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JEE Advanced 2024 — Paper 1 (Physics) Solutions

Step-by-step mathematical proofs, multi-correct partial marking evaluation, and interactive practice for Paper 1.

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Physics Questions (17 Questions)

Interactive Partial Marking Mode
Q1Paper 1PhysicsOne or More Correct (Partial Marking)Hard
Rotational Motion & Rigid Body Dynamics
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2024 Paper 1 Physics Q1] A uniform solid circular disc of mass MM and radius RR is placed on a rough horizontal surface with coefficient of friction μ\mu. At time t=0t=0, a horizontal impulse JJ is applied at a height h=R4h = \frac{R}{4} above the center of mass. Which of the following statements is/are CORRECT?
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Q2Paper 1PhysicsOne or More Correct (Partial Marking)Tough / Advanced
Electrostatics & Electric Potential
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2024 Paper 1 Physics Q2] A point charge +q+q is located at a distance d=3 cmd = 3\text{ cm} from the planar boundary of an infinite semi-infinite dielectric medium of relative permittivity K=2K = 2. Which of the following statements is/are CORRECT?
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Q3Paper 1PhysicsOne or More Correct (Partial Marking)Hard
Thermodynamics & Kinetic Theory
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2024 Paper 1 Physics Q3] One mole of an ideal gas has a temperature-dependent molar heat capacity at constant volume CV=C0+αTC_V = C_0 + \alpha T, where C0=52RC_0 = \frac{5}{2}R and α=0.040 J/(mol K2)\alpha = 0.040\text{ J/(mol K}^2). The gas undergoes a quasi-static adiabatic expansion from (T1,V1)(T_1, V_1) to (T2,V2)(T_2, V_2). Which relation holds?
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Q4Paper 1PhysicsOne or More Correct (Partial Marking)Hard
Electromagnetic Induction & Alternating Current
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2024 Paper 1 Physics Q4] A flat circular loop of radius r=0.1 mr = 0.1\text{ m} and resistance R=2.0 ΩR = 2.0\,\Omega has self-inductance L=0.02 HL = 0.02\text{ H}. It is placed in a normal magnetic field B(t)=3cos⁡(150t) TB(t) = 3 \cos(150 t)\text{ T}. Which of the following is/are CORRECT?
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Q5Paper 1PhysicsOne or More Correct (Partial Marking)Hard
Wave Optics & Interference
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2024 Paper 1 Physics Q5] In a Young's Double Slit setup with slit separation dd and screen distance DD, a film of thickness t=18 μmt = 18\,\mu\text{m} is placed in front of slit S1S_1. The refractive index of the film varies linearly across thickness as μ(x)=1.5+0.60(xt)\mu(x) = 1.5 + 0.60 \left(\frac{x}{t}\right) for 0≤x≤t0 \le x \le t. Which of the following statements is/are CORRECT?
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Q6Paper 1PhysicsOne or More Correct (Partial Marking)Hard
Modern Physics & Quantum Mechanics
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2024 Paper 1 Physics Q6] A hydrogen-like ion with atomic number Z=3Z = 3 consists of a nucleus of mass MM and an orbital electron of mass mem_e. Taking the finite nuclear mass into account with reduced mass μ=meMme+M\mu = \frac{m_e M}{m_e + M}, which of the following statements is/are CORRECT?
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Q7Paper 1PhysicsNumerical Value TypeMedium
Fluid Mechanics & Surface Tension
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2024 Paper 1 Physics Q7] A clean cylindrical glass capillary tube of internal radius r=0.20 mmr = 0.20\text{ mm} is held vertically and dipped into water of surface tension T=0.075 N/mT = 0.075\text{ N/m}, contact angle θ=0∘\theta = 0^\circ, and density ρ=1000 kg/m3\rho = 1000\text{ kg/m}^3. Taking acceleration due to gravity g=10 m/s2g = 10\text{ m/s}^2, calculate the equilibrium height hh (in mm) of the water column in the tube.
Q8Paper 1PhysicsNumerical Value TypeMedium
Gravitation & Satellite Motion
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2024 Paper 1 Physics Q8] A satellite orbits a spherically symmetric planet of mass M=4×1024 kgM = 4 \times 10^{24}\text{ kg} in a circular orbit of radius r=4×107 mr = 4 \times 10^7\text{ m}. Given universal gravitational constant G=6.67×10−11 N m2/kg2G = 6.67 \times 10^{-11}\text{ N m}^2/\text{kg}^2, determine the orbital speed v0v_0 of the satellite in km/s\text{km/s}. (Round off to two decimal places).
Q9Paper 1PhysicsNumerical Value TypeMedium
Wave Motion & Sound
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2024 Paper 1 Physics Q9] An organ pipe closed at one end and open at the other has length L=0.65 mL = 0.65\text{ m}. Taking the speed of sound in air as v=340 m/sv = 340\text{ m/s} and neglecting end correction, find the fundamental resonant frequency f1f_1 (in Hz).
Q10Paper 1PhysicsNumerical Value TypeMedium
Modern Physics & Quantum Mechanics
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2024 Paper 1 Physics Q10] Monochromatic ultraviolet light of wavelength λ=450 nm\lambda = 450\text{ nm} is incident on a clean metallic surface having work function ϕ=2.14 eV\phi = 2.14\text{ eV}. Using Planck's constant hc≈1240 eV⋅nmh c \approx 1240\text{ eV}\cdot\text{nm}, calculate the stopping potential V0V_0 (in Volts) required to reduce the photocurrent to zero.
Q11Paper 1PhysicsNumerical Value TypeMedium
Current Electricity & Transient Circuits
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2024 Paper 1 Physics Q11] A capacitor of capacitance C=20 μFC = 20\,\mu\text{F} is charged through a resistor R=80 kΩR = 80\text{ k}\Omega connected to a DC source of V0=12 VV_0 = 12\text{ V}. Find the capacitive time constant τ=RC\tau = R C of the charging circuit in seconds.
Q12Paper 1PhysicsNumerical Value TypeMedium
Magnetic Effects of Current & Magnetism
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2024 Paper 1 Physics Q12] A proton (m=1.67×10−27 kgm = 1.67 \times 10^{-27}\text{ kg}, q=1.6×10−19 Cq = 1.6 \times 10^{-19}\text{ C}) enters a uniform magnetic field B=1.00 TB = 1.00\text{ T} with speed v=3.0×106 m/sv = 3.0 \times 10^6\text{ m/s} perpendicular to the magnetic lines. Find the orbital radius rr of the resulting circular path in centimeters.
Q13Paper 1PhysicsSingle Correct OptionMedium
Ray Optics & Optical Instruments
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2024 Paper 1 Physics Q13] An equilateral glass prism (A=60∘A = 60^\circ) has refractive index μ=3\mu = \sqrt{3}. A monochromatic ray of light is incident at angle ii such that it suffers minimum deviation δmin⁡\delta_{\min}. What is the value of δmin⁡\delta_{\min}?
Q14Paper 1PhysicsSingle Correct OptionMedium
Oscillations & Simple Harmonic Motion
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2024 Paper 1 Physics Q14] A block of mass m=2 kgm = 2\text{ kg} is attached to a horizontal massless spring of force constant k=200 N/mk = 200\text{ N/m}. The block is pulled from equilibrium by x0=0.1 mx_0 = 0.1\text{ m} on a frictionless floor and released from rest. What is the maximum speed of the block?
Q15Paper 1PhysicsSingle Correct OptionMedium
Work, Energy and Power
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2024 Paper 1 Physics Q15] A small bob of mass mm tied to an inextensible string of length RR is whirled in a vertical circle. What is the minimum horizontal speed umin⁡u_{\min} that must be imparted to the bob at the lowest point so that it completes the full vertical loop without the string slacking?
Q16Paper 1PhysicsSingle Correct OptionMedium
Nuclear Physics & Radioactivity
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2024 Paper 1 Physics Q16] A radioactive sample contains N0N_0 active nuclei at time t=0t=0. Its half-life is T1/2=16 daysT_{1/2} = 16\text{ days}. What fraction of the original radioactive nuclei will remain undecayed after t=48 dayst = 48\text{ days}?
Q17Paper 1PhysicsSingle Correct OptionMedium
Fluid Mechanics & Properties of Matter
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2024 Paper 1 Physics Q17] A small spherical steel ball of radius rr falls vertically through a viscous liquid of density σ\sigma and viscosity η\eta. If the density of steel is ρ\rho, the terminal velocity vtv_t of the sphere is proportional to: