Q1. Consider two concentric, thin conducting spherical shells of radii 'a' and 'b' (where b > a). The inner shell is given a charge +Q, and the outer shell is earthed. What will be the electric potential of the inner shell?
Correct Answer: Option A ($\frac{1}{4\pi\epsilon_0} \frac{Q}{a}$)
Explanation: Detailed explanation will be updated shortly.
Q2. In a potentiometer experiment, the balancing length for a cell is found to be $L$. If the internal resistance of the driver cell (in the primary circuit) is increased, keeping its EMF constant, how will the new balancing length $L'$ be affected?
Correct Answer: Option A ($L' > L$)
Explanation: Detailed explanation will be updated shortly.
Q3. A proton enters a uniform magnetic field $\vec{B}$ with a velocity $\vec{v}$ such that the angle between $\vec{v}$ and $\vec{B}$ is 60°. The particle moves in a helical path. What is the work done by the magnetic field on the proton during the time it completes one full revolution of its circular path?
Correct Answer: Option A ($(\pi m v^2 \sin^2 60^\circ)$)
Explanation: Detailed explanation will be updated shortly.
Q4. A non-conducting rod of length L is rotating with a constant angular velocity ω about an axis passing through one of its ends and perpendicular to its length. The region has a non-uniform magnetic field $B = B_0 x$, where $B_0$ is a constant and x is the distance from the axis of rotation. The motional EMF induced between the ends of the rod is:
Correct Answer: Option A ($\frac{1}{2} B_0 \omega L^2$)
Explanation: Detailed explanation will be updated shortly.
Q5. In a series LCR circuit, the frequency of the AC source is adjusted such that the inductive reactance is exactly double the capacitive reactance. If $R$ is the resistance in the circuit, the phase difference ($\phi$) between the current and the voltage will be:
Correct Answer: Option A ($\tan^{-1}(1)$)
Explanation: Detailed explanation will be updated shortly.
Q6. An unpolarised light of intensity $I_0$ is passed through a polariser P1. The light emerging from P1 is then passed through a second polariser P2 whose axis is oriented at 60° to the axis of P1. The intensity of light emerging from P2 is $I$. What would be the intensity if P2 were rotated by an additional 30° (i.e., total angle of 90° with P1)?
Correct Answer: Option A ($I/3$)
Explanation: Detailed explanation will be updated shortly.
Q7. In a Young's Double Slit Experiment, the 5th order bright fringe for light of wavelength $\lambda_1 = 600$ nm coincides with the $n^{th}$ order dark fringe for light of wavelength $\lambda_2 = 500$ nm. What is the value of n?
Correct Answer: Option A (5)
Explanation: Detailed explanation will be updated shortly.
Q8. The de Broglie wavelength of a neutron at thermal equilibrium with heavy water at a temperature T (in Kelvin) and mass m, is:
Correct Answer: Option A ($\frac{h}{\sqrt{2mkT}}$)
Explanation: Detailed explanation will be updated shortly.
Q9. The ratio of the magnetic dipole moment to the angular momentum of an electron revolving in the $n=3$ orbit of a Hydrogen atom is $\gamma$. What would be the value of this ratio for an electron in the $n=5$ orbit?
Correct Answer: Option A ($\gamma$)
Explanation: Detailed explanation will be updated shortly.
Q10. Identify the logic gate represented by the given circuit diagram, where A and B are inputs and Y is the output.
(A diagram showing two diodes, D1 and D2. The anodes of both diodes are connected to inputs A and B respectively. The cathodes of both diodes are connected together at a point, which is the output Y. This point Y is also connected to the ground via a resistor R.)
Correct Answer: Option A (OR gate)
Explanation: Detailed explanation will be updated shortly.
Q11. A planet has a mass $M$ and radius $R$. Another planet has a mass of $8M$ and a radius of $2R$. The ratio of the escape velocity from the first planet to the second planet ($v_{e1}/v_{e2}$) is:
Correct Answer: Option A (1 : 2)
Explanation: Detailed explanation will be updated shortly.
Q12. A solid sphere is in pure rolling motion on an inclined plane with an inclination $\theta$. What is the minimum coefficient of static friction required to support pure rolling?
Correct Answer: Option A ($\frac{2}{7} \tan\theta$)
Explanation: Detailed explanation will be updated shortly.
Q13. The intensity of an electromagnetic wave is $60 \text{ W/m}^2$. The peak value of the magnetic field ($B_0$) associated with this wave is approximately: (Use $\mu_0 = 4\pi \times 10^{-7}$ TmA$^{-1}$ and $c = 3 \times 10^8$ m/s)
Correct Answer: Option A ($7.07 \times 10^{-7}$ T)
Explanation: Detailed explanation will be updated shortly.
Q14. A radioactive nucleus X undergoes a series of decays: $X \xrightarrow{\alpha} Y \xrightarrow{\beta^-} Z \xrightarrow{\alpha} W$. If the atomic number and mass number of W are 88 and 224 respectively, what are the corresponding numbers for the parent nucleus X?
Correct Answer: Option A (92, 232)
Explanation: Detailed explanation will be updated shortly.
Q15. A biconvex lens of focal length 20 cm is cut into two identical plano-convex lenses by a cut perpendicular to the principal axis. The power of each new lens will be:
Correct Answer: Option A (+5 D)
Explanation: Detailed explanation will be updated shortly.
Q16. In the photoelectric effect, the work function of a metal is $\phi$. When light of frequency $2\nu$ is incident, the maximum kinetic energy of photoelectrons is $K_1$. When the incident frequency is increased to $5\nu$, the maximum kinetic energy is $K_2$. If the threshold frequency is $\nu$, what is the ratio $K_1 : K_2$?
Correct Answer: Option A (2 : 5)
Explanation: Detailed explanation will be updated shortly.
Q17. A Zener diode with a breakdown voltage of 6V is used in a voltage regulator circuit as shown. If the input voltage varies from 10V to 16V, what is the change in current through the Zener diode? (The circuit shows a 200Ω series resistor $R_s$ and a 1kΩ load resistor $R_L$ in parallel with the Zener diode).
Correct Answer: Option A (24 mA)
Explanation: Detailed explanation will be updated shortly.
Q18. A monoatomic ideal gas is taken through a cyclic process A → B → C → A as shown on a P-V diagram. The path B → C is an isothermal expansion. The work done during the complete cycle is:
(A P-V diagram where A=(V, P), B=(V, 3P), C=(3V, P). A->B is isochoric, B->C is a curve, C->A is isobaric.)
Correct Answer: Option A ($2PV$)
Explanation: Detailed explanation will be updated shortly.
Q19. A parallel plate capacitor is charged by a battery, which is then disconnected. A dielectric slab of dielectric constant K is now inserted between the plates. Which of the following quantities decreases?
Correct Answer: Option A (Charge on the plates)
Explanation: Detailed explanation will be updated shortly.
Q20. The first line of the Balmer series in the hydrogen spectrum has a wavelength of 6561 Å. The wavelength of the second line of the Lyman series is:
Correct Answer: Option A (1215 Å)
Explanation: Detailed explanation will be updated shortly.