Board Paper of Class 12 2021 Physics Delhi (Set 055/1/4) - Solutions

Question 26

Two point charges + 16q and – 4q are located at x = 0 and x = L. The location of the point on X-axis at which the resultant electric field due to these charges is zero, is :

1. 8 L
2. 6 L
3. 4 L
4. 2 L

Question 27

An electric dipole of dipole moment $4 \times {10}^{-5}$ C-m, kept in a uniform electric field of ${10}^{-3}$, experiences a torque of 2 $\times$ ${10}^{-8}$ Nm. The angle which the dipole makes with the electric field is :

1. 30°
2. 45°
3. 60°
4. 90°

Question 28

Three identical charges are placed on x-axis from left to right with adjacent charges separated by a distance d. The magnitude of the force on a charge from its nearest neighbor charge is F. Let $\hat{\mathrm{i}}$ be the unit vector along + X-axis, then the net force on each charge from left to right is :

Question 29

Two students A and B calculate the charge flowing through a circuit. A concludes that 300 C of charge flows in 1 minute. B concludes that 3.125 × 10¹⁹ electrons flow in 1 second. If the current measured in the circuit is 5 A, then the correct calculation is done by :

1. A
2. B
3. both A and B
4. neither A nor B

Question 30

The resistances of two wires having same length and same area of cross-section are 2 Ω and 8 Ω respectively. If the resistivity of 2 Ω wire is 2.65 Ω 10^-8 Ω-m then the resistivity of 8 Ω wire is :

1. $10.60 \times {10}^{-8} \mathrm{\Omega }-\mathrm{m}$
2. $8.32 \times {10}^{-8} \mathrm{\Omega }-\mathrm{m}$
3. $7.61 \times {10}^{-8} \mathrm{\Omega }-\mathrm{m}$
4. $5.45 \times {10}^{-8} \mathrm{\Omega }-\mathrm{m}$

Question 31

In a certain region electric field $\overrightarrow{\mathrm{E}}$ and magnetic field $\overrightarrow{\mathrm{B}}$ are perpendicular to each other. An electron entersthe region perpendicular to the direction of both $\overrightarrow{\mathrm{E}}$ and $\overrightarrow{\mathrm{B}}$ and moves undeflected. The speed of the electron is :

Question 32

Question 33

In a series LCR circuit, at resonance the current is equal to :

Question 34

The frequency of an AC source for which a 10 $\mathrm{\mu }$F capacitor has a reactance of 1000 Ω is :

1. 
2. 50 Hz
3. 
4. 

Question 35

In the given network all capacitors used are identical and each one is of capacitance C. Which of the following is the equivalent capacitance between the points A and B ?

1. 6 C
2. 
3. 
4. 

Question 36

The given figure shows I – V graph of a copper wire whose length and area of cross-section are L and A respectively. The slope of this curve becomes :

1. less if the length of the wire is increased
2. more if the length of the wire is increased
3. more if a wire of steel of same dimension is used
4. more if the temperature of wire is increased

Question 37

When a potential difference V is applied across a conductor at temperature T, the drift velocity of the electrons is proportional to :

1. T
2. 
3. V
4. 

Question 38

Two identical thick wires and two identical thin wires, all of the same material and the same length form a square in three different ways P, Q and R as shown. Due to the current in these loops the magnetic field at the centre of the loop will be zero in case of :

1. P and R only
2. Q and R only
3. P and Q only
4. P, Q and R

Question 39

A circular current carrying coil produces a magnetic field B₀ at its centre. The coil is rewound so as to have three turns and the same current is passed through it. The new magnetic field at the centre is :

Question 40

Which one of the following statements is true ?

1. An inductor has infinite resistance in a dc circuit.
2. A inductor and a capacitor both cannot conduct in a dc circuit.
3. A capacitor can conduct in a dc circuit but not an inductor.
4. An inductor can conduct in a dc circuit but not a capacitor.

Question 41

The magnetic flux linked with a coil is given by $\mathrm{\varphi }$ = 5t² + 3t + 16, where $\mathrm{\varphi }$ is in weber and t in seconds. The induced emf in the coil at t = 5 s will be :

1. 53 V
2. 43 V
3. 10 V
4. 6 V

Question 42

If a charge is moved against a coulomb force of an electric field, then the :

1. intensity of the electric field increases
2. intensity of the electric field decreases
3. work is done by the electric field
4. work is done by the external source

Question 43

A charge Q is located at the centre of a circle of radius r. The work done in moving a test charge q0 from point A to point B (at opposite ends of diameter AB) so as to complete a semicircle is :

Question 44

A long solenoid carrying current produces a magnetic field B along its axis. If the number of turns in the solenoid is halved and current in it is doubled, the new magnetic field will be :

1. B/2
2. B
3. 2B
4. 4B

Question 45

Assertion (A) : A bar magnet experiences a torque when placed in a magnetic field.
Reason (R): A bar magnet exerts a torque on itself due to its own magnetic field.

Question 46

Assertion (A): In a series LCR circuit connected to an ac source, resonance can take place.
Reason (R): At resonance X_L = X_C.

Question 47

Assertion (A): When a charged particle moves with velocity $\overrightarrow{\mathrm{v}}$ in a magnetic field $\overrightarrow{\mathbf{B}}\mathbf{ }\mathbf{(}\mathbf{ }\overrightarrow{\mathbf{v}}\mathbf{ }\mathbf{\perp }\mathbf{ }\overrightarrow{\mathbf{B}}\mathbf{ }\mathbf{)}$, the force on the particle does no work.

Reason (R): The magnetic force is perpendicular to the velocity of the particle.

Question 48

Assertion (A): Induced emf in two coils made of wire of the same length and the same thickness, one of copper and another of aluminium is same. The current in copper coil is more than the aluminium coil.
Reason (R): Resistance of aluminium coil is more than that of copper coil.

Question 49

Assertion (A): A transformer is used to increase or decrease ac voltage only.
Reason (R) : A transformer works on the basis of mutual induction.

Question 50

Two charged spheres A and B having their radii in the ratio 1 : 2 are connected together with a conducting wire. The ratio of their surface charge densities will be :

1. 1/2
2. 2
3. 1/4
4. 4

Question 51

A current carrying square loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is , the net force on the remaining three arms of the loop will be :

Question 52

The equivalent emf of this combination is :

Question 53

For terminal B to be negative :

1. ε₁ r₂ > ε₂ -r₁
2. ε₁ r₂ < ε₂ r₁
3. ε₁ r₁ > ε₂ r₂
4. ε₂ r₂ = ε₁ r₁

Question 54

The current in the internal circuit is :

Question 55

The equivalent internal resistance of the combination is :