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

Question 26

A square sheet of side ‘a’ is lying parallel to XY plane at z = a. The electric field in the region is $\overrightarrow{\mathrm{E}} ={\mathrm{CZ}}^2\mathrm{k}$. 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

Question 27

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. $\frac{1}{\sqrt{2}}\frac{{\mathrm{Kqq}}_0}{{\mathrm{a}}^2}$

Question 28

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

Question 29

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

Question 30

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. $\frac{\mathrm{mg}l}{\mathrm{B}}$
3. $\frac{\mathrm{mg}}{l\mathit{ }\mathrm{B}}$
4. $\frac{l\mathit{ }\mathrm{B}}{\mathrm{mg}}$

Question 31

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

Question 32

A circuit is connected to an AC source of variable frequency. As the frequency of the source is increased, the current first increases and then decreases. Which of the following combinations of elements is likely to comprise the circuit?

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

Question 33

If n, e, $\tau$ and m have their usual meanings, then the resistance of a wire of length l and cross-sectional area A is given by -

1. $\frac{\mathrm{n} {\mathrm{e}}^2 \mathrm{A}}{3\mathrm{m} \tau l}$
2. $\frac{\mathrm{m} l}{\mathrm{n} {\mathrm{e}}^2\mathrm{\tau A}}$
3. $\frac{\mathrm{m} \mathrm{\tau A}}{\mathrm{n} {\mathrm{e}}^{2}l}$
4. $\frac{\mathrm{n} {\mathrm{e}}^2\mathrm{\tau A}}{2\mathrm{m}\mathit{ }l}$

Question 34

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. $\frac{9}{8}$

Question 35

A coil of area 100 cm² is kept at an angle of 30° with a magnetic field of 10^-1 T. The magnetic field is reduced to zero in 10^-4. The induced emf in the coil is -

1. $5\sqrt{3} \mathrm{V}$
2. $50\sqrt{3} \mathrm{V}$
3. 5.0 V
4. 50.0 V

Question 36

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 $\mathrm{\mu F}$

Question 37

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. $\frac{\mathrm{F}}{2}$

Question 38

Two sources of equal emf are connected in series. This combination is, in turn connected to an external resistance R. The internal resistance of two sources are r₁ and r₂ (r₂ > r₁). If the potential difference across the source of internal resistance r₂ is zero, then R equals to-

1. $\frac{{\mathrm{r}}_1 + {\mathrm{r}}_2}{{\mathrm{r}}_2 - {\mathrm{r}}_1}$
2. ${\mathrm{r}}_2 - {\mathrm{r}}_1$
3. $\frac{{\mathrm{r}}_1 {\mathrm{r}}_2}{{\mathrm{r}}_2- {\mathrm{r}}_1}$
4. $\frac{{\mathrm{r}}_1 + {\mathrm{r}}_2}{{\mathrm{r}}_2 {\mathrm{r}}_1}$

Question 39

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.

Question 40

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

1. 3R $\mathrm{\Omega }$
2. $\left(\frac{3}{2}\right) \mathrm{R} \mathrm{\Omega }$
3. 2R $\mathrm{\Omega }$
4. $\left(\frac{2}{3}\right) \mathrm{R} \mathrm{\Omega }$

Question 41

A bar magnet has magnetic dipole moment $\overrightarrow{\mathbf{M}}$. Its initial position is parallel to the direction of uniform magnetic field $\overrightarrow{\mathbf{B}}$. In this position, the magnitudes of torque and force acting on it respectively are –

1. 0 and MB
2. MB and MB
3. 0 and 0
4. $\left|\overrightarrow{\mathrm{M}} \mathrm{x} \overrightarrow{\mathrm{B}} \right| \mathrm{and} 0$

Question 42

Two charges 14 $\mathrm{\mu }$ C and -4 $\mathrm{\mu }$ C are placed at (-12 cm, 0, 0) and (12 cm, 0, 0) in an external electric field E = $\left(\frac{\mathrm{B}}{{\mathrm{r}}^2}\right)$ where B = 1.2 x 10⁶ N/cm² are r is in metres. The electrostatic potential energy of the configuration is

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

Question 43

A 300 $\mathrm{\Omega }$ resistor and a capacitor of $\mathbf{\left(}\frac{\mathbf{25}}{\mathbf{\pi }}\mathbf{\right)}$ $\mathrm{\mu }$F are connected in series to a 200 V - 50 Hz AC source. The current in the circuit is -

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

Question 44

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

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

Question 45

Assertion (A): A negative charge in an electric field moves along the direction of the electric field.
Reason (R): On a negative charge a force acts in the direction of the electric field

Question 46

Assertion (A): The poles of a bar magnet cannot be separated
Reason (R): Magnetic monopoles do not exist

Question 47

Assertion (A): When radius of a current carrying loop is doubled, its magnetic moment becomes four times.
Reason (R): The magnetic moment of a current carrying loop is directly proportional to the area of the loop

Question 48

Assertion (A): Higher the range, lower is the resistance of an ammeter.
Reason (R): To increase the range of an ammeter additional shunt is added in series to it.

Question 49

Assertion (A): A step-up transformer cannot be used as a step-down transformer.
Reason (R): A transformer works only in one direction.

Question 50

Equipotential at a large distance from a collection of charges whose total sum is not zero are-

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

Question 51

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. $\frac{1}{4\mathrm{\mu } {\in }_0} \frac{2q}{L}\left(1-\frac{1}{\sqrt{5}}\right)$
2. $\frac{1}{4\mathrm{\mu } {\in }_0} \frac{2q}{L}\left(1+\frac{1}{\sqrt{5}}\right)$
3. $\frac{1}{4\mathrm{\mu } {\in }_0} \frac{q}{2L}\left(1-\frac{1}{\sqrt{5}}\right)$
4. zero

Question 52

The points with the same potential are -

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

Question 53

The current through branch bg is:

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

Question 54

The power dissipated in R₁ is:

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

Question 55

The potential difference across R₃ is:

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