# Board Paper of Class 12 2021 Physics-G12 Delhi Set 55/2/4 - Solutions

#### General Instructions:

1. This question paper contains 55 questions out of which 45 questions are to be attempted. All questions carry equal marks.
2. This question paper consists of three sections , Section A, Section B and Section C.
3. Section A contains 25 questions. Attempt any 20 questions from Q. No. 1 to 25.
4. Section B contains 24 questions. Attempt any 20 questions from Q. No. 26 to 49.
5. Section C contains 6 questions. Attempt any 5 questions from . No. 50 to 55.
6. The first 20 questions in Section A and Sections B and first 5 questions attempted in Section C by a candidate will be evaluated.
7. There is only one correct option for every multiple choice question (MCQ). Marks will not be awarded for answering more than one option.
8. There is no negative marking.

#### Section – A

This Section consists of 25 multiple choice questions with overall choice to attempt any 20 questions. In case more than desirable number of questions are attempted, only first 20 questions will be considered for evaluation.

## A negative charged object X is repelled by another charged object Y. However an object Z is attracted to object Y. Which of the following is the most possibility for the object Z?

1. positively charged only
2. negatively charged only
3. neutral or positively charged
4. neutral or negatively charged

Ans. (c)

## In an experiment three microscopic latex spheres are sprayed into a chamber and became charged with charges +3e, +5e and -3e respectively. All the three spheres came in contact simultaneously for a moment and got separated. Which one of the following are possible values for the final charge on spheres?

1. +5e, -4e, +5e
2. +6e, +6e, -7e
3. -4e, +3.5e, +5.5e
4. +5e, -8e, +7e

Ans. (b)

1. -0.80 C
2. +0.80 C
3. +1.80 C
4. +0.20 C

Ans. (d)

## Kirchhoff’s first rule $\mathrm{\Sigma I}=0$ and second rule $\mathrm{\Sigma IR}=$ E (where the symbols have their usual meanings) are respectively based on–

1. conservation of momentum and conservation of charge
2. conservation of energy, conservation of charge
3. conservation of charge, conservation of momentum
4. conservation of charge, conservation of energy

Ans. (a)

1. 25 W
2. 30 W
3. 35 W
4. 45 W

Ans. (a)

## Which one of the following has negative temperature coefficient of resistivity?

1. metal
2. metal and semiconductor
3. semiconductor
4. metal and alloy

Ans. (c)

1. I
2. II
3. III
4. IV

Ans. (b)

Ans. (d)

## If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter a -

1. low resistance in parallel
2. low resistance in series
3. high resistance in parallel
4. high resistance in series

Ans. (d)

## The magnetic field at the centre of a current carrying circular loop of radius R, is ${\mathrm{B}}_{1}$. The magnetic field at a point on its axis at distance R from the center of the loop ${\mathrm{B}}_{2}$. Then the ratio (${\mathrm{B}}_{1}$/${\mathrm{B}}_{2}$) is

1. $2\sqrt{2}$
2. $\frac{1}{\sqrt{2}}$
3. $\sqrt{2}$
4. 2

Ans. (a)

1. 95 mH
2. 90 mH
3. 85 mH
4. 75 mH

Ans. (d)

## The rms current in a circuit connected to a 50 Hz AC source is 15 A. The value of the current in the circuit $\left(\frac{1}{600}\right)$ s after the instant the current is zero, is -

1. $\frac{\mathbf{15}}{\sqrt{\mathbf{2}}}\mathrm{A}$
2. 8 A

Ans. (a)

1. only C
2. only L
3. L and R
4. L or C

Ans. (c)

## The electric potential V at any point (x, y, z) is given by V = $3{\mathrm{x}}^{2}$ where x is in meters and V in volts. The electric field at the point (1 m, 0, 2m) is –

1. 6 V/m along -x-axis
2. 6 V/m along +x-axis
3. 1.5 V/m along -x-axis
4. 1.5 V/m along +x-axis

Ans. (a)

Ans. (d)

## A variable capacitor is connected to a 200 V battery. If its capacitance is changed from 2 $\text{μF}$ to x$\text{μF}$, the decrease in energy of the capacitor is 2 × ${10}^{-2}$ J. The value of x is -

1. 1 $\text{μF}$
2. 2 $\text{μF}$
3. 3 $\text{μF}$
4. 4 $\text{μF}$

Ans. (a)

Ans. (a)

## The impedance of a series LCR circuit is -

1. $\sqrt{\frac{1}{{\mathrm{X}}_{\mathrm{C}}^{2}}+\frac{1}{{\mathrm{X}}_{\mathrm{L}}^{2}}+{\mathrm{R}}^{2}}$
2. $\sqrt{{\mathrm{R}}^{2}+{\left({\mathrm{X}}_{\mathrm{L}}-{\mathrm{X}}_{\mathrm{C}}\right)}^{2}}$

Ans. (d)

1. Erms . Irms
2. E0 I0
3. Zero

Ans. (d)

## A current carrying wire kept in a uniform magnetic field, will experience a maximum force when it is

1. perpendicular to the magnetic field
2. parallel to the magnetic field
3. at an angle of 45° to the magnetic field
4. at an angle of 60° to the magnetic field

Ans. (a)

1. 5 V
2. 20 V
3. 25 V
4. 65 V

Ans. (c)

## In a DC circuit the direction of current inside the battery and outside the battery respectively are –

1. positive to negative terminal and negative to positive terminal
2. positive to negative terminal and positive to negative terminal
3. negative to positive terminal and positive to negative terminal
4. negative to positive terminal and negative to positive terminal

Ans. (c)

## The magnitude of electric field due to a point charge 2q, at distance r is E. Then the magnitude of electric field due to a uniformly charged thin spherical shell of radius R with total charge q at a distance

1. $\frac{\mathrm{E}}{4}$
2. 0
3. 2E
4. 4E

Ans. (c)

1. 30°
2. 45°
3. 60°
4. 90°

Ans. (c)

1. 50 V
2. 75 V
3. 100 V
4. 220 V

Ans. (a)

## A square sheet of side ‘a’ is lying parallel to XY plane at z = a. The electric field in the region is . The electric flux through the sheet is

1. a4c
2. $\frac{1}{3}{\mathrm{a}}^{3}\mathrm{c}$
3. $\frac{1}{3}{\mathrm{a}}^{4}\mathrm{c}$
4. 0

Ans. (a)

## Three charges q, –q and q0 are placed as shown in figure. The magnitude of the net force on the charge q0 at point O is $\left[K=\frac{1}{\left(4\pi \right){\in }_{0}}\right]$

1. 0
2. $\frac{2{\mathrm{Kqq}}_{0}}{{\mathrm{a}}^{2}}$
3. $\frac{\sqrt{2}{\mathrm{Kqq}}_{0}}{{\mathrm{a}}^{2}}$
4. $\frac{1}{\sqrt{2}}\frac{{\mathrm{Kqq}}_{0}}{{\mathrm{a}}^{2}}$

Ans. (c)

## A + 3.0 nC charge Q is initially at rest at a distance of r1 = 10 cm from a + 5.0 nC charge q fixed at the origin. The charge Q is moved away from q to a new position at r2 = 15 cm. In this process work done by the field is

1. 1.29 x 10-5 J
2. 3.6 x 105 J
3. -4.5 x 10-7 J
4. 4.5 x 10-7 J

Ans. (d)

## A car battery is charged by a 12 V supply, and energy stored in it is 7.20 x 105 J. The charge passed through the battery is –

1. 6.0 x 104 C
2. 5.8 x 103 J
3. 8.64 x 106 J
4. 1.6 x 106 C

Ans. (a)

## A straight conducting rod of length l and mass m is suspended in a horizontal plane by a pair of flexible strings in a magnetic field of magnitude B. To remove the tension in the supporting strings, the magnitude of the current in the wire is

1. $\frac{\mathrm{mgB}}{l}$
2. $\frac{\mathrm{mg}l}{\mathrm{B}}$

Ans. (c)

## A constant current is flowing through a solenoid. An iron rod is inserted in the solenoid along its axis. Which of the following quantities will not increase?

1. The magnetic field at the centre
2. The magnetic flux linked with the solenoid
3. The rate of heating
4. The self-inductance of the solenoid

Ans. (c)

1. L, C and R
2. L and C
3. L and R
4. R and C

Ans. (a)

Ans. (b)

## A proton and an alpha particle move in circular orbits in a uniform magnetic field. Their speeds are in the ratio of 9:4. The ratio of radii of their circular orbits $\left(\frac{{r}_{p}}{{r}_{\mathrm{alpha}}}\right)$ is

1. $\frac{3}{4}$
2. $\frac{4}{3}$
3. $\frac{8}{9}$
4. $\frac{9}{8}$

Ans. (d)

1. 5.0 V
2. 50.0 V

Ans.(c)

## A 15 $\mathbf{\Omega }$ resistor, an 80 mH inductor and a capacitor of capacitance C are connected in series with a 50 Hz AC source. If the source voltage and current in the circuit are in phase, then the value of capacitance is

1. 100 $\mathrm{\mu F}$
2. 127 $\mathrm{\mu F}$
3. 142 $\mathrm{\mu F}$
4. 160 $\mathrm{\mu F}$

Ans. (b)

## Four objects W, X, Y and Z, each with charge +q are held fixed at four points of a square of side d as shown in the figure. Objects X and Z are on the midpoints of the sides of the square. The electrostatic force exerted by object W on object X is F. Then the magnitude of the force exerted by object W on Z is

1. $\frac{\mathrm{F}}{7}$
2. $\frac{\mathrm{F}}{5}$
3. $\frac{\mathrm{F}}{3}$
4. $\frac{\mathrm{F}}{2}$

Ans. (b)

Ans. (b)

## Which of the following statements is correct?

1. Magnetic field lines do not form closed loops.
2. Magnetic field lines start from north pole and end at south pole of a magnet.
3. The tangent at a point on a magnetic field line represents the direction of the magnetic field at that point.
4. Two magnetic field lines may intersect each other.

Ans. (c)

## The equivalent resistance between A and B of the network shown in figure is

1. 3R $\mathrm{\Omega }$
2. 2R $\mathrm{\Omega }$

Ans. (c)

1. 0 and MB
2. MB and MB
3. 0 and 0

Ans. (c)

1. 97.9 J
2. 102.1 J
3. 2.1 J
4. -97.9 J

Ans. (a)

1. 0.1 A
2. 0.4 A
3. 0.6 A
4. 0.8 A

Ans. (b)

## The core of a transformer is laminated to reduce the effect of:

1. flux leakage
2. copper loss
3. hysteresis loss
4. eddy current

Ans. (d)

Question No. 45 to 49 are Assertion (A) and Reason (R) type questions. Given below are the two statements labelled as Assertion (A) and Reason (R). Select the most appropriate answer from the options given below as:
1. Both a. and (R) are true and (R) is correct explanation of a.
2. Both a. and (R) are true and (R) is not correct explanation of a.
3. (A) is true, but (R) is false.
4. (A) is false and (R) is also false.

Ans. (d)

Ans. (a)

Ans. (a)

Ans. (c)

Ans. (d)

1. spheres
2. planes
3. ellipsoids
4. paraboloids

Ans. (a)

## Four charges -q, -q, +q and +q are placed at the corners of a square of side 2L is shown in figure. The electric potential at point A midway between the two charges +q and +q is-

1. zero

Ans. (a)

### Case Study

An experiment was set up with the circuit diagram shown in figure. Given that R1 = 10 $\mathrm{\Omega }$, R2 = R3 = 5 $\mathrm{\Omega }$, r = 0 $\mathrm{\Omega }$ and E = 5 V

1. b, c, d
2. f, h, j
3. d, e, f
4. a, b, j

Ans. (b)

## The current through branch bg is:

1. 1 A
2. $\frac{1}{3}\mathrm{A}$
3. $\frac{1}{2}\mathrm{A}$
4. $\frac{2}{3}\mathrm{A}$

Ans. (c)

1. 2 W
2. 2.5 W
3. 3 W
4. 4.5 W

Ans. (b)

1. 1.5 V
2. 2 V
3. 2.5 V
4. 3 V

Ans. (c)