CBSE Class 12 2025 Physics 55-6-1 Question Paper Set-1: Download Solutions with Answer Key

The figure shows the voltage (V) versus the current (I) graphs for a wire at two temperatures \( T_1 \) and \( T_2 \). One can conclude that:

• (A) \( T_2 = 2T_1 \)
• (B) \( T_1 > T_2 \)
• (C) \( T_1 = \frac{T_2}{3} \)
• (D) \( T_1 < T_2 \)

If \( R_s \) and \( R_p \) are the equivalent resistances of \( n \) resistors, each of value \( R \), in series and parallel combinations respectively, then the value of \( (R_s - R_p) \) is:

• (A) \( \left( \frac{n^2 - 1}{n^2} \right) R \)
• (B) \( \left( \frac{n^2 + 1}{n^2 - 1} \right) R \)
• (C) \( \left( \frac{n^2 - 1}{n} \right) R \)
• (D) \( \frac{(n^2 + 1)R}{n^2} \)

The value of magnetic field at point \( O \) in the given figure is:

• (A) \( \frac{\mu_0 I}{2\pi R} \)
• (B) \( \frac{\mu_0 I}{\pi R} \)
• (C) \( \frac{\mu_0 I}{4R} \)
• (D) \( \frac{\mu_0 I}{R} \)

A piece of a diamagnetic material, free to move when placed in a uniform magnetic field:

• (A) moves along the field
• (B) moves opposite to the field
• (C) moves perpendicular to the field
• (D) does not move at all

A galvanometer can be converted into an ammeter of desired range by connecting a:

• (A) small resistance in series
• (B) large resistance in series
• (C) small resistance in parallel
• (D) large resistance in parallel

A proton and an \( \alpha \)-particle enter with the same velocity \( \vec{v} \) in a uniform magnetic field \( \vec{B} \) such that \( \vec{v} \perp \vec{B} \). The ratio of the radii of their paths is:

• (A) 2
• (B) \( \frac{1}{2} \)
• (C) \( \frac{1}{4} \)
• (D) 4

A vertically held bar magnet is dropped along the axis of a copper ring having a cut as shown in the diagram. The acceleration of the falling magnet is:

• (A) zero
• (B) less than \( g \)
• (C) \( g \)
• (D) greater than \( g \)

An AC source is connected to a resistor and an inductor in series. The voltage across the resistor and inductor are 8 V and 6 V respectively. The voltage of the source is:

• (A) 10 V
• (B) 12 V
• (C) 14 V
• (D) 16 V

Two coherent waves, each of intensity \( I_0 \), produce interference pattern on a screen. The average intensity of light on the screen is:

• (A) zero
• (B) \( I_0 \)
• (C) \( 2I_0 \)
• (D) \( 4I_0 \)

The work function of a material is 2.21 eV. Which of the following cannot produce photoelectrons from it?

• (A) Red light
• (B) Blue light
• (C) Violet light
• (D) Green light

The momentum (in kg·m/s) of a photon of frequency \( 6.0 \times 10^{14} \) Hz is:

• (A) \( 6.63 \times 10^{-25} \)
• (B) \( 1.326 \times 10^{-27} \)
• (C) \( 2.652 \times 10^{-26} \)
• (D) \( 3.978 \times 10^{-24} \)

Inside a nucleus, the nuclear forces between proton and proton, proton and neutron, neutron and neutron are \( F_{pp} \), \( F_{pn} \), and \( F_{nn} \) respectively. Then:

• (A) \( F_{pp} > F_{pn} > F_{nn} \)
• (B) \( F_{pn} > F_{nn} > F_{pp} \)
• (C) \( F_{nn} > F_{pp} > F_{pn} \)
• (D) \( F_{pp} = F_{pn} = F_{nn} \)

Two statements are given one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.

Assertion (A): In a reflecting telescope, the image does not have chromatic aberration.

Reason (R): Chromatic aberration occurs only due to refraction of light through an optical medium.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Both Assertion (A) and Reason (R) are false.

Two statements are given one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.

Assertion (A): A hole is an apparent free particle with effective positive electronic charge.

Reason (R): A hole is not necessarily a vacancy left behind by an electron in the valence band.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Both Assertion (A) and Reason (R) are false.

Two statements are given one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.

Assertion (A): X-rays are produced when slow moving electrons are stopped by a metal target of high atomic number.

Reason (R): X-rays consist of low-energy photons.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Both Assertion (A) and Reason (R) are false.

Two statements are given one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.

Assertion (A): The binding energy per nucleon is practically constant for mass number in the range \( 30 < A < 170 \).

Reason (R): Nuclear forces between the nucleons for mass numbers in the range \( 30 < A < 170 \) are not short-range.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Both Assertion (A) and Reason (R) are false.

Find the equivalent resistance between points A and B for the network shown in the figure.

Find the intensity at a point on the screen in Young’s double slit experiment, at which the interfering waves of intensity \( I_0 \) each, have a path difference of (i) \( \frac{\lambda}{3} \), and (ii) \( \frac{\lambda}{2} \).

A point source of light in air is kept at a distance of 12 cm in front of a convex spherical surface of glass of refractive index 1.5 and radius of curvature 30 cm. Find the nature and position of the image formed.

A laser beam of frequency \( 3.0 \times 10^{14} \) Hz produces average power of 9 mW. Find (i) the energy of a photon of the beam, and (ii) the number of photons emitted per second on an average by the source.

A right-angled isosceles glass prism ABC is kept in contact with an equilateral triangular prism DBC as shown in the figure. Both prisms are made of the same glass of refractive index 1.6. Trace the path of the ray MN incident normally on face AB as it passes through the combination.

In an n-type semiconductor, electron-hole combination is a continuous process at room temperature. Yet the electron concentration is always greater than the hole concentration in it. Explain.

(a) What is the difference between ‘emf’ and ‘terminal voltage’ of a cell?

A rectangular loop carries a current of 1 A. A straight long wire carrying 2 A current is kept near the loop in the same plane as shown in the figure.




Find:

(i) the torque acting on the loop, and

(ii) the magnitude and direction of the net force on the loop.

State Lenz’s law. A rod MN of length \( L \) is rotated about an axis passing through its end M perpendicular to its length, with a constant angular velocity \( \omega \) in a uniform magnetic field \( \vec{B} \) parallel to the axis. Obtain an expression for emf induced between its ends.

Define ‘self-inductance’ of a coil. Derive an expression for self-inductance of a long solenoid of cross-sectional area \( A \) and length \( l \), having \( n \) turns per unit length.

Name the electromagnetic wave used (i) in radar, (ii) in eye surgery, and (iii) as a diagnostic tool in medicine. Write their wavelength range also.

Draw a ray diagram showing the image formation when a concave mirror produces a real, inverted, and magnified image of an object and hence obtain the mirror formula.

How is the necessary force provided to an electron to keep it moving in a circular orbit according to Bohr model of hydrogen atom? Derive an expression for the total energy of an electron moving in an orbit of radius \( r \) in hydrogen atom. Give the significance of the negative sign in this expression.

(a) Consider the so-called ‘D-T reaction’ (Deuterium-Tritium reaction).

In a thermonuclear fusion reactor, the following nuclear reaction occurs: \[ \ ^{2}_1 H + \ ^{3}_1 H \longrightarrow \ ^{4}_2 He + \ ^{1}_0 n + Q \]
Find the amount of energy released in the reaction.


% Given data
Given:
\( m\left(^{2}_1 H\right) = 2.014102 \, u \)
\( m\left(^{3}_1 H\right) = 3.016049 \, u \)
\( m\left(^{4}_2 He\right) = 4.002603 \, u \)
\( m\left(^{1}_0 n\right) = 1.008665 \, u \)
\( 1 \, u = 931 \, MeV/c^2 \)

Consider a capacitor of capacitance \( C \), with plate area \( A \) and plate separation \( d \), filled with air [Fig. (a)]. The distance between the plates is increased to \( 2d \) and one of the plates is shifted as shown in Fig. (b). The capacitance of the new system now is:



% option
(A) \( \frac{C}{4} \)

• (B) \( \frac{C}{2} \)
• (C) \( 2C \)
• (D) \( 4C \)

A slab (area A and thickness \( d_1 \)) of a linear dielectric of dielectric constant \( K \) is inserted between charged plates (charge density \( \sigma \)) of a parallel plate capacitor [plate area A and plate separation \( d > d_1 \)] and opposite charges with charge density of magnitude \( \sigma_p \) appear on the faces of the slab. The dielectric constant K is given by:

• (A) \( \frac{\sigma + \sigma_p}{\sigma} \)
• (B) \( \frac{\sigma}{\sigma - \sigma_p} \)
• (C) \( \frac{\sigma + \sigma_p}{\sigma_p} \)
• (D) \( \frac{\sigma}{\sigma_p} \)

An electric field \( E \) is established between the plates of an air-filled parallel plate capacitor, with charges \( Q \) and \( -Q \). \( V \) is the volume of the space enclosed between the plates. The energy stored in the capacitor is:

• (A) \( \frac{1}{2} \epsilon_0 E^2 \)
• (B) \( \epsilon_0 Q^2 E \)
• (C) \( \frac{1}{2} \epsilon_0 E^2 V \)
• (D) \( \epsilon_0 E Q V \)

Three capacitors A, B, and M, each of capacitance \( C \), are connected to a capacitor N of capacitance \( 2C \) and a battery as shown in the figure. If the charges on A and N are \( Q \) and \( Q' \) respectively, then \( \frac{Q'}{Q} \) is:

• (A) \( \frac{1}{6} \)
• (B) \( \frac{1}{3} \)
• (C) 3
• (D) \( \frac{7}{3} \)

A slab (area A and thickness \( \frac{d}{2} \)) of dielectric constant \( K \) is inserted in a parallel plate capacitor of plate area \( A \) and plate separation \( d \). If \( C \) and \( C_0 \) are the capacitances of the capacitors with and without the dielectric, then \( \frac{C}{C_0} \) is:

• (A) \( \frac{K + 1}{2K} \)
• (B) \( \frac{2K}{K + 1} \)
• (C) \( \frac{K}{K - 1} \)
• (D) \( \frac{K - 1}{K} \)

Which of the following is a donor impurity atom for Ge?

• (A) Boron
• (B) Antimony
• (C) Aluminium
• (D) Indium

When a pentavalent atom occupies the position of an atom in the crystal lattice of Si, four of its electrons form covalent bonds with four silicon neighbours, while the fifth remains bound to the parent atom. The energy required to set this electron free is about:

• (A) 0.5 eV
• (B) 0.1 eV
• (C) 0.05 eV
• (D) 0.01 eV

During formation of a p-n junction:

• (A) a layer of negative charge on n-side and a layer of positive charge on p-side appear.
• (B) a layer of positive charge on n-side and a layer of negative charge on p-side appear.
• (C) the electrons on p-side of the junction move to n-side initially.
• (D) initially diffusion current is small and drift current is large.

In reverse-biased p-n junction:

• (A) the drift current is of the order of few mA
• (B) the applied voltage mostly drops across the depletion region.
• (C) the depletion region width decreases.
• (D) the current increases with increase in applied voltage.

The output frequency of a full-wave rectifier with 50 Hz as input frequency is:

• (A) 25 Hz
• (B) 50 Hz
• (C) 100 Hz
• (D) 200 Hz

In reverse-biased p-n junction:

• (A) the drift current is of the order of few mA
• (B) the applied voltage mostly drops across the depletion region.
• (C) the depletion region width decreases.
• (D) the current increases with increase in applied voltage.

The output frequency of a full-wave rectifier with 50 Hz as input frequency is:

• (A) 25 Hz
• (B) 50 Hz
• (C) 100 Hz
• (D) 200 Hz

(i) Write the principle of working of an ac generator. Draw its labelled diagram and explain its working.

A resistor of 400 \( \Omega \), an inductor of \( \frac{5}{\pi} \) H, and a capacitor of \( \frac{50}{\pi} \) µF are joined in series across an AC source \( v = 140 \sin (100 \pi t) \) V. Find the rms voltages across these three circuit elements. The algebraic sum of these voltages is more than the rms voltage of source. Explain.

Write the principle of working of a transformer. With the help of a labelled diagram, explain the working of a step-up transformer.

(i) Draw a ray diagram to show the image formation by a compound microscope. Obtain the expression for the total magnification of the microscope when the final image is formed at infinity.

In a compound microscope, an object is placed at a distance of 1.5 cm from the objective of focal length 1.25 cm. The eyepiece has a focal length of 5 cm. The final image is formed at infinity. Calculate the distance between the objective and the eyepiece.

(i) Using Huygens’ principle, explain the refraction of a plane wavefront, propagating in air, at a plane interface between air and glass. Hence verify Snell’s law.

Use the mirror formula to deduce that a convex mirror always produces a virtual image of an object kept in front of it.

(i) The electric field in a region is given by \( \vec{E} = 40x \hat{i} \, N/C. \) Find the amount of work done in taking a unit positive charge from a point (0, 3m) to the point (5m, 0).

A charge \( Q \) is distributed over two concentric hollow spheres of radii \( r \) and \( R \) (\( R > r \)) such that their surface charge densities are equal. Find:

the electric field, and
the potential at their common center.

Obtain an expression for the electric field \( \vec{E} \) due to a dipole of dipole moment \( \vec{p} \) at a point on its equatorial plane and specify its direction. Hence, find the value of electric field:

at the centre of the dipole (\( r = 0 \)), and
at a point \( r \gg a \), where \( 2a \) is the length of the dipole.

An electric field \( \vec{E} = (10x + 5) \hat{i} \, N/C \) exists in a region in which a cube of side \( L \) is kept as shown in the figure. Here \( x \) and \( L \) are in metres. Calculate the net flux through the cube.