Class – XII

Sample Paper - 4

­General Instructions:

Read the following instructions very carefully and strictly follow them:

(i) This question paper comprises four Sections – A, B, C and D.

(ii) There are 37 questions in the question paper. All questions are compulsory.

(iii) Section A – Questions no. 1 to 20 are very short answer type questions, carrying one mark each.

(iv) Section B – Questions no. 21 to 27 are short answer type questions, carrying two marks each.

(v) Section C – Questions no. 28 to 34 are long answer type questions, carrying three marks each.

(vi) Section D – Questions no. 35 to 37 are also long answer type questions, carrying five marks each.

(vii) There is no overall choice in the question paper.

(viii) In addition to this, separate instructions are given with each section and

question, wherever necessary.

(ix) Use of calculators and log tables is not permitted.

(x) You may use the following values of physical constants wherever necessary.

Mass of neutron = 1.675 × 10⁻²⁷ kg

Mass of proton = 1.673 × 10²⁷ kg

Avogadro’s number = 6.023 × 10²³ per gram mole

Boltzmann constant = 1.38 × 10⁻²³ JK^-1

 

Section - A

Question 1:

 If an object is positively charged, theoretically the mass of the object ______
(a) increases slightly by a factor of 9.11×10^-31 kg
(b) decreases slightly by a factor of 9.11×10^-31 kg
(c) remains the same
(d) may increase or decrease

 

Question 2:

Coulomb’s Law is valid for ______
(a) only point charge
(b) for both point charge and distributed charge
(c) only distributed charges
(d) neither distributed nor point charge

 

Question 3:

Which one of the following, when suspended freely, slowly sets itself parallel to the direction of the magnetic field?
(a) ferromagnetic materials
(b) diamagnetic materials
(c) paramagnetic materials
(d) ferrimagnetic materials

 

Question 4:

Dipole moment depends on _______
(a) Charge only
(b) Charge and length of a dipole
(c) Charge, length of a dipole and dielectric constant of the medium
(d) Charge and dielectric constant of the medium

 

Question 5:

What is the half-time of a radioactive sample (in minutes), if its mean life is 200 s?
(a) 0.69 min
(b) 2 min
(c) 2.57 min
(d) 2.31 min

 

Question 6:

Faraday’s laws are result of the conservation of which quantity?
(a) momentum
(b) energy
(c) charge
(d) magnetic field

 

Question 7:

Identify the function of a phasor from the following.

(a) phasor is a vector quantity used to represent a sinusoidal signal

(b) phasor is a scalar quantity used to represent a sinusoidal signal

(c) phasor is a vector quantity used to represent a cosine signal

(d) phasor is a scalar quantity used to represent a cosine signal

 

Question 8:

If a positively charged sphere is taken close to another uncharged sphere then which of the following statements is true?

(a) induction and attraction occur simultaneously

(b) induction occurs before the attraction

(c) attraction occurs before induction

(d) attraction or repulsion may occur

 

Question 9:

Why is there a sudden increase in current in Zener diode?

(a) due to the rupture of ionic bonds

(b) due to rupture of covalent bonds

(c) due to viscosity

(d) due to potential difference

 

Question 10:

Calculate the mutual inductance between two coils if a current 10 A in the primary coil changes the flux by 500 Wb per turn in the secondary coil of 200 turns.

(a) 10 H

(b) 10⁴ H

(c) 1000 H

(d) 100 H

 

Question 11:

What is the relative permeability of an air-core inductor, if its self-inductance increases from 0.5 mH to 50 mH due to the introduction of an iron core into it?

 

Question 12:

A transformer is used to light 100 W 25-volt lamp from 250 Volt ac mains. The current in the main cable is 0.5 A. Calculate the efficiency of the transformer.

 

Question 13:

Find the energy stored in the capacitor between the terminals A and B of the combination shown below. Given – Capacitance of each capacitor C = 1μF

 

Question 14:

Show the variation of u and v in the case of a convex mirror.

 

Question 15:

Is it more difficult to remove a free electron from copper than from sodium? Why?

 

Question 16:

Boron has two stable isotopes, ¹⁰₅Band ¹¹₅B. Their respective masses are 10.01294u and 11.00931u, and the atomic mass of boron is 10.811u. Find the abundances of ¹⁰₅B and ¹¹₅B.

 

Question 17:

Draw the voltage current characteristics of a Zener diode.

 

Question 18:

For an extrinsic semiconductor, indicate on the energy band diagram the donor and acceptor levels.

 

Question 19:

Why the transformer cannot be used to step up d.c. voltage?

 

Question 20:

Obtain the resonant frequency and Q-factor of a series LCR circuit with L=3.0H, C=27μF and R=7.4Ω. It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2. Suggest a suitable way.

 

SECTION - B

Question 21:

Figure shows a series LCR circuit connected to a variable frequency 230V source. L=5.0H, C=80μF, R=40Ω.

(a)Determine the source frequency which drives the circuit in resonance.

(b)Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.

 

Question 22:

When a Glass Rod is Rubbed with a Silk Cloth, Charges Appear on Both. A Similar Phenomenon is Observed with Many Other Pairs of Bodies. Explain How This Observation is Consistent With the Law of Conservation of Charge.

 

Question 23:

If the Net Outward Flux Through the Surface of Box Were Zero, Could You Conclude That There Were No Charges Inside the Box? Why or Why Not?

 

Question 24:

Two parallel wires in free space are 20 cm apart and each carries a current of 20 A in the same direction. What is the force exerted by one wire on the other?

 

Question 25:

Keeping the voltage of the charging source constant. What would be the percentage change in the energy stored in a parallel plate capacitor if the separation between its plates were to be decreased by 10?

 

Question 26:

Two heated wires of the same dimensions are first connected in series and then it’s parallel to a source of supply. What will be the ratio of heat produced in the two cases?

 

Question 27:

A steady current flow in the network shown in the figure. What will be the magnetic field at the centre of the network?

 

Question 28:

A Rowland ring of mean radius 15 cm has 3500 turns of wire wound on a ferromagnetic core of relative permeability 800. What is the magnetic field B in the core for a magnetising current of 1.2 A? 

 

Question 29:

Explain the term ‘drift velocity’ of electrons in a conductor. Hence obtain the expression for the current through a conductor in terms of ‘drift velocity’.

 

Question 30:

(a)A coil of inductance 0.25 H is connected to 18V battery. Calculate the rate of growth of current.

(b)Two coils have mutual inductance of 1.5 H. If current in primary circuit is raised to 5 A in 1ms after closing the circuit, what is the emf induced in the secondary?

 

Question 31:

(a)Why is the transmission of signals using ground waves restricted to frequencies up to 15 kHz?

(b)Give a reason to show that microwaves are better signals for long transmission than radio waves?

 

Question 32:

The four arms of a Wheatstone bridge (Fig.) have the following resistances: AB = 100Ω, BC = 10Ω, CD = 5Ω, and DA = 60Ω.

A galvanometer of 15Ω resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10 V is maintained across AC.

 

Question 33:

What is meant by the statement that the electric field of a point charge has spherical symmetry whereas that of an electric dipole is cylindrically symmetrical?

 

Question 34:

State and prove Gauss Theorem

                                                                                                          

Section - D

Question 35:

(i) When an AC source is connected to an ideal inductor show that the average power supplied by the source over a complete cycle is zero.

(ii) A lamp is connected in series with an inductor and an AC source. What happens to the brightness of the lamp when the key is plugged in and an iron rod is inserted inside the inductor? Explain.

OR

(i) Explain with the help of a diagram the formation of depletion region and barrier potential in a p-n junction.

(ii) Draw the circuit diagram of a half wave rectifier and explain its working.

 

Question 36:

Define the term wave front. State Huygens’s principle. Consider a plane wave front incident on a thin convex lens. Draw a proper diagram to show how the incident wave front traverses through the lens and after refraction focuses on the focal point of the lens, giving the shape of the emergent wave front.

OR

Explain the following, giving reasons:

(i) When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have the same frequency as the incident frequency.

(ii) When light travels from a rarer to a denser medium, the speed decreases. Does this decrease in speed imply a reduction in the energy carried by the wave?

(iii) In the wave picture of light, intensity of light is determined by the square of the amplitude of the wave. What determines the intensity in the photon picture of light?

 

Question 37:

Describe the working principle of a moving coil galvanometer. Why is it necessary to use

(i) a radial magnetic field and

(ii) a cylindrical soft iron core in a galvanometer? Write the expression for current sensitivity of the galvanometer. Can a galvanometer as such be used for measuring the current? Explain.

OR

(a) Define the term ‘self-inductance’ and write its S.I. unit.

(b) Obtain the expression for the mutual inductance of two long co-axial solenoids S₁ and S₂ wound one over the other, each of length L and radii r₁ and r₂ and n₁ and n, number of turns per unit length, when a current I is set up in the outer solenoid S₂.

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