CBSE Class 12 2025 Physics 55-5-3 Question Paper Set-3: Download Solutions with Answer Key

A beam of light of wavelength \(720\;\text{nm}\) in air enters water (refractive index \(= \dfrac{4}{3}\)). Its wavelength in water will be:

• (A) \(540\;\text{nm}\)
• (B) \(480\;\text{nm}\)
• (C) \(420\;\text{nm}\)
• (D) \(720\;\text{nm}\)

A capacitor of capacitance \(C\) has reactance \(X\) in an ac circuit. If the capacitance and the frequency of the applied voltage are doubled, the new reactance will become:

• (A) \(4X\)
• (B) \(2X\)
• (C) \(\dfrac{X}{2}\)
• (D) \(\dfrac{X}{4}\)

Four point charges \(Q\) each, are held at the four corners of a square of side \(l\). The amount of work done in bringing a charge \(Q\) from infinity to the centre of the square will be:

• (A) \(\dfrac{Q^2}{\pi\varepsilon_0 l}\)
• (B) \(\dfrac{\sqrt{2}\,Q^2}{\pi\varepsilon_0 l}\)
• (C) \(\dfrac{Q^2}{2\pi\varepsilon_0 l}\)
• (D) Zero

A metal sheet is inserted between the plates of a parallel plate capacitor of capacitance \(C\). If the sheet partly occupies the space between the plates, the capacitance:

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

Four resistors, each of resistance \(R\) and a key \(K\) are connected as shown in the figure. The equivalent resistance between points \(A\) and \(B\) when key \(K\) is open, will be:

• (A) \(4R\)
• (B) \(\infty\)
• (C) \(\dfrac{R}{4}\)
• (D) \(\dfrac{4R}{3}\)

A charged particle gains a speed of \(10^6\,\text{ms}^{-1}\), when accelerated from rest through a potential difference 10 kV. It enters a region of magnetic field of 0.4 T such that \(\vec{v} \perp \vec{B}\). The radius of circular path described by it is:

• (A) 2.5 cm
• (B) 5 cm
• (C) 8 cm
• (D) 10 cm

A current of \(\left(\dfrac{10}{\pi}\right)\;\text{A}\) is maintained in a circular loop of radius \(14\;\text{cm}\). The value of dipole moment associated with the loop is:

• (A) \(0.019\;\text{Am}^2\)
• (B) \(0.14\;\text{Am}^2\)
• (C) \(0.196\;\text{Am}^2\)
• (D) \(0.615\;\text{Am}^2\)

Which of the following rays coming from the Sun plays an important role in maintaining the Earth's warmth?

• (A) Infrared rays
• (B) \(\gamma\) rays
• (C) UV rays
• (D) Visible light rays

The dimensions of \( (\mu \epsilon)^{-1} \), where \( \epsilon \) is permittivity and \( \mu \) is permeability of a medium, are:

• (A) \( [M^0 L^1 T^{-1}] \)
• (B) \( [M^0 L^2 T^{-2}] \)
• (C) \( [M^1 L^2 T^{-2}] \)
• (D) \( [M^1 L^{-1} T^{1}] \)

Which of the following electromagnetic waves has photons of largest momentum?

• (A) X-rays
• (B) AM radio waves
• (C) Microwaves
• (D) TV waves

The kinetic energy of an alpha particle is four times the kinetic energy of a proton. The ratio \(\dfrac{\lambda_\alpha}{\lambda_p}\) of de Broglie wavelengths associated with them will be:

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

Two coherent light waves, each having amplitude '\(a\)', superpose to produce an interference pattern on a screen. The intensity of light as seen on the screen varies between:

• (A) \(0\) and \(2a^2\)
• (B) \(0\) and \(4a^2\)
• (C) \(a^2\) and \(2a^2\)
• (D) \(2a^2\) and \(4a^2\)

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): During formation of a nucleus, the mass defect produced is the source of the binding energy of the nucleus.
Reason (R): For all nuclei, the value of binding energy per nucleon increases with mass number.

• (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): In Rutherford's alpha particle scattering experiment, the presence of only few alpha particles at angle of scattering \(\pi\) led him to the discovery of nucleus.

Reason (R): The size of nucleus is approximately \(10^{-4}\) times the size of an atom and therefore only few alpha particles are rebounded.

• (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 impurities in p-type Si are not pentavalent atoms.
Reason (R): The hole density in the valence band in a p-type semiconductor is almost equal to the acceptor density.

• (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.
  

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 Balmer series in hydrogen atom spectrum is formed when the electron jumps from higher energy state to the ground state.
Reason (R): In Bohr's model of hydrogen atom, the electron can jump between successive orbits only.

• (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.
  

Find the effective resistance of the network of resistors between points A and F as shown in the figure.

A current of \(5\;\text{A}\) is passing along \(+X\) direction through a wire lying along \(X\)-axis. Find the magnetic field \(\vec{B}\) at a point \(\vec{r} = (3\hat{i} + 4\hat{j})\;\text{m}\) due to \(1\;\text{cm}\) element of the wire, centered at origin.

Define the term, 'distance of closest approach'. A proton of \(3.95\;\text{MeV}\) energy approaches a target nucleus \(Z = 79\) in head-on position. Calculate its distance of closest approach.

A point object is placed in air at a distance \(R/3\) in front of a convex surface of radius of curvature \(R\), separating air from a medium of refractive index \(n\;(\lt 4)\). Find the nature and position of the image formed.

In Young's double slit experimental set-up, the intensity of the central maximum is \(I_0\). Calculate the intensity at a point where the path difference between two interfering waves is \(\lambda/3\).

The threshold frequency for a given metal is \( 3.6 \times 10^{14} \) Hz. If monochromatic radiations of frequency \( 6.8 \times 10^{14} \) Hz are incident on this metal, find the cut-off potential for the photoelectrons.

(a) "There is a limit to the amount of charge that can be stored on a given capacitor." Explain.

(b) A capacitor is charged by a battery to a potential difference \(V\). It is disconnected from the battery and connected across another identical uncharged capacitor. Calculate the ratio of total energy stored in the combination to the initial energy stored in the capacitor.

(a) "You cannot see a person standing on the other side of a boundary wall but can hear him." Explain with reason.

(b) Light of wavelength \(750\;\text{nm}\) is incident normally on a slit of width \(1.5\;\text{mm}\). Diffraction pattern is obtained on a screen \(1.0\;\text{m}\) away from the slit. Find the distance of the nearest point from the central maxima at which the intensity is zero.

The magnetic moment (\(5\;\text{J/T}\)) of a bar magnet points along a uniform magnetic field \(0.4\;\text{T}\).

(a) Calculate (i) the potential energy of the bar magnet, and (ii) the work done in turning the magnet by \(180^{\circ}\).

(b) In which case is the potential energy of the magnet minimum ?

A right-angled prism \(ABC\) (refractive index \(\sqrt{2}\)) is kept on a plane mirror as shown in the figure. A ray of light is incident normally on the face \(AC\).

(a) Trace the path of the ray as it passes through the prism.

(b) Find the angle of deviation produced by the prism.

Two small solid metal balls \(A\) and \(B\) of radii \(R\) and \(2R\) having charge densities \(2\sigma\) and \(3\sigma\) respectively are kept far apart. Find the charge densities on \(A\) and \(B\) after they are connected by a conducting wire.

Two infinitely long straight wires '1' and '2' are placed \(d\) distance apart, parallel to each other, as shown in the figure. They are uniformly charged having charge densities \(\lambda\) and \(-\dfrac{\lambda}{2}\) respectively. Locate the position of the point from wire '1' at which the net electric field is zero and identify the region in which it lies.

(a) Draw the energy-band diagrams for conductors, semiconductors and insulators at \(T = 0\;\text{K}\). How is an electron-hole pair formed in a semiconductor at room temperature?

(b) Carbon and silicon both, are members of IV group of periodic table and have the same lattice structure. Carbon is an insulator whereas silicon is a semiconductor. Explain.

Differentiate between half-wave and full-wave rectification. With the help of a circuit diagram, explain the working of a full-wave rectifier.

Comprehension:

Case Study: A galvanometer is an instrument used to show the direction and strength of the current passing through it. In a galvanometer, a coil placed in a magnetic field experiences a torque and hence gets deflected when a current passes through it. The name is derived from the surname of Italian scientist L. Galvani, who in 1791 discovered that electric current makes a dead frog's leg jerk. A spring attached with the coil provides a counter torque. In equilibrium, the deflecting torque is balanced by the restoring torque of the spring and we have: \(NBAI = k\phi\), where \(N\) is the total number

(i) The value of the current sensitivity of a galvanometer is given by:

• (A) \(\dfrac{k}{NBA}\)
• (B) \(\dfrac{NBA}{k}\)
• (C) \(\dfrac{kBA}{N}\)
• (D) \(\dfrac{kNB}{A}\)

(ii) A galvanometer of resistance \(6\;\Omega\) shows full scale deflection for a current of \(0.2\;\text{A}\). The value of shunt to be used with this galvanometer to convert it into an ammeter of range \((0 - 5\;\text{A})\) is:

• (A) \(0.25\;\Omega\)
• (B) \(0.30\;\Omega\)
• (C) \(0.50\;\Omega\)
• (D) \(6.0\;\Omega\)

(iii) The value of resistance of the ammeter in case (ii) will be:

• (A) \(0.20\;\Omega\)
• (B) \(0.24\;\Omega\)
• (C) \(6.0\;\Omega\)
• (D) \(6.25\;\Omega\)

A galvanometer of resistance \(G\) is converted into a voltmeter of range \((0 - V)\) by connecting a resistor of \(250\ \Omega\) with it. If resistor of \(250\ \Omega\) is replaced by another resistor of \(900\ \Omega\), its range becomes \((0 - 3\text{ V})\). The resistance \(G\) of the galvanometer is :

• (A) \(150\ \Omega\)
  
• (B) \(125\ \Omega\)
  
• (C) \(100\ \Omega\)
  
• (D) \(75\ \Omega\)
  

Comprehension:

Case Study: Einstein explained photoelectric effect on the basis of Planck's quantum theory, where light travels in the form of small bundles of energy called photons. The energy of each photon is \(h\nu\), where \(\nu\) is the frequency of incident light and \(h\) is Planck's constant. The number of photons in a beam of light determines

Which of the following graphs shows the variation of photoelectric current \(I\) with the intensity of light?

• (A)

• (B)

• (C)

• (D)

(ii) When the frequency of the incident light is increased without changing its intensity, the saturation current:

• (A) increases linearly
• (B) decreases
• (C) increases non-linearly
• (D) remains the same

(iii) Which of the following graphs can be used to obtain the value of Planck's constant?

• (A) Photocurrent versus Intensity of incident light
• (B) Photocurrent versus Frequency of incident light
• (C) Cut-off potential versus Frequency of incident light
• (D) Cut-off potential versus Intensity of incident light

Radiations of two frequencies are incident on a metal surface of work function 2.0 eV one by one. The energies of their photons are 2.5 eV and 4.5 eV respectively. Find the ratio of the maximum speed of the electrons emitted in the two cases.

(i) Draw a ray diagram of a reflecting telescope (Cassegrain) and explain the formation of image. State two important advantages that a reflecting telescope has over a refracting telescope.

(ii) In a refracting telescope, the focal length of the objective is \(50\) times the focal length of the eyepiece. When the final image is formed at infinity, the length of the tube is \(102\;\text{cm}\). Find the focal lengths of the two lenses.

(i) Write any two advantages of a compound microscope over a simple microscope. Draw a ray diagram for the image formation at the near point by a compound microscope and explain it.

(ii) A thin planoconcave lens with its curved face of radius of curvature \(R\) is made of glass of refractive index \(n_1\). It is placed coaxially in contact with a thin equiconvex lens of same radius of curvature of refractive index \(n_2\). Obtain the power of the combination lens.

(i) Three batteries \(E_1\), \(E_2\) and \(E_3\) of emfs and internal resistances \((4\;\text{V}, 2\;\Omega)\), \((2\;\text{V}, 4\;\Omega)\) and \((6\;\text{V}, 2\;\Omega)\) respectively are connected as shown in the figure. Find the values of the currents passing through batteries \(E_1\), \(E_2\) and \(E_3\).

(ii) The ends of six wires, each of resistance \(R\;(= 10\;\Omega)\) are joined as shown in the figure. The points \(A\) and \(B\) of the arrangement are connected in a circuit. Find the value of the effective resistance offered by it to the circuit.

(i) Current \(I\;(= 1\;\text{A})\) is passing through a copper rod (\(n = 8.5 \times 10^{28}\;\text{m}^{-3}\)) of varying cross-sections as shown in the figure. The areas of cross-section at points \(A\) and \(B\) along its length are \(1.0 \times 10^{-7}\;\text{m}^2\) and \(2.0 \times 10^{-7}\;\text{m}^2\) respectively. Calculate:

(I) the ratio of electric fields at points \(A\) and \(B\).

(II) the drift velocity of free electrons at point \(B\).

(ii) Two point charges \(q_1\;(= 16\;\mu\text{C})\) and \(q_2\;(= 1\;\mu\text{C})\) are placed at points \(\vec{r}_1 = (3\;\text{m})\hat{i}\) and \(\vec{r}_2 = (4\;\text{m})\hat{j}\). Find the net electric field \(\vec{E}\) at point \(\vec{r} = (3\;\text{m})\hat{i} + (4\;\text{m})\hat{j}\).

(i) Define self-inductance of a coil. Derive the expression for the energy required to build up a current \(I\) in a coil of self-inductance \(L\).

(ii) The currents passing through two inductors of self-inductances \(10\;\text{mH}\) and \(20\;\text{mH}\) increase with time at the same rate. Draw graphs showing the variation of:

(I) the magnitude of emf induced with the rate of change of current in each inductor.

(II) the energy stored in each inductor with the current flowing through it.

(i) Define the term mutual inductance. Deduce the expression for the mutual inductance of two long coaxial solenoids of the same length having different radii and different number of turns.

(ii) The current through an inductor is uniformly increased from zero to \(2\;\text{A}\) in \(40\;\text{s}\). An emf of \(5\;\text{mV}\) is induced during this period. Find the flux linked with the inductor at \(t = 10\;\text{s}\).