energy of reaction for a given reaction. | Chemistry | Hard | 72% |
| 1014 | Find the determinant of a given matrix using Laplace expansion. | Mathematics | Hard | 71% |
| 1015 | Explain the mechanism of addition-substitution reactions. | Chemistry | Hard | 74% |
| 1016 | Solve the system of linear equations using QR decomposition. | Mathematics | Hard | 73% |
| 1017 | Calculate the standard enthalpy of formation for a given compound. | Chemistry | Hard | 72% |
| 1018 | Find the eigenvalues of a given matrix using power method. | Mathematics | Hard | 71% |
| 1019 | Explain the concept of chemical kinetics and rate laws. | Chemistry | Hard | 74% |
| 1020 | Solve the differential equation for a damped coupled harmonic oscillator. | Mathematics | Hard | 73% |
| 1021 | Calculate the standard free energy of formation for a given compound. | Chemistry | Hard | 72% |
| 1022 | Find the inverse of a given matrix using Gauss-Jordan elimination. | Mathematics | Hard | 71% |
| 1023 | Find the maximum and minimum values of the function f(x) = x³ - 3x² + 4 on the interval [-1, 3]. | Calculus | Hard | 72% |
| 1024 | Solve the differential equation: dy/dx + y = e^x. | Calculus | Hard | 73% |
| 1025 | Find the number of real solutions to the equation x⁴ - 4x³ + 5x² - 2x + 1 = 0. | Algebra | Hard | 71% |
| 1026 | Find the equation of the tangent to the curve y = x³ - 3x² + 2x - 1 at the point (1, -1). | Calculus | Hard | 74% |
| 1027 | Find the area bounded by the curves y = x² and y = 2x - x². | Calculus | Hard | 73% |
| 1028 | Find the shortest distance between the lines (x-1)/2 = (y-2)/3 = (z-3)/4 and (x-2)/3 = (y-3)/4 = (z-4)/5. | Coordinate Geometry | Hard | 72% |
| 1029 | Find the equation of the plane passing through the points (1, 2, 3), (2, 3, 1), and (3, 1, 2). | Coordinate Geometry | Hard | 71% |
| 1030 | Find the number of positive integer solutions to the equation x + y + z = 10. | Algebra | Hard | 74% |
| 1031 | Find the value of lim(x→0) (sin(x) - x)/x³. | Calculus | Hard | 73% |
| 1032 | Evaluate the integral ∫(x² + 2x + 1)dx from 0 to 1. | Calculus | Medium | 85% |
| 1033 | Find the derivative of f(x) = e^(x²) + ln(x). | Calculus | Medium | 82% |
| 1034 | Solve the differential equation dy/dx = y/x. | Calculus | Hard | 78% |
| 1035 | Find the area enclosed by the curve y = x³ and the x-axis from x = 0 to x = 2. | Calculus | Medium | 80% |
| 1036 | Evaluate lim(x→∞) (1 + 1/x)^x. | Calculus | Hard | 75% |
| 1037 | Find the maximum value of the function f(x) = x³ - 3x² + 4. | Calculus | Medium | 83% |
| 1038 | Determine the convergence of the series ∑(n=1 to ∞) 1/n². | Calculus | Hard | 77% |
| 1039 | Find the volume of the solid formed by rotating y = √x around the x-axis from x = 0 to x = 4. | Calculus | Hard | 76% |
| 1040 | Solve the differential equation d²y/dx² + 4y = 0. | Calculus | Hard | 74% |
| 1041 | Find the equation of the tangent to the curve y = x³ - 3x + 2 at x = 1. | Calculus | Medium | 81% |
| 1042 | Evaluate ∫(sin(x) + cos(x))dx from 0 to π/2. | Calculus | Medium | 84% |
| 1043 | Find the critical points of the function f(x) = x⁴ - 2x². | Calculus | Medium | 82% |
| 1044 | Determine if the function f(x) = |x| is differentiable at x = 0. | Calculus | Hard | 73% |
| 1045 | Find the length of the curve y = x^(3/2) from x = 0 to x = 4. | Calculus | Hard | 76% |
| 1046 | Evaluate the improper integral ∫(1/x²)dx from 1 to ∞. | Calculus | Hard | 75% |
| 1047 | Find the area between the curves y = x² and y = 2x - x². | Calculus | Medium | 80% |
| 1048 | Determine the interval of convergence for the power series ∑(n=1 to ∞) (x^n)/n. | Calculus | Hard | 74% |
| 1049 | Find the derivative of the implicit function x² + y² = 25. | Calculus | Medium | 81% |
| 1050 | Evaluate ∫(x³ + sin(x))dx from -1 to 1. | Calculus | Medium | 83% |
| 1051 | Find the general solution to the differential equation dy/dx = xy. | Calculus | Hard | 77% |
| 1052 | Determine the nature of the critical point of f(x,y) = x² + y² - 2x - 4y. | Calculus | Hard | 76% |
| 1053 | Evaluate the double integral ∫∫(x + y)dxdy over the region 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. | Calculus | Hard | 75% |
| 1054 | Find the volume of the solid bounded by z = 4 - x² - y² and z = 0. | Calculus | Hard | 74% |
| 1055 | Determine if the series ∑(n=1 to ∞) (-1)^n/n converges absolutely, conditionally, or diverges. | Calculus | Hard | 73% |
| 1056 | Find the equation of the normal to the curve y = x³ - 3x² + 2 at x = 2. | Calculus | Medium | 81% |
| 1057 | Evaluate the integral ∫(e^x + 1/x)dx from 1 to e. | Calculus | Medium | 82% |
| 1058 | Find the area bounded by the parabola y² = 4x and the line y = 2x. | Calculus | Medium | 80% |
| 1059 | Determine the maximum and minimum values of f(x) = x³ - 6x² + 9x + 1 on the interval [0, 4]. | Calculus | Medium | 83% |
| 1060 | Evaluate the limit lim(x→0) (tan(x) - x)/x³. | Calculus | Hard | 75% |
| 1061 | Find the length of the curve x = t², y = t³ from t = 0 to t = 1. | Calculus | Hard | 76% |
| 1062 | Determine the radius of convergence of the power series ∑(n=1 to ∞) (x^n)/n!. | Calculus | Hard | 74% |
| 1063 | Find the volume of the solid generated by rotating the region bounded by y = x² and y = x around the x-axis. | Calculus | Hard | 75% |
| 1064 | Evaluate the line integral ∫(x² + y²)ds along the curve y = x from (0,0) to (1,1). | Calculus | Hard | 73% |
| 1065 | Find the general solution to the differential equation d²y/dx² - 4dy/dx + 4y = 0. | Calculus | Hard | 77% |
| 1066 | Determine the nature of the critical points of f(x,y) = x³ + y³ - 3xy. | Calculus | Hard | 76% |
| 1067 | Evaluate the triple integral ∫∫∫(x + y + z)dxdydz over the region 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1. | Calculus | Hard | 74% |
| 1068 | Find the surface area of the solid generated by rotating y = √x around the x-axis from x = 0 to x = 4. | Calculus | Hard | 75% |
| 1069 | Determine if the series ∑(n=1 to ∞) 1/(n ln n) converges or diverges. | Calculus | Hard | 73% |
| 1070 | Find the equation of the tangent plane to the surface z = x² + y² at the point (1,1,2). | Calculus | Hard | 76% |
| 1071 | Evaluate the integral ∫(x³ + cos(x))dx from -π to π. | Calculus | Medium | 82% |
| 1072 | Find the area bounded by the curves y = sin(x) and y = cos(x) from x = 0 to x = π/2. | Calculus | Medium | 81% |
| 1073 | Determine the maximum and minimum values of f(x) = x⁴ - 2x² + 1 on the interval [-2, 2]. | Calculus | Medium | 83% |
| 1074 | Evaluate the limit lim(x→0) (e^x - 1 - x)/x². | Calculus | Hard | 75% |
| 1075 | Find the length of the curve y = ln(cos(x)) from x = 0 to x = π/4. | Calculus | Hard | 76% |
| 1076 | Determine the radius of convergence of the power series ∑(n=1 to ∞) (x^n)/n². | Calculus | Hard | 74% |
| 1077 | Find the volume of the solid generated by rotating the region bounded by y = x² and y = 4 around the y-axis. | Calculus | Hard | 75% |
| 1078 | Evaluate the line integral ∫(x + y)ds along the curve y = x² from (0,0) to (1,1). | Calculus | Hard | 73% |
| 1079 | Find the general solution to the differential equation d²y/dx² + y = 0. | Calculus | Hard | 77% |
| 1080 | Determine the nature of the critical points of f(x,y) = x⁴ + y⁴ - 4xy. | Calculus | Hard | 76% |
| 1081 | Evaluate the triple integral ∫∫∫(x² + y² + z²)dxdydz over the region 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1. | Calculus | Hard | 74% |
| 1082 | Find the surface area of the solid generated by rotating y = x² around the y-axis from y = 0 to y = 4. | Calculus | Hard | 75% |
| 1083 | Determine if the series ∑(n=1 to ∞) 1/(n² + 1) converges or diverges. | Calculus | Hard | 73% |
| 1084 | Find the equation of the tangent plane to the surface z = x³ + y³ at the point (1,1,2). | Calculus | Hard | 76% |
| 1085 | Evaluate the integral ∫(x⁴ + sin(x))dx from -1 to 1. | Calculus | Medium | 82% |
| 1086 | Find the area bounded by the curves y = e^x and y = e^(-x) from x = 0 to x = 1. | Calculus | Medium | 81% |
| 1087 | Determine the maximum and minimum values of f(x) = x³ - 3x² + 3x + 1 on the interval [0, 3]. | Calculus | Medium | 83% |
| 1088 | Evaluate the limit lim(x→0) (sin(x) - x)/x³. | Calculus | Hard | 75% |
| 1089 | Find the length of the curve y = e^x from x = 0 to x = 1. | Calculus | Hard | 76% |
| 1090 | Determine the radius of convergence of the power series ∑(n=1 to ∞) (x^n)/n³. | Calculus | Hard | 74% |
| 1091 | Find the volume of the solid generated by rotating the region bounded by y = x² and y = x around the y-axis. | Calculus | Hard | 75% |
| 1092 | Evaluate the line integral ∫(x² + y²)ds along the curve y = x² from (0,0) to (1,1). | Calculus | Hard | 73% |
| 1093 | Find the general solution to the differential equation d²y/dx² + 2dy/dx + y = 0. | Calculus | Hard | 77% |
| 1094 | Find the value of ∫(x² + 3x + 2)dx from 0 to 1. | Calculus | Medium | 85% |
| 1095 | Find the equation of the tangent to the curve y = x³ at x = 1. | Calculus | Medium | 82% |
| 1096 | Find the area enclosed by the curves y = x² and y = x. | Calculus | Hard | 78% |
| 1097 | Find the general solution of the differential equation dy/dx = y/x. | Calculus | Hard | 77% |
| 1098 | Find the value of lim(x→0) (e^x - 1)/x. | Calculus | Medium | 84% |
| 1099 | Find the derivative of f(x) = ln(x² + 1). | Calculus | Medium | 83% |
| 1100 | Find the maximum value of the function f(x) = x³ - 3x² + 2x + 1 in the interval [0, 2]. | Calculus | Hard | 79% |
| 1101 | Find the volume of the solid formed by rotating the curve y = x² about the x-axis from x = 0 to x = 1. | Calculus | Hard | 78% |
| 1102 | Find the length of the curve y = x^(3/2) from x = 0 to x = 1. | Calculus | Hard | 77% |
| 1103 | Find the value of ∫(sin(x) + cos(x))dx from 0 to π/2. | Calculus | Medium | 84% |
| 1104 | Find the equation of the normal to the curve y = x² at x = 2. | Calculus | Medium | 82% |
| 1105 | Find the area bounded by the curves y = x³ and y = x. | Calculus | Hard | 78% |
| 1106 | Find the general solution of the differential equation d²y/dx² - 3dy/dx + 2y = 0. | Calculus | Hard | 77% |
| 1107 | Find the value of lim(x→∞) (x² + 1)/(x³ + 1). | Calculus | Medium | 84% |
| 1108 | Find the derivative of f(x) = e^(x²) + ln(x). | Calculus | Medium | 83% |
| 1109 | Find the minimum value of the function f(x) = x⁴ - 2x² + 1 in the interval [-1, 1]. | Calculus | Hard | 79% |
| 1110 | Find the volume of the solid formed by rotating the curve y = √x about the x-axis from x = 0 to x = 1. | Calculus | Hard | 78% |
| 1111 | Find the length of the curve y = ln(cos(x)) from x = 0 to x = π/4. | Calculus | Hard | 77% |
| 1112 | Find the value of ∫(e^x + 1)dx from 0 to 1. | Calculus | Medium | 84% |
| 1113 | Find the equation of the tangent to the curve y = x² at x = 3. | Calculus | Medium | 82% |
| 1114 | Find the area enclosed by the curves y = x³ and y = x². | Calculus | Hard | 78% |
| 1115 | Find the general solution of the differential equation d²y/dx² + 4y = 0. | Calculus | Hard | 77% |
| 1116 | Find the value of lim(x→0) (sin(2x))/x. | Calculus | Medium | 84% |
| 1117 | Find the derivative of f(x) = x²ln(x). | Calculus | Medium | 83% |
| 1118 | Find the maximum value of the function f(x) = x³ - 6x² + 9x + 1 in the interval [0, 3]. | Calculus | Hard | 79% |
| 1119 | Find the volume of the solid formed by rotating the curve y = x³ about the x-axis from x = 0 to x = 1. | Calculus | Hard | 78% |
| 1120 | Find the length of the curve y = ln(x) from x = 1 to x = e. | Calculus | Hard | 77% |
| 1121 | Find the value of ∫(cos(x) + sin(x))dx from 0 to π/2. | Calculus | Medium | 84% |
| 1122 | Find the equation of the normal to the curve y = x³ at x = 1. | Calculus | Medium | 82% |
| 1123 | Find the area bounded by the curves y = x⁴ and y = x. | Calculus | Hard | 78% |
| 1124 | Find the general solution of the differential equation d²y/dx² - 2dy/dx + y = 0. | Calculus | Hard | 77% |
| 1125 | Find the value of lim(x→∞) (x³ + 1)/(x⁴ + 1). | Calculus | Medium | 84% |
| 1126 | Find the derivative of f(x) = e^(x³) + ln(x). | Calculus | Medium | 83% |
| 1127 | Find the minimum value of the function f(x) = x⁴ - 4x² + 4 in the interval [-2, 2]. | Calculus | Hard | 79% |
| 1128 | Find the volume of the solid formed by rotating the curve y = x² about the x-axis from x = 0 to x = 2. | Calculus | Hard | 78% |
| 1129 | Find the length of the curve y = ln(sin(x)) from x = π/6 to x = π/3. | Calculus | Hard | 77% |
| 1130 | Find the value of ∫(e^(2x) + 1)dx from 0 to 1. | Calculus | Medium | 84% |
| 1131 | Find the equation of the tangent to the curve y = x⁴ at x = 1. | Calculus | Medium | 82% |
| 1132 | Find the area enclosed by the curves y = x⁵ and y = x. | Calculus | Hard | 78% |
| 1133 | Find the general solution of the differential equation d²y/dx² + 9y = 0. | Calculus | Hard | 77% |
| 1134 | Find the value of lim(x→0) (sin(3x))/x. | Calculus | Medium | 84% |
| 1135 | Find the derivative of f(x) = x³ln(x). | Calculus | Medium | 83% |
| 1136 | Find the maximum value of the function f(x) = x³ - 9x² + 24x + 1 in the interval [0, 4]. | Calculus | Hard | 79% |
| 1137 | Find the volume of the solid formed by rotating the curve y = x⁴ about the x-axis from x = 0 to x = 1. | Calculus | Hard | 78% |
| 1138 | Find the length of the curve y = ln(x²) from x = 1 to x = e. | Calculus | Hard | 77% |
| 1139 | Find the value of ∫(cos(2x) + sin(2x))dx from 0 to π/2. | Calculus | Medium | 84% |
| 1140 | Find the equation of the normal to the curve y = x⁴ at x = 1. | Calculus | Medium | 82% |
| 1141 | Find the area bounded by the curves y = x⁶ and y = x. | Calculus | Hard | 78% |
| 1142 | Find the general solution of the differential equation d²y/dx² - 4dy/dx + 4y = 0. | Calculus | Hard | 77% |
| 1143 | Find the value of lim(x→∞) (x⁴ + 1)/(x⁵ + 1). | Calculus | Medium | 84% |
| 1144 | Find the derivative of f(x) = e^(x⁴) + ln(x). | Calculus | Medium | 83% |
| 1145 | Find the minimum value of the function f(x) = x⁴ - 6x² + 9 in the interval [-3, 3]. | Calculus | Hard | 79% |
| 1146 | Find the volume of the solid formed by rotating the curve y = x² about the x-axis from x = 0 to x = 3. | Calculus | Hard | 78% |
| 1147 | Find the length of the curve y = ln(cos(2x)) from x = 0 to x = π/8. | Calculus | Hard | 77% |
| 1148 | Find the value of ∫(e^(3x) + 1)dx from 0 to 1. | Calculus | Medium | 84% |
| 1149 | Find the equation of the tangent to the curve y = x⁵ at x = 1. | Calculus | Medium | 82% |
| 1150 | Find the area enclosed by the curves y = x⁷ and y = x. | Calculus | Hard | 78% |
| 1151 | Find the general solution of the differential equation d²y/dx² + 16y = 0. | Calculus | Hard | 77% |
| 1152 | Find the value of lim(x→0) (sin(4x))/x. | Calculus | Medium | 84% |
| 1153 | Find the derivative of f(x) = x⁴ln(x). | Calculus | Medium | 83% |
| 1154 | Find the maximum value of the function f(x) = x³ - 12x² + 36x + 1 in the interval [0, 6]. | Calculus | Hard | 79% |
| 1155 | Find the volume of the solid formed by rotating the curve y = x⁵ about the x-axis from x = 0 to x = 1. | Calculus | Hard | 78% |
| 1156 | Find the length of the curve y = ln(x³) from x = 1 to x = e. | Calculus | Hard | 77% |
| 1157 | Find the value of ∫(cos(3x) + sin(3x))dx from 0 to π/2. | Calculus | Medium | 84% |
| 1158 | Find the equation of the normal to the curve y = x⁵ at x = 1. | Calculus | Medium | 82% |
| 1159 | Find the area bounded by the curves y = x⁸ and y = x. | Calculus | Hard | 78% |
| 1160 | Find the number of real solutions to the equation x³ - 3x² + 2x - 1 = 0. | Algebra | Hard | 75% |
| 1161 | Find the equation of the tangent to the curve y = x³ - 3x² + 2x at x = 1. | Calculus | Medium | 80% |
| 1162 | Find the shortest distance between the lines (x-1)/2 = (y+2)/3 = (z-3)/4 and (x+2)/3 = (y-3)/4 = (z+4)/5. | Coordinate Geometry | Hard | 72% |
| 1163 | Find the value of ∫(e^x sinx)dx from 0 to π/2. | Calculus | Hard | 73% |
| 1164 | Find the number of positive integer solutions to the equation x + y + z + w = 15. | Algebra | Hard | 74% |
| 1165 | Find the area bounded by the curves y = x² and y = √x. | Calculus | Medium | 81% |
| 1166 | Find the equation of the plane passing through the points (1, 0, 0), (0, 1, 0), and (0, 0, 1). | Coordinate Geometry | Hard | 71% |
| 1167 | Find the value of lim(x→0) (tan(x) - x)/x³. | Calculus | Hard | 73% |
| 1168 | Find the number of onto functions from A (6) to B (4). | Algebra | Hard | 72% |
| 1169 | Find the sum of the series 1/1·3 + 1/3·5 + ... + 1/(2n-1)(2n+1). | Algebra | Hard | 74% |
| 1170 | Find the value of ∫(x² + 3x + 2)dx from 0 to 2. | Calculus | Medium | 82% |
| 1171 | Find the derivative of f(x) = ln(x² + 1) + e^(2x). | Calculus | Medium | 83% |
| 1172 | Solve the differential equation dy/dx = y²/x. | Calculus | Hard | 78% |
| 1173 | Find the area enclosed by the curve y = x⁴ and the x-axis from x = -1 to x = 1. | Calculus | Medium | 80% |
| 1174 | Find the number of ways to arrange 5 boys and 3 girls in a row so that no two girls are adjacent. | Algebra | Hard | 75% |
| 1175 | Find the equation of the circle passing through the points (1, 2), (2, 3), and (3, 1). | Coordinate Geometry | Hard | 71% |
| 1176 | Find the value of lim(x→∞) (x + √(x² + x)). | Calculus | Hard | 73% |
| 1177 | Find the number of divisors of 720. | Algebra | Medium | 81% |
| 1178 | Find the value of ∫(sin²x)dx from 0 to π. | Calculus | Medium | 82% |
| 1179 | Find the equation of the tangent to the parabola y² = 4x at the point (1, 2). | Coordinate Geometry | Medium | 80% |
| 1180 | Find the number of ways to select 3 distinct numbers from {1, 2, 3, 4, 5, 6} such that their sum is even. | Algebra | Hard | 75% |
| 1181 | Find the value of ∫(x³ + 2x² + x)dx from 0 to 1. | Calculus | Medium | 83% |
| 1182 | Find the derivative of f(x) = sin(x²) + cos(2x). | Calculus | Medium | 82% |
| 1183 | Solve the differential equation dy/dx = y + x. | Calculus | Hard | 78% |
| 1184 | Find the area enclosed by the curve y = x³ and the line y = x. | Calculus | Medium | 80% |
| 1185 | Find the number of ways to arrange the letters of the word 'MATHEMATICS' so that all vowels are together. | Algebra | Hard | 75% |
| 1186 | Find the equation of the ellipse with foci at (1, 0) and (-1, 0) and major axis length 4. | Coordinate Geometry | Hard | 71% |
| 1187 | Find the value of lim(x→0) (e^x - 1 - x)/x². | Calculus | Hard | 73% |
| 1188 | Find the number of positive integer solutions to the equation x + y + z = 12. | Algebra | Hard | 74% |
| 1189 | Find the value of ∫(cos²x)dx from 0 to π/2. | Calculus | Medium | 82% |
| 1190 | Find the derivative of f(x) = ln(x³ + 1) + e^(3x). | Calculus | Medium | 83% |
| 1191 | Solve the differential equation dy/dx = y² + 1. | Calculus | Hard | 78% |
| 1192 | Find the area enclosed by the curve y = x⁴ and the line y = x². | Calculus | Medium | 80% |
| 1193 | Find the number of ways to select 4 distinct numbers from {1, 2, 3, 4, 5, 6, 7} such that their sum is odd. | Algebra | Hard | 75% |
| 1194 | Find the equation of the hyperbola with foci at (2, 0) and (-2, 0) and vertices at (1, 0) and (-1, 0). | Coordinate Geometry | Hard | 71% |
| 1195 | Find the value of lim(x→0) (ln(1 + x) - x)/x². | Calculus | Hard | 73% |
| 1196 | Find the number of positive integer solutions to the equation x + y + z + w = 20. | Algebra | Hard | 74% |
| 1197 | Find the value of ∫(sin³x)dx from 0 to π/2. | Calculus | Medium | 82% |
| 1198 | Find the derivative of f(x) = sin(x³) + cos(3x). | Calculus | Medium | 82% |
| 1199 | Solve the differential equation dy/dx = y + x². | Calculus | Hard | 78% |
| 1200 | Find the area enclosed by the curve y = x⁵ and the line y = x³. | Calculus | Medium | 80% |
| 1201 | Find the number of ways to arrange the letters of the word 'PHYSICS' so that all consonants are together. | Algebra | Hard | 75% |
| 1202 | Find the equation of the parabola with focus at (1, 0) and directrix x = -1. | Coordinate Geometry | Hard | 71% |
| 1203 | Find the value of lim(x→0) (tan(x) - sin(x))/x³. | Calculus | Hard | 73% |
| 1204 | Find the number of positive integer solutions to the equation x + y + z = 18. | Algebra | Hard | 74% |
| 1205 | Find the value of ∫(cos³x)dx from 0 to π/2. | Calculus | Medium | 82% |
| 1206 | Find the derivative of f(x) = ln(x⁴ + 1) + e^(4x). | Calculus | Medium | 83% |
| 1207 | Solve the differential equation dy/dx = y² + x. | Calculus | Hard | 78% |
| 1208 | Find the area enclosed by the curve y = x⁶ and the line y = x⁴. | Calculus | Medium | 80% |
| 1209 | Find the number of ways to select 5 distinct numbers from {1, 2, 3, 4, 5, 6, 7, 8} such that their sum is even. | Algebra | Hard | 75% |
| 1210 | Find the equation of the ellipse with foci at (3, 0) and (-3, 0) and major axis length 6. | Coordinate Geometry | Hard | 71% |
| 1211 | Find the value of lim(x→0) (e^x - 1 - x - x²/2)/x³. | Calculus | Hard | 73% |
| 1212 | Find the number of positive integer solutions to the equation x + y + z + w = 25. | Algebra | Hard | 74% |
| 1213 | Find the value of ∫(sin⁴x)dx from 0 to π/2. | Calculus | Medium | 82% |
| 1214 | Find the derivative of f(x) = sin(x⁴) + cos(4x). | Calculus | Medium | 82% |
| 1215 | Solve the differential equation dy/dx = y² + x². | Calculus | Hard | 78% |
| 1216 | Find the area enclosed by the curve y = x⁷ and the line y = x⁵. | Calculus | Medium | 80% |
| 1217 | Find the number of ways to arrange the letters of the word 'CHEMISTRY' so that all vowels are together. | Algebra | Hard | 75% |
| 1218 | Find the equation of the hyperbola with foci at (4, 0) and (-4, 0) and vertices at (2, 0) and (-2, 0). | Coordinate Geometry | Hard | 71% |
| 1219 | Find the value of lim(x→0) (ln(1 + x) - x + x²/2)/x³. | Calculus | Hard | 73% |
| 1220 | Find the number of positive integer solutions to the equation x + y + z = 24. | Algebra | Hard | 74% |
| 1221 | Find the value of ∫(cos⁴x)dx from 0 to π/2. | Calculus | Medium | 82% |
| 1222 | Find the derivative of f(x) = ln(x⁵ + 1) + e^(5x). | Calculus | Medium | 83% |
| 1223 | Solve the differential equation dy/dx = y² + x³. | Calculus | Hard | 78% |
| 1224 | Find the area enclosed by the curve y = x⁸ and the line y = x⁶. | Calculus | Medium | 80% |
| 1225 | Find the number of ways to select 6 distinct numbers from {1, 2, 3, 4, 5, 6, 7, 8, 9} such that their sum is odd. | Algebra | Hard | 75% |
| 1226 | Find the derivative of f(x) = ln(x⁶ + 1) + e^(6x). | Calculus | Medium | 83% |
| 1227 | Solve the differential equation dy/dx = y² + x⁴. | Calculus | Hard | 78% |
| 1228 | Find the area enclosed by the curve y = x⁹ and the line y = x⁷. | Calculus | Medium | 80% |
| 1229 | Find the number of ways to select 7 distinct numbers from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} such that their sum is even. | Algebra | Hard | 75% |
| 1230 | Find the equation of the ellipse with foci at (5, 0) and (-5, 0) and major axis length 10. | Coordinate Geometry | Hard | 71% |
| 1231 | Find the value of lim(x→0) (e^x - 1 - x - x²/2 - x³/6)/x⁴. | Calculus | Hard | 73% |
| 1232 | Find the number of positive integer solutions to the equation x + y + z + w = 30. | Algebra | Hard | 74% |
| 1233 | Find the value of ∫(sin⁵x)dx from 0 to π/2. | Calculus | Medium | 82% |
| 1234 | Find the derivative of f(x) = sin(x⁵) + cos(5x). | Calculus | Medium | 82% |
| 1235 | Solve the differential equation dy/dx = y² + x⁵. | Calculus | Hard | 78% |
| 1236 | Find the area enclosed by the curve y = x¹⁰ and the line y = x⁸. | Calculus | Medium | 80% |
| 1237 | Find the number of ways to arrange the letters of the word 'PHYSICS' so that all vowels are together. | Algebra | Hard | 75% |
| 1238 | Find the equation of the hyperbola with foci at (6, 0) and (-6, 0) and vertices at (3, 0) and (-3, 0). | Coordinate Geometry | Hard | 71% |
| 1239 | Find the value of lim(x→0) (ln(1 + x) - x + x²/2 - x³/3)/x⁴. | Calculus | Hard | 73% |
| 1240 | Find the number of positive integer solutions to the equation x + y + z = 30. | Algebra | Hard | 74% |
| 1241 | Find the value of ∫(cos⁵x)dx from 0 to π/2. | Calculus | Medium | 82% |
| 1242 | Find the derivative of f(x) = ln(x⁶ + 1) + e^(6x). | Calculus | Medium | 83% |
| 1243 | Solve the differential equation dy/dx = y² + x⁶. | Calculus | Hard | 78% |
| 1244 | Find the area enclosed by the curve y = x¹¹ and the line y = x⁹. | Calculus | Medium | 80% |
| 1245 | Find the number of ways to select 8 distinct numbers from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} such that their sum is odd. | Algebra | Hard | 75% |
| 1246 | Find the equation of the ellipse with foci at (7, 0) and (-7, 0) and major axis length 14. | Coordinate Geometry | Hard | 71% |
| 1247 | Find the value of lim(x→0) (e^x - 1 - x - x²/2 - x³/6 - x⁴/24)/x⁵. | Calculus | Hard | 73% |
| 1248 | Find the number of positive integer solutions to the equation x + y + z + w = 35. | Algebra | Hard | 74% |
| 1249 | Find the value of ∫(sin⁶x)dx from 0 to π/2. | Calculus | Medium | 82% |
| 1250 | Find the derivative of f(x) = sin(x⁶) + cos(6x). | Calculus | Medium | 82% |
| 1251 | Solve the differential equation dy/dx = y² + x⁷. | Calculus | Hard | 78% |
| 1252 | Find the area enclosed by the curve y = x¹² and the line y = x¹⁰. | Calculus | Medium | 80% |
| 1253 | Find the number of ways to arrange the letters of the word 'MATHEMATICS' so that all vowels are together. | Algebra | Hard | 75% |
| 1254 | Find the equation of the hyperbola with foci at (8, 0) and (-8, 0) and vertices at (4, 0) and (-4, 0). | Coordinate Geometry | Hard | 71% |
| 1255 | Find the value of lim(x→0) (ln(1 + x) - x + x²/2 - x³/3 + x⁴/4)/x⁵. | Calculus | Hard | 73% |
| 1256 | Find the number of positive integer solutions to the equation x + y + z = 35. | Algebra | Hard | 74% |
| 1257 | Find the value of ∫(cos⁶x)dx from 0 to π/2. | Calculus | Medium | 82% |
| 1258 | Find the derivative of f(x) = ln(x⁷ + 1) + e^(7x). | Calculus | Medium | 83% |
| 1259 | Solve the differential equation dy/dx = y² + x⁸. | Calculus | Hard | 78% |
| 1260 | Find the area enclosed by the curve y = x¹³ and the line y = x¹¹. | Calculus | Medium | 80% |
| 1261 | Find the number of ways to select 9 distinct numbers from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} such that their sum is even. | Algebra | Hard | 75% |
| 1262 | Find the equation of the ellipse with foci at (9, 0) and (-9, 0) and major axis length 18. | Coordinate Geometry | Hard | 71% |
| 1263 | Find the value of lim(x→0) (e^x - 1 - x - x²/2 - x³/6 - x⁴/24 - x⁵/120)/x⁶. | Calculus | Hard | 73% |
| 1264 | Find the number of positive integer solutions to the equation x + y + z + w = 40. | Algebra | Hard | 74% |
| 1265 | Find the value of ∫(sin⁷x)dx from 0 to π/2. | Calculus | Medium | 82% |
| 1266 | Find the derivative of f(x) = sin(x⁷) + cos(7x). | Calculus | Medium | 82% |
| 1267 | Solve the differential equation dy/dx = y² + x⁹. | Calculus | Hard | 78% |
| 1268 | Find the area enclosed by the curve y = x¹⁴ and the line y = x¹². | Calculus | Medium | 80% |
| 1269 | Find the number of ways to arrange the letters of the word 'STATISTICS' so that all vowels are together. | Algebra | Hard | 75% |
| 1270 | Find the equation of the hyperbola with foci at (10, 0) and (-10, 0) and vertices at (5, 0) and (-5, 0). | Coordinate Geometry | Hard | 71% |
| 1271 | Find the value of lim(x→0) (ln(1 + x) - x + x²/2 - x³/3 + x⁴/4 - x⁵/5)/x⁶. | Calculus | Hard | 73% |
| 1272 | Find the number of positive integer solutions to the equation x + y + z = 40. | Algebra | Hard | 74% |
| 1273 | Find the value of ∫(cos⁷x)dx from 0 to π/2. | Calculus | Medium | 82% |
| 1274 | Find the derivative of f(x) = ln(x⁸ + 1) + e^(8x). | Calculus | Medium | 83% |
| 1275 | Solve the differential equation dy/dx = y² + x¹⁰. | Calculus | Hard | 78% |
| 1276 | Find the area enclosed by the curve y = x¹⁵ and the line y = x¹³. | Calculus | Medium | 80% |
| 1277 | Find the number of ways to select 10 distinct numbers from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} such that their sum is odd. | Algebra | Hard | 75% |
| 1278 | Find the equation of the ellipse with foci at (11, 0) and (-11, 0) and major axis length 22. | Coordinate Geometry | Hard | 71% |
| 1279 | Find the value of lim(x→0) (e^x - 1 - x - x²/2 - x³/6 - x⁴/24 - x⁵/120 - x⁶/720)/x⁷. | Calculus | Hard | 73% |
| 1280 | Find the number of positive integer solutions to the equation x + y + z + w = 45. | Algebra | Hard | 74% |
| 1281 | Find the value of ∫(sin⁸x)dx from 0 to π/2. | Calculus | Medium | 82% |
| 1282 | Find the derivative of f(x) = sin(x⁸) + cos(8x). | Calculus | Medium | 82% |
| 1283 | Solve the differential equation dy/dx = y² + x¹¹. | Calculus | Hard | 78% |
| 1284 | Find the area enclosed by the curve y = x¹⁶ and the line y = x¹⁴. | Calculus | Medium | 80% |
| 1285 | Find the number of ways to arrange the letters of the word 'PROBABILITY' so that all vowels are together. | Algebra | Hard | 75% |
| 1286 | Find the equation of the hyperbola with foci at (12, 0) and (-12, 0) and vertices at (6, 0) and (-6, 0). | Coordinate Geometry | Hard | 71% |
| 1287 | Find the value of lim(x→0) (ln(1 + x) - x + x²/2 - x³/3 + x⁴/4 - x⁵/5 + x⁶/6)/x⁷. | Calcul
|
| 1288 | Explain the concept of hybridization in organic molecules. | Organic Chemistry | Hard | 73% |
| 1289 | Calculate the pH of a buffer solution. | Physical Chemistry | Hard | 74% |
| 1290 | Explain the structure and bonding in benzene. | Organic Chemistry | Hard | 75% |
| 1291 | Derive the Nernst equation and its applications. | Physical Chemistry | Hard | 72% |
| 1292 | Explain the mechanism of electrophilic aromatic substitution. | Organic Chemistry | Hard | 73% |
| 1293 | Calculate the degree of dissociation of a weak electrolyte. | Physical Chemistry | Hard | 74% |
| 1294 | Explain the concept of resonance in organic molecules. | Organic Chemistry | Hard | 75% |
| 1295 | Calculate the solubility product of a sparingly soluble salt. | Physical Chemistry | Hard | 72% |
| 1296 | Explain the mechanism of nucleophilic substitution reactions. | Organic Chemistry | Hard | 73% |
| 1297 | Calculate the equivalent conductance of an electrolyte. | Physical Chemistry | Hard | 74% |
| 1298 | Explain the concept of stereoisomerism in organic molecules. | Organic Chemistry | Hard | 75% |
| 1299 | Calculate the rate of a chemical reaction using the Arrhenius equation. | Physical Chemistry | Hard | 72% |
| 1300 | Explain the mechanism of addition reactions in alkenes. | Organic Chemistry | Hard | 73% |
| 1301 | Calculate the heat of reaction using Hess's law. | Physical Chemistry | Hard | 74% |
| 1302 | Explain the concept of optical activity in organic molecules. | Organic Chemistry | Hard | 75% |
| 1303 | Calculate the standard electrode potential of a cell. | Physical Chemistry | Hard | 72% |
| 1304 | Explain the mechanism of elimination reactions in alkyl halides. | Organic Chemistry | Hard | 73% |
| 1305 | Calculate the entropy change in a chemical reaction. | Physical Chemistry | Hard | 74% |
| 1306 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 75% |
| 1307 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 1308 | Explain the mechanism of free radical substitution reactions. | Organic Chemistry | Hard | 73% |
| 1309 | Calculate the Gibbs free energy change in a chemical reaction. | Physical Chemistry | Hard | 74% |
| 1310 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 75% |
| 1311 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 72% |
| 1312 | Explain the mechanism of rearrangement reactions in organic molecules. | Organic Chemistry | Hard | 73% |
| 1313 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 74% |
| 1314 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 75% |
| 1315 | Calculate the cell potential using the Nernst equation. | Physical Chemistry | Hard | 72% |
| 1316 | Explain the mechanism of pericyclic reactions in organic molecules. | Organic Chemistry | Hard | 73% |
| 1317 | Calculate the osmotic pressure of a solution. | Physical Chemistry | Hard | 74% |
| 1318 | Explain the concept of mesomeric effect in organic molecules. | Organic Chemistry | Hard | 75% |
| 1319 | Calculate the degree of ionization of a weak acid. | Physical Chemistry | Hard | 72% |
| 1320 | Explain the mechanism of oxidation reactions in organic molecules. | Organic Chemistry | Hard | 73% |
| 1321 | Calculate the standard enthalpy of formation of a compound. | Physical Chemistry | Hard | 74% |
| 1322 | Explain the concept of stereoselectivity in organic reactions. | Organic Chemistry | Hard | 75% |
| 1323 | Calculate the heat capacity of a substance. | Physical Chemistry | Hard | 72% |
| 1324 | Explain the mechanism of reduction reactions in organic molecules. | Organic Chemistry | Hard | 73% |
| 1325 | Calculate the rate of a chemical reaction using the rate law. | Physical Chemistry | Hard | 74% |
| 1326 | Explain the concept of stereospecificity in organic reactions. | Organic Chemistry | Hard | 75% |
| 1327 | Calculate the equilibrium constant for a chemical reaction using the van't Hoff equation. | Physical Chemistry | Hard | 72% |
| 1328 | Explain the mechanism of cycloaddition reactions in organic molecules. | Organic Chemistry | Hard | 73% |
| 1329 | Calculate the standard entropy of a substance. | Physical Chemistry | Hard | 74% |
| 1330 | Explain the concept of regioselectivity in organic reactions. | Organic Chemistry | Hard | 75% |
| 1331 | Calculate the rate of a chemical reaction using the collision theory. | Physical Chemistry | Hard | 72% |
| 1332 | Explain the mechanism of sigmatropic rearrangements in organic molecules. | Organic Chemistry | Hard | 73% |
| 1333 | Calculate the standard Gibbs free energy of formation of a compound. | Physical Chemistry | Hard | 74% |
| 1334 | Explain the concept of enantioselectivity in organic reactions. | Organic Chemistry | Hard | 75% |
| 1335 | Calculate the rate of a chemical reaction using the transition state theory. | Physical Chemistry | Hard | 72% |
| 1336 | Explain the mechanism of electrocyclic reactions in organic molecules. | Organic Chemistry | Hard | 73% |
| 1337 | Calculate the standard enthalpy of combustion of a compound. | Physical Chemistry | Hard | 74% |
| 1338 | Explain the concept of diastereoselectivity in organic reactions. | Organic Chemistry | Hard | 75% |
| 1339 | Calculate the rate of a chemical reaction using the steady-state approximation. | Physical Chemistry | Hard | 72% |
| 1340 | Explain the mechanism of cyclization reactions in organic molecules. | Organic Chemistry | Hard | 73% |
| 1341 | Calculate the standard enthalpy of neutralization of an acid. | Physical Chemistry | Hard | 74% |
| 1342 | Explain the concept of chemoselectivity in organic reactions. | Organic Chemistry | Hard | 75% |
| 1343 | Calculate the rate of a chemical reaction using the Lindemann mechanism. | Physical Chemistry | Hard | 72% |
| 1344 | Explain the mechanism of ring-opening reactions in organic molecules. | Organic Chemistry | Hard | 73% |
| 1345 | Calculate the standard enthalpy of hydration of an ion. | Physical Chemistry | Hard | 74% |
| 1346 | Explain the concept of stereocontrol in organic reactions. | Organic Chemistry | Hard | 75% |
| 1347 | Calculate the rate of a chemical reaction using the Michaelis-Menten mechanism. | Physical Chemistry | Hard | 72% |
| 1348 | Explain the mechanism of ring-closing reactions in organic molecules. | Organic Chemistry | Hard | 73% |
| 1349 | Calculate the standard enthalpy of sublimation of a substance. | Physical Chemistry | Hard | 74% |
| 1350 | Explain the concept of atropisomerism in organic molecules. | Organic Chemistry | Hard | 75% |
| 1351 | Calculate the rate of a chemical reaction using the enzyme kinetics. | Physical Chemistry | Hard | 72% |
| 1352 | Explain the mechanism of photochemical reactions in organic molecules. | Organic Chemistry | Hard | 73% |
| 1353 | Calculate the standard enthalpy of fusion of a substance. | Physical Chemistry | Hard | 74% |
| 1354 | Explain the concept of axial chirality in organic molecules. | Organic Chemistry | Hard | 75% |
| 1355 | Calculate the rate of a chemical reaction using the Marcus theory. | Physical Chemistry | Hard | 72% |
| 1356 | Explain the mechanism of thermal reactions in organic molecules. | Organic Chemistry | Hard | 73% |
| 1357 | Calculate the standard enthalpy of vaporization of a substance. | Physical Chemistry | Hard | 74% |
| 1358 | Explain the concept of planar chirality in organic molecules. | Organic Chemistry | Hard | 75% |
| 1359 | Calculate the rate of a chemical reaction using the Eyring equation. | Physical Chemistry | Hard | 72% |
| 1360 | Explain the mechanism of radical reactions in organic molecules. | Organic Chemistry | Hard | 73% |
| 1361 | Calculate the standard enthalpy of solution of a substance. | Physical Chemistry | Hard | 74% |
| 1362 | Explain the concept of helical chirality in organic molecules. | Organic Chemistry | Hard | 75% |
| 1363 | Calculate the rate of a chemical reaction using the Kramers theory. | Physical Chemistry | Hard | 72% |
| 1364 | Explain the mechanism of nucleophilic aromatic substitution reactions. | Organic Chemistry | Hard | 73% |
| 1365 | Calculate the standard enthalpy of adsorption of a substance. | Physical Chemistry | Hard | 74% |
| 1366 | Explain the concept of central chirality in organic molecules. | Organic Chemistry | Hard | 75% |
| 1367 | Calculate the rate of a chemical reaction using the Rice-Ramsperger-Kassel theory. | Physical Chemistry | Hard | 72% |
| 1368 | Explain the mechanism of electrophilic addition reactions in alkenes. | Organic Chemistry | Hard | 73% |
| 1369 | Calculate the standard enthalpy of desorption of a substance. | Physical Chemistry | Hard | 74% |
| 1370 | Explain the concept of chemical kinetics and its applications. | Physical Chemistry | Hard | 73% |
| 1371 | Calculate the rate of reaction using the Arrhenius equation. | Physical Chemistry | Hard | 72% |
| 1372 | Discuss the mechanism of SN1 and SN2 reactions. | Organic Chemistry | Hard | 74% |
| 1373 | Explain the concept of resonance in organic molecules. | Organic Chemistry | Hard | 73% |
| 1374 | Calculate the equilibrium constant using the van't Hoff equation. | Physical Chemistry | Hard | 72% |
| 1375 | Discuss the mechanism of E1 and E2 elimination reactions. | Organic Chemistry | Hard | 74% |
| 1376 | Explain the concept of hybridization in organic molecules. | Organic Chemistry | Hard | 73% |
| 1377 | Calculate the Gibbs free energy change in a chemical reaction. | Physical Chemistry | Hard | 72% |
| 1378 | Discuss the mechanism of electrophilic aromatic substitution. | Organic Chemistry | Hard | 74% |
| 1379 | Explain the concept of stereochemistry in organic molecules. | Organic Chemistry | Hard | 73% |
| 1380 | Calculate the entropy change in a chemical reaction. | Physical Chemistry | Hard | 72% |
| 1381 | Discuss the mechanism of nucleophilic addition to carbonyl compounds. | Organic Chemistry | Hard | 74% |
| 1382 | Explain the concept of tautomerism in organic molecules. | Organic Chemistry | Hard | 73% |
| 1383 | Calculate the activation energy of a chemical reaction. | Physical Chemistry | Hard | 72% |
| 1384 | Discuss the mechanism of aldol condensation. | Organic Chemistry | Hard | 74% |
| 1385 | Explain the concept of hyperconjugation in organic molecules. | Organic Chemistry | Hard | 73% |
| 1386 | Calculate the enthalpy change in a chemical reaction. | Physical Chemistry | Hard | 72% |
| 1387 | Discuss the mechanism of Claisen rearrangement. | Organic Chemistry | Hard | 74% |
| 1388 | Explain the concept of inductive effect in organic molecules. | Organic Chemistry | Hard | 73% |
| 1389 | Calculate the rate constant for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 1390 | Discuss the mechanism of Beckmann rearrangement. | Organic Chemistry | Hard | 74% |
| 1391 | Explain the concept of protecting groups in organic synthesis. | Organic Chemistry | Hard | 73% |
| 1392 | Calculate the activity coefficient using Debye-Hückel theory. | Physical Chemistry | Hard | 72% |
| 1393 | Discuss the mechanism of Diels-Alder reaction. | Organic Chemistry | Hard | 74% |
| 1394 | Explain the concept of aromaticity using Hückel's rule. | Organic Chemistry | Hard | 73% |
| 1395 | Calculate the chemical potential in thermodynamics. | Physical Chemistry | Hard | 72% |
| 1396 | Discuss the mechanism of Wittig reaction. | Organic Chemistry | Hard | 74% |
| 1397 | Explain the concept of stereoselectivity in organic reactions. | Organic Chemistry | Hard | 73% |
| 1398 | Calculate the equilibrium constant for a chemical reaction. | Physical Chemistry | Hard | 72% |
| 1399 | Discuss the mechanism of Grignard reaction. | Organic Chemistry | Hard | 74% |