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# Board Paper of Class 12 Physics Term-I 2021 Delhi(SET 4) (Series : SSJ/1)- Solutions

General Instructions:

(i) This question paper contains 55 questions out of which 45 questions are to be attempted. All questions carry equal marks.

(ii) The question paper consists of three Sections - Section A, B and C.

(iii) Section - A contains 25 questions. Attempt any 20 questions from Q. No. 01 to 25.

(iv) Section - B contains 24 questions. Attempt any 20 questions from Q. No. 26 to 49.

(v) Section - C contains 6 questions. Attempt any 5 questions from Q. No. 50 to 55.

(vi) The first 20 Questions attempted in Section - A & Section - B and first 5 questions attempted in

Section - C by a candidate will be evaluated.

(vii) There is only one correct option for every multiple choice question (MCQ).

Marks will not be awarded for answering more than one option.

(viii) There is no negative marking.

• Question 1
An electric dipole placed in a non-uniform electric field will experience:
(a) only a force
(b) only a torque
(c) both force and torque
(d) neither force nor torque VIEW SOLUTION

• Question 2
Let N1 be the number of electric field lines going out of an imaginary cube of side a that encloses an isolated point charge 2q and N2 be the corresponding number for an imaginary sphere of radius a that encloses an isolated point charge 3q. Then (N1/N2) is :
(a) $\frac{1}{\pi }$

(b) $\frac{2}{3}$

(c) $\frac{9}{4}$

(d) π
VIEW SOLUTION

• Question 3
In the circuit given below P ≠ R and the reading of the galvanometer is same with switch S open or closed. Then :

(a) IQ = IR
(b) IR = IG
(c) IP = IG
(d) IQ = IG
VIEW SOLUTION

• Question 4
Two wires A and B, of the same material having length in the ratio 1 : 2 and diameter in the ratio 2 : 3 are connected in series with a battery. The ratio of the potential differences (VA/VB) across the two wires respectively is :
(a) $\frac{1}{3}$

(b) $\frac{3}{4}$

(c) $\frac{4}{5}$

(d) $\frac{9}{8}$ VIEW SOLUTION

• Question 5
Two moving coil galvanometers G1 and G2 have the following particulars respectively :
N1 = 30, A1 = 3.6 × 10–3 m2, B1 = 0.25 T
N2 = 42, A2 = 1.8 × 10–3 m2, B2 = 0.50 T
The spring constant is same for both the galvanometers. The ratio of current sensitivities of G1 and G2 is :
(a) 5 : 7
(b) 7 : 5
(c) 1 : 4
(d) 1 : 1 VIEW SOLUTION

• Question 6
A current I is flowing through the loop as shown in the figure (MA = R, MB = 2R). The magnetic field at the centre of the loop is $\frac{{\mu }_{0}I}{R}$ times :

(a) $\frac{5}{16}$, into the plane of the paper

(b) $\frac{5}{16}$, out of the plane of the paper

(c) $\frac{7}{16}$, out of the plane of the paper

(d) $\frac{7}{16}$, into the plane of the paper VIEW SOLUTION

• Question 7
A capacitor and an inductor are connected in two different ac circuits with a bulb glowing in each circuit. The bulb glows more brightly when :
(a) the number of turns in the inductor is increased
(b) the separation between the plates of the capacitor is increased
(c) an iron rod is introduced into the inductor
(d) a dielectric is introduced into the gap between the plates of the capacitor VIEW SOLUTION

• Question 8
A pure inductor of 318 mH and a pure resistor of 75 Ω are connected in series to an ac source of 50 Hz. The voltage across 75 Ω resistor is found to be 150 V. The source voltage is :
(a) 150 V
(b) 175 V
(c) 220 V
(d) 250 V VIEW SOLUTION

• Question 9
The electric potential at a point on the axis of a short electric dipole, at a distance x from the mid-point of dipole is proportional to :
(a) $\frac{1}{{x}^{4}}$

(b) $\frac{1}{{x}^{\frac{3}{2}}}$

(c) $\frac{1}{{x}^{3}}$

(d) $\frac{1}{{x}^{2}}$ VIEW SOLUTION

• Question 10
Let F1 be the magnitude of the force between two small spheres, charged to a constant potential in free space and F2 be the magnitude of the force between them in a medium of dielectric constant k. Then $\left(\frac{{\mathrm{F}}_{1}}{{\mathrm{F}}_{2}}\right)$ is :
(a) $\frac{1}{k}$

(b) k

(c) k2

(d) $\frac{1}{{k}^{2}}$ VIEW SOLUTION

• Question 11
Infinity resistance in a resistance box has :
(a) a resistance of 105 Ω
(b) a resistance of 10Ω
(c) a resistance of ∞ resistance
(d) a gap only VIEW SOLUTION

• Question 12
A battery of 15 V and negligible internal resistance is connected across a 50 Ω resistor. The amount of energy dissipated as heat in the resistor in one minute is :
(a) 122 J
(b) 270 J
(c) 420 J
(d) 720 J VIEW SOLUTION

• Question 13
Lenz's law is the consequence of the law of conservation of :
(a) energy
(b) charge
(c) mass
(d) momentum VIEW SOLUTION

• Question 14
The vertical component of earth's magnetic field at a place is $\left(\frac{1}{\sqrt{3}}\right)$ times the horizontal component. The angle of dip at that place is :
(a) 0º
(b) 30º
(c) 45º
(d) 60º VIEW SOLUTION

• Question 15
A long straight wire in the horizontal plane carries a current of 15 A in north to south direction. The magnitude and direction of magnetic field at a point 2.5 m east of the wire respectively are:
(a) 1·2 μT, vertically upward
(b) 1·2 μT, vertically downward
(c) 0·6 μT, vertically upward
(d) 0·6 μT, vertically downward VIEW SOLUTION

• Question 16
The emf induced in a 10 H inductor in which current changes from 11 A to 2 A in 9 × 10–1 s is:
(a) 104 V
(b) 103 V
(c) 102 V
(d) 10 V VIEW SOLUTION

• Question 17
A charge Q is placed at the centre of the line joining two charges q and q. The system of the three charges will be in equilibrium if Q is:

(a) $+\frac{q}{3}$

(b) $-\frac{q}{3}$

(c) $+\frac{q}{4}$

(d) $-\frac{q}{4}$ VIEW SOLUTION

• Question 18
Electric flux of an electric field $\stackrel{\to }{\mathrm{E}}$ through an area $d\stackrel{\to }{A}$ is given by:

(a) $\stackrel{\to }{\mathrm{E}}×d\stackrel{\to }{\mathrm{A}}$

(b) $\frac{\stackrel{\to }{\mathrm{E}}×d\stackrel{\to }{\mathrm{A}}}{{\mathrm{\epsilon }}_{0}}$

(c)

(d)  VIEW SOLUTION

• Question 19
In a potentiometer experiment, the balancing length with a cell is 120 cm. When the cell is shunted by a 1 Ω resistance, the balancing length becomes 40 cm. The internal resistance of the cell is:
(a) 10 Ω
(b) 7 Ω
(c) 3 Ω
(d) 2 Ω VIEW SOLUTION

• Question 20
An electron is projected with velocity $\stackrel{\to }{v}$ along the axis of a current carrying long solenoid. Which one of the following statements is true?
(a) The path of the electron will be circular about the axis.
(b) The electron will be accelerated along the axis.
(c) The path of the electron will be helical.
(d) The electron will continue to move with the same velocity $\stackrel{\to }{v}$ along the axis of the solenoid. VIEW SOLUTION

• Question 21
If the speed v of a charged particle moving in a magnetic field $\stackrel{\to }{\mathrm{B}}$ ($\stackrel{\to }{v}$ is perpendicular to $\stackrel{\to }{\mathrm{B}}$) is halved, then the radius of its path will
(a) not change
(b) become two times
(c) become one-fourth
(d) become half VIEW SOLUTION

• Question 22
A metal plate is getting heated. Which one of following statements is incorrect?
(a) It is placed in a space varying magnetic field that does not vary with time.
(b) A direct current is passing through the plate.
(c) An alternating current is passing through the plate.
(d) It is placed in a time varying magnetic field. VIEW SOLUTION

• Question 23
In an ac circuit the applied voltage and resultant current are $E={E}_{0}\mathrm{sin}\omega t$ and I = Isin$\left(\omega t+\frac{\mathrm{\pi }}{2}\right)$ respectively. The average power consumed in the circuit is:
(a) E0I0

(b) $\frac{{\mathrm{E}}_{0}{\mathrm{I}}_{0}}{2}$

(c) $\frac{{\mathrm{E}}_{0}{\mathrm{I}}_{0}}{\sqrt{2}}$

(d) Zero VIEW SOLUTION

• Question 24
The speed acquired by a free electron when accelerated from rest through a potential difference of 100 V is:
(a) 6 × 106 ms–1
(b) 3 × 106 ms–1
(c) 4 × 10ms–1
(d) 2 × 10ms–1 VIEW SOLUTION

• Question 25
Which one of the following is not affected by the presence of a magnetic field?
(a) A current carrying conductor
(b) A moving charge
(c) A stationary charge
(d) A rectangular current loop with its plane parallel to the field VIEW SOLUTION

• Question 26
Two point charges + 16q and – 4q are located at x = 0 and = L. The location of the point on x-axis at which the resultant electric field due to these charges is zero, is:
(a) 8L
(b) 6L
(c) 4L
(d) 2L  VIEW SOLUTION

• Question 27
An electric dipole of dipole moment 4 × 10–5 C-m, kept in a uniform electric field of 10–3 NC–1, experiences a torque of 2 × 10–8 Nm. The angle which the dipole makes with the electric field is:
(a) 30º
(b) 45º
(c) 60º
(d) 90º VIEW SOLUTION

• 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 neighbour charge is F. Let $\stackrel{^}{i}$ be the unit vector along + x-axis, then the net force on each charge from left to right is:
(a)

(b)

(c)

(d)  VIEW SOLUTION

• 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 seconds. If the current measured in the circuit is 5 A, then the correct calculation is done by:
(a) A
(b) B
(c) both A and B
(d) neither A nor B VIEW SOLUTION

• Question 30
The resistances of two wires having same length and same area of cross-section are  and  respectively. If the resistivity of  wire is 2.65 × 10–8 $\mathrm{\Omega }-\mathrm{m}$ then the resistivity of :
(a) 10.60 × 10–8 $\mathrm{\Omega }-\mathrm{m}$
(b) 8.32 × 10–8 $\mathrm{\Omega }-\mathrm{m}$
(c) 7.61 × 10–8 $\mathrm{\Omega }-\mathrm{m}$
(d) 5.45 × 10–8 $\mathrm{\Omega }-\mathrm{m}$
VIEW SOLUTION

• Question 31
In a certain region electric field $\stackrel{\to }{\mathrm{E}}$ and magnetic field $\stackrel{\to }{\mathrm{B}}$ are perpendicular to each other. An electron enters  region perpendicular to the direction of both $\stackrel{\to }{\mathrm{E}}$ and $\stackrel{\to }{\mathrm{B}}$ and moves undeflected. The speed of the electron is:
(a)
(b) $\left|\stackrel{\to }{\mathrm{E}}×\stackrel{\to }{\mathrm{B}}\right|$
(c) $\frac{\left|\stackrel{\to }{\mathrm{E}}\right|}{\left|\stackrel{\to }{\mathrm{B}}\right|}$
(d) $\frac{\left|\stackrel{\to }{\mathrm{B}}\right|}{\left|\stackrel{\to }{\mathrm{E}}\right|}$ VIEW SOLUTION

• Question 32
A test charge of 1.6 × 10–19 C is moving with a velocity $\stackrel{\mathit{\to }}{v}=\left(4\stackrel{^}{i}+3\stackrel{^}{k}\right){\mathrm{ms}}^{-1}$ in a magnetic field $\stackrel{\mathit{\to }}{B}=\left(3\stackrel{^}{k}+4\stackrel{^}{i}\right)T.$ The force on this test charge is:
(a)
(b)
(c)
(d) 0 VIEW SOLUTION

• Question 33
In a series LCR circuit, at resonance the current is equal to:
(a) $\frac{\mathrm{V}}{\mathrm{R}}$
(b) $\frac{\mathrm{V}}{{\mathrm{X}}_{\mathrm{C}}}$
(c)
(d)  VIEW SOLUTION

• Question 34
The frequency of an ac source for which a  capacitor has a reactance of 1000 $\mathrm{\Omega }$ is:
(a)
(b) 50 Hz
(c)
(d)
VIEW SOLUTION

• 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?

(a) 6 C
(b)
(c)
(d)  VIEW SOLUTION

• 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 :

(a) less if the length of the wire is increased
(b) more if the length of the wire is increased
(c) more if a wire of steel of same dimension is used
(d) more if the temperature of wire is increased VIEW SOLUTION

• Question 37
When a potential difference V is applied across a conductor at temperature T, the drift velocity of the electrons is proportional to :

(a) T

(b) $\sqrt{\mathrm{T}}$

(c) V

(d) $\sqrt{\mathrm{V}}$ VIEW SOLUTION

• 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:

(a) P and R only
(b) Q and R only
(c) P and Q only
(d) P, Q and R VIEW SOLUTION

• 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 :

(a) 3 B0

(b) $\frac{{\mathrm{B}}_{0}}{3}$

(c) $\frac{{\mathrm{B}}_{0}}{9}$

(d) 9 B0 VIEW SOLUTION

• Question 40
Which one of the following statements is true?
(a) An inductor has infinite resistance in a dc circuit.
(b) A inductor and a capacitor both cannot conduct in a dc circuit.
(c) A capacitor can conduct in a dc circuit but not an inductor.
(d) An inductor can conduct in a dc circuit but not a capacitor VIEW SOLUTION

• Question 41
The magnetic flux linked with a coil is given by ϕ = 5t2 + 3t + 16, where ϕ is in webers and t in seconds. The induced emf in the coil at t = 5 s will be :
(a) 53 V
(b) 43 V
(c) 10 V
(d) 6 V VIEW SOLUTION

• Question 42
If a charge is moved against a coulomb  force of an electric field, then the :
(a) intensity of the electric field increases
(b) intensity of the electric field, decreases
(c) work is done by the electric field
(d) work is done by the external source VIEW SOLUTION

• 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 $\left[k=\frac{1}{\left(4{\mathrm{\pi \epsilon }}_{0}\right)}\right]$:
(a) $k\frac{{q}_{0}Q}{r}$

(b) $k\frac{Q{q}_{0}}{{r}^{2}}$

(c) k q0 Q r

(d) Zero
VIEW SOLUTION

• 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 :

(a) $\frac{\mathrm{B}}{2}$

(b) B

(c) 2B

(d) 4B
VIEW SOLUTION

• Question 45
The question consists of two statements – Assertion (A) and Reason (R).
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.
Select the appropriate option given below:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true. VIEW SOLUTION

• Question 46
The question consists of two statements – Assertion (A) and Reason (R).
Assertion (A): In a series LCR circuit connected to an ac source, resonance can take place.
Reason (R): At resonance XL = XC.
Select the appropriate option given below:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true. VIEW SOLUTION

• Question 47
The question consists of two statements – Assertion (A) and Reason (R).
Assertion (A): When a charged particle moves with velocity $\stackrel{\to }{v}$ in a magnetic field $\stackrel{\to }{B}$ ($\stackrel{\to }{v}\perp \stackrel{\to }{B}$), the force on the particle does no work.
Reason (R): The magnetic force is perpendicular to the velocity of the particle.
Select the appropriate option given below:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
VIEW SOLUTION

• Question 48
The question consists of two statements – Assertion (A) and Reason (R).
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 the copper coil is more than the aluminium coil.
Reason (R): Resistance of aluminium coil is more than that of copper coil.
Select the appropriate option given below:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
VIEW SOLUTION

• Question 49
The question consists of two statements – Assertion (A) and Reason (R).
Assertion (A): A transformer is used to increase or decrease ac voltage only.
Reason (R): A transformer works on the basis of mutual induction.
Select the appropriate option given below:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.

VIEW SOLUTION

• 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 $\left(\frac{{\sigma }_{A}}{{\sigma }_{B}}\right)$ will be:
(a) $\frac{1}{2}$

(b) 2

(c) $\frac{1}{4}$

(d) 4 VIEW SOLUTION

• 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 $\stackrel{\to }{F}$, the net force on the remaining three arm of the loop will be:
(a)

(b)

(c) $\stackrel{\to }{F}$

(d) $–\stackrel{\to }{F}$ VIEW SOLUTION

• Question 52
Case-Study
A battery is a combination of two or more cells. In the following figure a single battery is represented in which two cells of emf ε1 and ε2 and internal resistance r1 and r2 respectively are connected.

The equivalent emf of this combination is:
(a) $\frac{{\epsilon }_{1}{r}_{1}+{\epsilon }_{2}{r}_{2}}{{r}_{1}+{r}_{2}}$

(b) $\frac{{\epsilon }_{1}{r}_{1}-{\epsilon }_{2}{r}_{2}}{{r}_{1}+{r}_{2}}$

(c) $\frac{{\epsilon }_{1}{r}_{2}-{\epsilon }_{2}{r}_{1}}{{r}_{1}+{r}_{2}}$

(d) ε1 – ε2 VIEW SOLUTION

• Question 53
Case-Study
A battery is a combination of two or more cells. In the following figure a single battery is represented in which two cells of emf ε1 and ε2 and internal resistance r1 and rrespectively are connected.

For terminal B to be negative:
(a) ε1r2 > ε2r1
(b)
ε1r2 < ε2r1
(c) ε1r1 > ε2r2
(d)
ε2r2 = ε1r1
VIEW SOLUTION

• Question 54
Case-Study
A battery is a combination of two or more cells. In the following figure a single battery is represented in which two cells of emf ε1 and ε2 and internal resistance r1 and rrespectively are connected.

The current in the internal circuit is:
(a) $\frac{{\epsilon }_{1}+{\epsilon }_{2}}{{r}_{1}+{r}_{2}}$

(b)
$\frac{{\epsilon }_{2}-{\epsilon }_{1}}{{r}_{1}+{r}_{2}}$

(c) $\frac{{\epsilon }_{1}}{{r}_{1}}-\frac{{\epsilon }_{2}}{{r}_{2}}$

(d) $\frac{{\epsilon }_{1}}{{r}_{2}}-\frac{{\epsilon }_{2}}{{r}_{1}}$ VIEW SOLUTION

• Question 55
Case-Study
A battery is a combination of two or more cells. In the following figure a single battery is represented in which two cells of emf ε1 and ε2 and internal resistance r1 and rrespectively are connected.

The equivalent internal resistance of the combination is:
(a) $\frac{{r}_{1}+{r}_{2}}{{r}_{1}{r}_{2}}$

(b) ${r}_{1}+{r}_{2}$

(c) $\frac{{r}_{1}{r}_{2}}{{r}_{1}+{r}_{2}}$

(d) r1 – r2 VIEW SOLUTION
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