CBSE Class 12 2025 Physics 55-7-2 Question Paper Set-2: Download Solutions with Answer Key

The electric field (\( \vec{E} \)) and electric potential (\( V \)) at a point inside a charged hollow metallic sphere are respectively:

• (A) \( E = 0, \quad V = 0 \)
• (B) \( E = 0, \quad V = V_0 (a constant) \)
• (C) \( E \ne 0, \quad V \ne 0 \)
• (D) \( E = E_0 (a constant), \quad V = 0 \)

The dimensions of ‘self-inductance’ are:

• (A) \( [MLT^{-2}A^{-2}] \)
• (B) \( [ML^2T^{-1}A^{-1}] \)
• (C) \( [ML^{-1}T^{-2}A^{-2}] \)
• (D) \( [ML^2T^{-2}A^{-2}] \)

In a circular loop of radius \( R \), current \( I \) enters at point \( A \) and exits at point \( B \), as shown in the figure. The value of the magnetic field at the centre \( O \) of the loop is:

• (A) \( \dfrac{\mu_0 I}{R} \)
• (B) zero
• (C) \( \dfrac{\mu_0 I}{2R} \)
• (D) \( \dfrac{\mu_0 I}{4R} \)

The frequency of a photon of energy 1.326eV is:

• (A) \(1.18 \times 10^{14}\,Hz\)
• (B) \(3.20 \times 10^{14}\,Hz\)
• (C) \(4.20 \times 10^{15}\,Hz\)
• (D) \(4.80 \times 10^{15}\,Hz\)

A metal rod of length 50 cm is held vertically and moved with a velocity of 10 m/s towards east. The horizontal component of the Earth’s magnetic field at the place is 0.4G. The emf induced across the ends of the rod is:

• (A) 0.1mV
• (B) 0.2mV
• (C) 0.8mV
• (D) 1.6mV

Germanium crystal is doped at room temperature with a minute quantity of boron. The charge carriers in the doped semiconductors will be:

• (A) electrons only
• (B) holes only
• (C) holes and few electrons
• (D) electrons and few holes

The effective resistance between points A and B in the given circuit is:

• (A) \(6\,\Omega\)
• (B) \( \dfrac{8}{3}\,\Omega \)
• (C) \( \dfrac{16}{3}\,\Omega \)
• (D) \(2\,\Omega\)

A capacitor and an inductor are connected in series across an ac source of voltage of variable frequency. The frequency is increased continuously. The nature of the circuit before and after the resonance will be:

• (A) inductive only
• (B) capacitive only
• (C) capacitive and inductive respectively
• (D) inductive and capacitive respectively

An alternating current is given by \( I = I_0 \cos(100\pi t) \). The least time the current takes to decrease from its maximum value to zero will be:

• (A) \( \left(\frac{1}{200}\right)\,s \)
• (B) \( \left(\frac{1}{150}\right)\,s \)
• (C) \( \left(\frac{1}{100}\right)\,s \)
• (D) \( \left(\frac{1}{50}\right)\,s \)

The mass numbers of two nuclei A and B are 27 and 64 respectively. The ratio of their radii \( \left(\frac{r_A}{r_B}\right) \) will be:

• (A) \( \frac{27}{64} \)
• (B) \( \frac{9}{16} \)
• (C) \( \frac{3\sqrt{3}}{8} \)
• (D) \( \frac{3}{4} \)

Isotones are the nuclides having:

• (A) same mass numbers
• (B) same atomic numbers
• (C) same neutron number, but different atomic number
• (D) different neutron number, and different mass number

A p-n junction diode is forward biased. As a result,

• (A) both the potential barrier height and the width of depletion layer decrease
• (B) both the potential barrier height and the width of depletion layer increase
• (C) the potential barrier height decreases and the width of depletion layer increases
• (D) the potential barrier height increases and the width of depletion layer decreases

Assertion (A): A ray of light is incident normally on the face of a prism. The emergent ray will graze along the opposite face of the prism when the critical angle at the glass-air interface is equal to the angle of the prism.

Reason (R): The refractive index of a prism depends on the angle of the prism.

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

Assertion (A): A charged particle is moving with velocity \( \vec{v} \) in the x–y plane, making an angle \( \theta \ (0 < \theta < \frac{\pi}{2}) \) with the x-axis. If a uniform magnetic field \( \vec{B} \) is applied in the region, along y-axis, the particle will move in a helical path with its axis parallel to the x-axis.

Reason (R): The direction of the magnetic force acting on a charged particle moving in a magnetic field is along the velocity of the particle.

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

Assertion (A): The minimum negative potential applied to the anode in a photoelectric experiment at which photoelectric current becomes zero, is called cut-off voltage.

Reason (R): The threshold frequency for a metal is the minimum frequency of incident radiation below which emission of photoelectrons does not take place.

• (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.

Assertion (A): EM waves do not require a medium for their propagation.

Reason (R): EM waves are transverse waves.

• (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 wires made of the same material have the same length \( l \) but different cross-sectional areas \( A_1 \) and \( A_2 \). They are connected together with a cell of voltage \( V \). Find the ratio of the drift velocities of free electrons in the two wires when they are joined in:
(i) series, and
(ii) parallel.

Draw energy band diagrams of n-type and p-type semiconductors at temperature \( T > 0\,K \). Show the donor/acceptor energy levels with the order of difference of their energies from the bands.

The ratio of the intensities at maxima to minima in Young’s double-slit experiment is \( 25 : 9 \). Calculate the ratio of intensities of the interfering waves.

Using the mirror equation and the formula of magnification, deduce that “the virtual image produced by a convex mirror is always diminished in size and is located between the pole and the focus.”

A convex lens of focal length 10 cm, a concave lens of focal length 15 cm and a third lens of unknown focal length are placed coaxially in contact. If the focal length of the combination is \( +12\,cm \), find the nature and focal length of the third lens, if all lenses are thin. Will the answer change if the lenses were thick?

Calculate the binding energy per nucleon (in MeV) of a helium nucleus \(\left( ^4_2He \right)\).

Given: \[ \begin{aligned} m\left(^4_2He\right) &= 4.002603\,u
m_n &= 1.008665\,u
m_H &= 1.007825\,u
1\,u &= 931.5\,MeV/c^2 \end{aligned} \]

Write the mathematical forms of three postulates of Bohr’s theory of the hydrogen atom. Using them, prove that for an electron revolving in the \( n^{th} \) orbit:

(a) the radius of the orbit is proportional to \( n^2 \), and

(b) the total energy of the atom is proportional to \( \left( \frac{1}{n^2} \right) \).

(a) Briefly explain Einstein’s photoelectric equation.

(b) Four metals with their work functions are listed below:

K = 2.3 eV, Na = 2.75 eV, Mo = 4.17 eV, Ni = 5.15 eV.

The radiation of wavelength 330 nm from a laser source placed 1 m away, falls on these metals.
Which of these metals will not show photoelectric emission?
What will happen if the laser source is brought closer to a distance of 50 cm?

(a)
(i) Write Biot–Savart’s law in vector form.

(ii) Two identical circular coils A and B, each of radius \( R \), carrying currents \( I \) and \( \sqrt{3}I \) respectively, are placed concentrically in XY and YZ planes respectively.
Find the magnitude and direction of the net magnetic field at their common centre.

(i) A rectangular loop of sides \( l \) and \( b \) carries a current \( I \) clockwise. Write the magnetic moment \( \vec{m} \) of the loop and show its direction in a diagram.

(ii) The loop is placed in a uniform magnetic field \( \vec{B} \) and is free to rotate about an axis which is perpendicular to \( \vec{B} \). Prove that the loop experiences no net force, but a torque \( \vec{\tau} = \vec{m} \times \vec{B} \).

(a) How are electromagnetic waves produced?

(b) Write the wavelength range and one use of:

(i) Microwaves, and

(ii) Ultraviolet waves.

Two concentric circular coils of radii \( r_1 \) and \( r_2 \) (\( r_2 \gg r_1 \)) are placed coaxially with their centres coinciding. If a current \( I \) is passed through the outer coil, obtain the expression for mutual inductance of the arrangement.

The current in a solenoid decreases steadily from 6 mA to 2 mA in 50 ms. If an average emf of 0.4 V is induced, find the self-inductance of the solenoid.

Explain the process of formation of ‘depletion layer’ and ‘potential barrier’ in a p-n junction region of a diode, with the help of a suitable diagram.
Which feature of junction diode makes it suitable for its use as a rectifier?

Two point charges of \( -5\,\mu C \) and \( 2\,\mu C \) are located in free space at \( (-4\,cm, 0) \) and \( (6\,cm, 0) \) respectively.

(a) Calculate the amount of work done to separate the two charges at infinite distance.

(b) If this system of charges was initially kept in an electric field \[ \vec{E} = \frac{A}{r^2}, where A = 8 \times 10^4\, N\,C^{-1}\,m^2, \]
calculate the electrostatic potential energy of the system.

A small bulb is placed at the bottom of a tank containing a transparent liquid (refractive index \( n \)) to a depth \( H \). The radius of the circular area of the surface of liquid, through which the light from the bulb can emerge out, is \( R \). Then \( \left( \frac{R}{H} \right) \) is:

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

A parallel beam of light is incident on a face of a prism with refracting angle 60°. The angle of minimum deviation is found to be 30°. The refractive index of the material of the prism is close to:

• (A) 1.3
• (B) 1.4
• (C) 1.5
• (D) 1.6

The angle of minimum deviation for a ray of light incident on a thin prism, made of crown glass (\( n = 1.52 \)) is \( \delta_m \). If the prism was made of dense flint glass (\( n = 1.62 \)) instead of crown glass, the angle of minimum deviation will:

• (A) decrease by 4%
• (B) increase by 4%
• (C) decrease by 19%
• (D) increase by 19%

An object is placed in front of a convex spherical glass surface (\( n = 1.5 \) and radius of curvature \( R \)) at a distance of \( 4R \) from it. As the object is moved slowly close to the surface, the image formed is:

• (A) always real
• (B) always virtual
• (C) first real and then virtual
• (D) first virtual and then real

A double-convex lens, made of glass of refractive index 1.5, has focal length 10 cm. The radius of curvature of its each face, is:

• (A) 10 cm
• (B) 15 cm
• (C) 20 cm
• (D) 40 cm

Consider two cylindrical conductors A and B, made of the same metal connected in series to a battery. The length and the radius of B are twice that of A. If \( \mu_A \) and \( \mu_B \) are the mobility of electrons in A and B respectively, then \( \frac{\mu_A}{\mu_B} \) is:

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

A wire of length 0.5 m and cross-sectional area \( 1.0 \times 10^{-7} \, m^2 \) is connected to a battery of 2 V that maintains a current of 1.5 A in it. The conductivity of the material of the wire (in \( \Omega^{-1} \cdot m^{-1} \)) is:

• (A) \( 2.5 \times 10^4 \)
• (B) \( 3.0 \times 10^5 \)
• (C) \( 3.75 \times 10^6 \)
• (D) \( 5.0 \times 10^7 \)

The temperature coefficient of resistance of nichrome is \( 1.70 \times 10^{-4} \, ^\circC^{-1} \). In order to increase the resistance of a nichrome wire by 8.5%, the temperature of the wire should be increased by:

• (A) \( 250^\circC \)
• (B) \( 500^\circC \)
• (C) \( 850^\circC \)
• (D) \( 1000^\circC \)

Consider the contribution of the following two factors I and II in resistivity of a metal:

I. Relaxation time of electrons

II. Number of electrons per unit volume

The resistivity of a metal increases with increase in its temperature because:

• (A) I decreases and II increases.
• (B) I increases and II is almost constant.
• (C) Both I and II increase.
• (D) I decreases and II is almost constant.

A steady current flows in a copper wire of non-uniform cross-section. Consider the following three physical quantities:

I. Electric field

II. Current density

III. Drift speed

Then at the different points along the wire:

• (A) II and III change, but I is constant.
• (B) I and II change, but III is constant.
• (C) I and III change, but II is constant.
• (D) All I, II, and III change.

Explain with the help of a labelled ray diagram the formation of final image by an astronomical telescope at infinity. Write the expression for its magnifying power.

The total magnification produced by a compound microscope is 20. The magnification produced by the eyepiece is 5. When the microscope is focused on a certain object, the distance between the objective and eyepiece is observed to be 14 cm. Calculate the focal lengths of the objective and the eyepiece. (Given that the least distance of distinct vision = 25 cm)

Two coherent light waves, each of intensity \( I_0 \), superpose and produce an interference pattern on a screen. Obtain the expression for the resultant intensity at a point where the phase difference between the waves is \( \phi \). Write its maximum and minimum possible values.

In a single slit diffraction experiment, the aperture of the slit is 3 mm and the separation between the slit and the screen is 1.5 m. A monochromatic light of wavelength 600 nm is normally incident on the slit. Calculate the distance of (I) first order minimum, and (II) second order maximum, from the centre of the screen.

A parallel plate capacitor with plate area \( A \) and plate separation \( d \) has a capacitance \( C_0 \). A slab of dielectric constant \( K \) having area \( A \) and thickness \( \left( \frac{d}{4} \right) \) is inserted in the capacitor, parallel to the plates. Find the new value of its capacitance.

You are provided with a large number of 1 µF identical capacitors and a power supply of 1200 V. The dielectric medium used in each capacitor can withstand up to 200 V only. Find the minimum number of capacitors and their arrangement required to build a capacitor system of equivalent capacitance of 2 µF for use with this supply.

An electric dipole of dipole moment \( \vec{p} \) consists of point charges \( +q \) and \( -q \), separated by \( 2a \). Derive an expression for the electric potential in terms of its dipole moment at a point at a distance \( x \gg a \) from its centre and lying:
(I) along its axis, and
(II) along its bisector (equatorial) line.

An electric dipole of dipole moment \( \vec{p} = (0.8\,\hat{i} + 0.6\,\hat{j}) \times 10^{-29} \,Cm \) is placed in an electric field \( \vec{E} = 1.0 \times 10^7\,\hat{k} \,V/m \). Calculate the magnitude of the torque acting on it and the angle it makes with the x-axis at this instant.

With the help of a labelled diagram, explain the principle of working of a moving coil galvanometer. Write the purpose of using (i) radial magnetic field, and (ii) soft iron core, in it.

Define current sensitivity of a galvanometer. “Increasing the current sensitivity may not necessarily increase the voltage sensitivity.” Give reason.