CBSE Class 12 Physics 2024 — Set 55/5/1

The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and 2 cm respectively. If the tube length of the microscope is 10 cm, the magnification obtained by the microscope for the most suitable viewing by a relaxed eye is ___. (A) 250 (B) 200 (C) 150 (D) 125

The variation of the stopping potential (V₀) with the frequency (nu) of the incident radiation for four metals A, B, C and D is shown in the figure. For the same frequency of incident radiation producing photo-electrons in all the metals, the kinetic energy of the photo-electrons will be maximum for metal ___. (A) A (B) B (C) C (D) D

The energy of an electron in the ground state of a hydrogen atom is -13.6eV. The kinetic and potential energy of the electron in the first excited state will be ___. (A) -13.6eV,27.2eV (B) -6.8eV,13.6eV (C) 3.4eV,-6.8eV (D) 6.8eV,-3.4eV

A Young's double-slit experimental set-up is kept in a medium of refractive index (4)/(3). Which maximum in this case will coincide with the 6th maximum obtained if the medium is replaced by air? (A) 4th (B) 6th (C) 8th (D) 10th

The potential energy between two nucleons inside a nucleus is minimum at a distance of about ___. (A) 0.8 fm (B) 1.6 fm (C) 2.0 fm (D) 2.8 fm

A pure Si crystal having 5×10²⁸ atoms m⁻³ is doped with 1 ppm concentration of antimony. If the concentration of holes in the doped crystal is found to be 4.5×10⁹ m⁻³, the concentration (in m⁻³) of intrinsic charge carriers in the Si crystal is about ___. (A) 1.2×10¹⁵ (B) 1.5×10¹⁶ (C) 3.0×10¹⁵ (D) 2.0×10¹⁶

Assertion (A): The energy of a charged particle moving in a magnetic field does not change. Reason (R): It is because the work done by the magnetic force on a charge moving in a magnetic field is zero. (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true but R is NOT the correct explanation of A. (C) A is true but R is false. (D) Both A and R are false.

Assertion (A): In Young's double slit experiment, when the two coherent sources are infinitely close to each other, the interference pattern cannot be observed. Reason (R): The fringe width is proportional to the separation between the two sources. (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true but R is NOT the correct explanation of A. (C) A is true but R is false. (D) Both A and R are false.

Assertion (A): An alpha particle is moving towards a gold nucleus. The impact parameter is maximum for the scattering angle of 180°. Reason (R): The impact parameter in an alpha particle scattering experiment does not depend upon the atomic number of the target nucleus. (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true but R is NOT the correct explanation of A. (C) A is true but R is false. (D) Both A and R are false.

Assertion (A): Equal amount of positive and negative charges are distributed uniformly on two halves of a thin circular ring as shown in figure. The resultant electric field at the centre O of the ring is along OC. Reason (R): It is so because the net potential at O is not zero. (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true but R is NOT the correct explanation of A. (C) A is true but R is false. (D) Both A and R are false.

(a) Four point charges of 1μ C, -2μ C, 1μ C and -2μ C are placed at the corners A, B, C and D respectively, of a square of side 30 cm. Find the net force acting on a charge of 4μ C placed at the centre of the square. OR (b) Three point charges, 1pC each, are kept at the vertices of an equilateral triangle of side 10 cm. Find the net electric field at the centroid of the triangle.

Derive an expression for the magnetic force vecF acting on a straight conductor of length L carrying current I in an external magnetic field vecB. Is it valid when the conductor is in zig-zag form? Justify.

A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. Calculate its magnifying power in normal adjustment and the distance of the image formed by the objective.

(a) Two energy levels of an electron in a hydrogen atom are separated by 2.55 eV. Find the wavelength of radiation emitted when the electron makes a transition from the higher energy level to the lower energy level. (b) In which series of the hydrogen spectrum does this line fall?

The earth revolves around the sun in an orbit of radius 1.5×10¹¹ m with an orbital speed of 30 km/s. Find the quantum number that characterises its revolution using Bohr's model in this case (mass of earth = 6.0×10²⁴ kg).

(a) Write Einstein's photoelectric equation. How did Millikan prove the validity of this equation? (b) Explain the existence of a threshold frequency of incident radiation for photoelectric emission from a given surface.

(a) Define electric flux. Write the dimensions of electric flux. (b) A plane surface, in the shape of a square of side 1 cm, is placed in an electric field vecE = (100N/C)hati such that the unit vector normal to the surface is given by hatn = 0.8hati + 0.6hatk. Find the electric flux through the surface.

(a) (i) State Lenz's law. In a closed circuit, the induced current opposes the change in magnetic flux that produced it, as per the law of conservation of energy. Justify. (ii) A metal rod of length 2 m is rotated with a frequency of 60 rev/s about an axis passing through its centre and perpendicular to its length. A uniform magnetic field of 2 T perpendicular to its plane of rotation is switched on in the region. Calculate the emf induced between the centre and the end of the rod. OR (b) (i) State and explain Ampere's circuital law. (ii) Two long straight parallel wires separated by 20 cm carry 5 A and 10 A current respectively, in the same direction. Find the magnitude and direction of the net magnetic field at a point midway between them.

An electron moving with a velocity vecv = (1.0×10⁷m/s)hati + (0.5×10⁷m/s)hatj enters a region of uniform magnetic field vecB = (0.5mT)hatj. Find the radius of the circular path described by it. While rotating, does the electron trace a linear path too? If so, calculate the linear distance covered by it during the period of one revolution.

(a) Name the parts of the electromagnetic spectrum which are: (i) also known as heat waves, and (ii) absorbed by the ozone layer in the atmosphere. (b) Write briefly one method each for the production and detection of these radiations.

(a) Explain the characteristic of a p-n junction diode that makes it suitable for its use as a rectifier. (b) With the help of a circuit diagram, explain the working of a full-wave rectifier.

Explain the following, giving reasons: (a) A doped semiconductor is electrically neutral. (b) In a p-n junction under equilibrium, there is no net current. (c) In a diode, the reverse current is practically independent of the applied voltage.

Case Study (Dielectrics): Read the case and answer the sub-questions. (a) Which of the following is a polar molecule? (i) O₂ (ii) H₂ (iii) N₂ (iv) HCl (b) Which of the following statements about dielectrics is correct? (i) A polar dielectric has a net dipole moment in the absence of an external electric field which gets modified due to the induced dipoles. (ii) The net dipole moment of the induced dipoles is along the direction of the applied electric field. (iii) Dielectrics contain free charges. (iv) The electric field produced due to induced surface charges inside a dielectric is along the external electric field. (c) When a dielectric slab is inserted between the plates of an isolated charged capacitor, the energy stored in it ___. (i) increases and the electric field inside it also increases (ii) decreases and the electric field also decreases (iii) decreases and the electric field increases (iv) increases and the electric field decreases (d) (i) An air-filled capacitor with plate area A and plate separation d has capacitance C₀. A slab of dielectric constant K, area A and thickness d/5 is inserted between the plates. The capacitance of the capacitor becomes ___. (1) (4K)/(5K+1)C₀ (2) (K+5)/(4)C₀ (3) (5K)/(4K+1)C₀ (4) (K+4)/(5K)C₀ OR (d) (ii) Two capacitors of capacitances 2C₀ and 6C₀ are first connected in series and then in parallel across the same battery. The ratio of energies stored in the series combination to that in the parallel combination is ___. (1) (1)/(4) (2) (1)/(6) (3) (2)/(15) (4) (3)/(16)

Case Study (Refraction and Prism): Given aμg = 1.5 and aμw = 1.33. Read the case and answer the sub-questions. (a) The critical angle for glass is θ₁ and that for water is θ₂. The critical angle for the glass–water interface would be ___. (i) less than θ₂ (ii) between θ₁ and θ₂ (iii) greater than θ₂ (iv) less than θ₁ (b) When a ray of light of wavelength λ and frequency nu is refracted into a denser medium, ___. (i) λ and nu both increase (ii) λ increases but nu is unchanged (iii) λ decreases but nu is unchanged (iv) λ and nu both decrease (c) (i) The critical angle for a ray of light passing from glass to water is minimum for ___. (1) red colour (2) blue colour (3) yellow colour (4) violet colour OR (c) (ii) Three beams of red, yellow and violet colours are passed through a prism, one by one, under the same condition. When the prism is in the position of minimum deviation, the angles of refraction from the second surface are rr, ry and rv respectively. Then ___. (1) rv < ry < rr (2) ry < rr < rv (3) rr < ry < rv (4) rr = ry = rv (d) A ray of light is incident normally on a prism ABC of refractive index √(2), as shown in the figure. After it strikes face AC, it will ___. (i) go straight, undeviated (ii) just graze along the face AC (iii) refract and go out of the prism (iv) undergo total internal reflection

(a) (i) Draw equipotential surfaces for an electric dipole. (ii) Two point charges q₁ and q₂ are located at vecr₁ and vecr₂ respectively in an external electric field vecE. Obtain an expression for the potential energy of the system. (iii) The dipole moment of a molecule is 10⁻³⁰ C·m. It is placed in an electric field vecE of 10⁵ V/m such that its axis is along the electric field. The direction of vecE is suddenly changed by 60° at an instant. Find the change in the potential energy of the dipole at that instant. OR (b) (i) A thin spherical shell of radius R has a uniform surface charge density σ. Using Gauss's law, deduce an expression for the electric field (i) outside and (ii) inside the shell. (ii) Two long straight thin wires AB and CD have linear charge densities 10μ C/m and -20μ C/m respectively. They are kept parallel to each other at a distance of 1 m. Find the magnitude and direction of the net electric field at a point midway between them.

(a) (i) You are given three circuit elements X, Y and Z. They are connected one by one across a given ac source. It is found that V and I are in phase for element X; V leads I by (π)/(4) for element Y; while I leads V by (π)/(4) for element Z. Identify the elements X, Y and Z. (ii) Establish the expression for the impedance of the circuit when elements X, Y and Z are connected in series to an ac source. Show the variation of current in the circuit with the frequency of the applied ac source. (iii) In a series LCR circuit, obtain the conditions under which (1) the impedance is minimum, and (2) wattless current flows in the circuit. OR (b) (i) Describe the construction and working of a transformer and hence obtain the relation for (Vs)/(Vp) in terms of the number of turns of the primary and secondary. (ii) Discuss four main causes of energy loss in a real transformer.

(a) (i) A plane light wave propagating from a rarer into a denser medium is incident at an angle i on the surface separating the two media. Using Huygens's principle, draw the refracted wave and hence verify Snell's law of refraction. (ii) In a Young's double-slit experiment, the slits are separated by 0.30 mm and the screen is kept 1.5 m away. The wavelength of light used is 600 nm. Calculate the distance between the central bright fringe and the 4th dark fringe. OR (b) (i) Discuss briefly the diffraction of light from a single slit and draw the shape of the diffraction pattern. (ii) An object is placed between the pole and the focus of a concave mirror. Using the mirror formula, prove mathematically that it produces a virtual and enlarged image.