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# Board Paper of Class 12-Science 2023 Physics Delhi(Set 3) - Solutions

General Instructions:

(i) This question paper comprises 35 questions. All questions are compulsory.

(ii) Question paper is divided into FIVE sections – Section A, B, C, D and E.

(ii) In section A: question number 1 to 18 are Multiple Choice (MCQ) type questions carrying 1 mark each.

(iii) In section B: question number 19 to 25 are Short Answver-1 (SA-1) type questions carrying 2 marks each.

(iv) In section - C: question number 26 to 30 are Short Answer-2 (SA-2) type questions carrying 3 marks each.

(v) In section - D: question number 31 to 33 are Long Answer (LA) type questions carrying 5 marks each.

(vii) In section - E: question number 34 and 35 are case-based questions carrying 4 marks each.

(viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 2 questions in Section - C, 3 questions in Section - D and 2 questions in Section - E.

(ix) Use of calculators is NOT allowed.

c = 3 × 108 m/s
h = 6.63 × 10–34 Js
e = 1.6 × 10–19 C
μo = 4π × 10–7 T m A–1
ε0 = 8.854 × 10–12 C2 N–1 m–2 = 9 × 109 N m2 C–2
Mass of electron (me) = 9.1 × 10–31 kg
Mass of neutron = 1.675 × 10–27 kg
Mass of proton = 1.673 × 10–27 kg
Avogadro’s number = 6.023 × 1023 per gram mole
Boltzmann constant = 1.38 × 10–23 JK–1

• Question 1
An electric dipole of length 2 cm is placed at an angle of 30° with an electric field $2×{10}^{5}$ N/C. It the dipole experiences a torque of $8×{10}^{-3}$ Nm, the magnitude of either charge of the dipole, is
(A) 4 μC
(B) 7 μC
(C) 8 mC
​(D) 2 mC VIEW SOLUTION

• Question 2

Two horizontal thin long parallel wires, separated by a distance r carry current I each in the opposite directions. The net magnetic field at a point midway between them, will be
(a) zero
(b)
(c)
(d)

VIEW SOLUTION

• Question 3
Which of the following cannot modify an external magnetic field as shown in the figure 3? (a) Nickel
(b) Silicon
(c) Sodium Chloride
(d) Copper VIEW SOLUTION

• Question 4
A square shaped coil of side 10 cm, having 100 turns is placed perpendicular to a magnetic field which is increasing at 1 T/s. The induced emf in the coil is
(A) 0.1 V
(B) 0.5 V
(C) 0.75 V
(D) 1.0 V VIEW SOLUTION

• Question 5
Which one of the following electromagnetic radiation has the least wavelength?
(A) Gamma rays
(B) Microwaves
(C) Visible light
(D) X-rays VIEW SOLUTION

• Question 6
In a Young's double-slit experiment, the screen is moved away from the plane of the slits. What will be its effect on the following?
(i) Angular separation of the fringes.
(ii) Fringe-width.
(A) Both (i) and (ii) remain constant.
(B) (i) remains constant, but (ii) decreases.
(C) (i) remains constant, but (ii) increases,
(D) Both (i) and (ii) increase.  VIEW SOLUTION

• Question 7
E, c and v represent the energy, velocity and frequency of a photon. Which of the following represents its wavelength?
(a) $\frac{hv}{{c}^{2}}$
(b) hv
(c) $\frac{hc}{E}$
(d) $\frac{hv}{c}$VIEW SOLUTION

• Question 8
The ratio of the nuclear densities of two nuclei having mass numbers 64 and 125 is
(A) $\frac{64}{125}$
(B) $\frac{4}{5}$
(C) $\frac{5}{4}$
(D) 1 VIEW SOLUTION

• Question 9
The energy required by an electron to jump the forbidden band in silicon at room temperature is about
(a) 0.01 eV
(b) 0.05 eV
(c) 0.7 eV
(d) 1.1 eV VIEW SOLUTION

• Question 10
The diagram shows four energy level of an electron in Bohr model of hydrogen atom. Identify the transition in which the emitted photon will have the highest energy. (A) I
(B) II
(C) III
(D) IV VIEW SOLUTION

• Question 11
Which of the following graphs correctly represents the variation of a particle momentum with its associated de-Broglie wavelength?
(A) (B) (C) (D) VIEW SOLUTION

• Question 12
The capacitors, each of 4 μF are to be connected in such a way that the effective capacitance of the combination is 6 μF. This can be achieved by connecting
(A) All three in parallel
(B) All three in series
(C) Two of them connected in series and the combination in parallel to the third.
(D) we of them connected in parallel and the combination in series to the third. VIEW SOLUTION

• Question 13
What is the ratio of inductive and capacitive reactance in an ac circuit?
(a) ${\mathrm{\omega }}^{2}\mathrm{LC}$
(b) LC2
(c) $\frac{\mathrm{LC}}{{\mathrm{\omega }}^{2}}$
(d) ${\mathrm{\omega }}^{2}\mathrm{L}$VIEW SOLUTION

• Question 14
In an interference experiment, third bright fringe is obtained at a point on the screen with a light of 700 nm. What should be the wavelength of the light source in order to obtain the fifth bright fringe at the same point?
(A) 420 nm
(B) 750 nm
(C) 630 nm
​(D) 500 nm VIEW SOLUTION

• Question 15
The radius of the nth orbit in Bohr model of hydrogen atom is proportional to
(A) n2
(B) $\frac{1}{{\mathrm{n}}^{2}}$
(C) n
(D) $\frac{1}{\mathrm{n}}$ VIEW SOLUTION

• Question 16
Assertion (A) : The resistance of an intrinsic semiconductor decreases with increase in its temperature.
Reason (R) : The number of conduction electrons as well as hole increase in an intrinsic semiconductor with rise in its temperature.
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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 17
Assertion(A): The given figure does not show a balanced Wheatstone bridge. Reason(R): For a balanced bridge small current should flow through the galvanometer.
​​(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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 18
Assertion (A) : The deflecting torque acting on a current carrying loop is zero when its plane is perpendicular to the direction of magnetic
field.
Reason (R) : The deflecting torque acting on a loop of magnetic moment $\stackrel{\to }{\mathrm{m}}$ in a magnetic field $\stackrel{\to }{\mathrm{B}}$ is given by the dot product of $\stackrel{\to }{\mathrm{m}}$ and $\stackrel{\to }{\mathrm{B}}$.
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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 19
Plot a graph showing the variation of photo electric current, as a function of anode potential for two light beams having the same frequency but different intensities I1 and I2 (I1 > I2). Mention its important features. VIEW SOLUTION

• Question 20
How will the De Broglie wavelength associated with an electron be affected affected when the (i) velocity of the electron decreases? and (ii) accelerating potential is increased? Justify your answer.

OR

How would the stopping potential for a given photosensitive surface change if (i) the frequency of the incident radiation were increased? and (ii) the intensity of incident radiation were decreased? Justify your answer.  VIEW SOLUTION

• Question 21
How are electromagnetic waves produced? Write their two characteristics. VIEW SOLUTION

• Question 22
Three point charges Q, q and −q are kept at the vertices of an equilateral triangle of side L as shown in figure. What is (i) the electrostatic potential energy of the arrangement? and
(ii) the potential at point D? VIEW SOLUTION

• Question 23
A long straight conductor kept along X' X axis, carries a steady current I along + x direction. At an instant t, a particle of mass m and charge q at point (x, y) moves with a velocity $\stackrel{\to }{v}$ along + y direction. Find the magnitude and direction of the force on the particle due to the conductor.

OR

Two identical circular loops P and Q, each of radius R carrying current I are kept in perpendicular planes such that they have a common centre O as shown in the figure. Find the magnitude and direction of the net magnetic field at point O. VIEW SOLUTION

• Question 24
Two conductors, made of the same material have equal lengths but different cross-sectional areas A1 and A2 (A1 > A2). They are connected in
parallel across a cell. Show that the drift velocities of electrons in two conductors are equal. VIEW SOLUTION

• Question 25
Two coils C1 and C2 are placed close to each other. The magnetic flux $\mathrm{\varphi }$2 linked with the coil C2 varies with the current I1 flowing in coil C1, as shown in the figure. Find (i) the mutual inductance of the arrangement, and
(ii) the rate of change of current $\left(\frac{{\mathrm{dI}}_{1}}{\mathrm{dt}}\right)$ that will induce an emf of 100 V in coil C2. VIEW SOLUTION

• Question 26
Using Huygen's construction, show how a plane wave is reflected from a surface. Hence verify the law of reflection.

OR

A plane wave-front propagating in a medium of refractive index $\text{'}{\mathrm{\mu }}_{1}\text{'}$ is incident on a plane surface making an angle of incidence (i). It enters into a medium of refractive index ${\mathrm{\mu }}_{2}\left({\mathrm{\mu }}_{2}>{\mathrm{\mu }}_{1}\right).$
Use Huygen's construction of secondary wavelets to trace the retracted wave-front. Hence verify Snell's law of refraction. VIEW SOLUTION

• Question 27
An alternating current I = 14 sin (100 πt) A passes through a series combination of a resistor of 30 Ω and an inductor of $\left(\frac{2}{5\mathrm{\pi }}\right)$ H. Taking
$\sqrt{2}=1.4$, calculate the
(i) rms value of the voltage drops across the resistor and the inductor, and
(ii) power factor of the circuit. VIEW SOLUTION

• Question 28
State the basic principle behind the working of an ac generator. Briefly describe its working and obtain the expression for the instantaneous
value of emf induced. VIEW SOLUTION

• Question 29
(a) Briefly describe how the current sensitivity of a moving coil galvanometer can be increased.
(b) A galvanometer shows full scale deflection for current Ig. A resistance R1 is required to convert it into a voltmeter of range (0 – V) and a
resistance R2 to convert it into a voltmeter of range (0 – 2V). Find the resistance of the galvanometer. VIEW SOLUTION

• Question 30
(a) Calculate the binding energy of an alpha particle in MeV. Given
mass of a proton = 1.007825 u
mass of a neutron = 1.008665 u
mass of He nucleus = 4.002800 u
lu = 931 MeV/c2

OR

A heavy nucleus P of mass number 240 and binding energy 7.6 MeV per nucleon splits into two nuclei Q and R of mass number 110 and 130 and binding energy per nucleon 8.5 MeV and 8.4 MeV respectively. Calculate the energy released in the fission. VIEW SOLUTION

• Question 31
Draw the circuit arrangement for studying V-I characteristics of a p-n junction diode in (i) forward biasing and (ii) reverse biasing. Draw the typical V-I characteristics of a silicon diode. Describe briefly the following terms : (i) minority carrier injection in forward biasing and (ii) breakdown voltage in reverse biasing.

OR

Name two important processes involved in the formation of a p-n junction diode. With the help of a circuit diagram, explain the working of junction diode as a full wave rectifier. Draw its input and output wave forms. State the characteristic property of a junction diode that makes it suitable for rectification. VIEW SOLUTION

• Question 32
(i) Draw a ray diagram to show the working of a compound microscope. Obtain the expression for the total magnification for the final image to be formed at the near point.
(ii) In a compound microscope an object is placed at a distance of 1.5 cm from the objective of focal length 1.25 cm. If the eye-piece has a focal length of 5 cm and the final image is formed at the near point, find the magnifying power of the microscope.

OR

(i) Draw a ray diagram for the formation of image of an object by an astronomical telescope, in normal adjustment. Obtain the expression for its magnifying power.

(ii) The magnifying power of an astronomical telescope in normal adjustment is 2.9 and the objective and the eyepiece are separated by a distance of 150 cm. Find the focal lengths of the two lenses. VIEW SOLUTION

• Question 33
(i) Explain how free electrons in a metal at constant temperature attain an average velocity under the action of an electric field. Hence obtain an expression for it.
(ii) Consider two conducting wires A and B of the same diameter but made of different materials joined in series across a battery. The number density of electrons in A is 1.5 times that in B. Find the ratio of drift velocity of electrons in wire A to that in wire B.

OR

(i) A cell emf of (E) and internal resistance. (r) is connected across a variable load resistance (R). Draw plots showing the variation of terminal voltage V with (i) R and (ii) the current (I) in the load.
(ii) Three cells, each of emf E but internal resistances 2r, 3r and 6r are connected in parallel across a resistor R.
Obtain expressions for (i) current flowing in the circuit, and (ii) the terminal potential difference across the equivalent cell. VIEW SOLUTION

• Question 34
Note : Questions number 34 and 35 are Case Study based questions.

A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Considering image formation by a single spherical surface successively at the two surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature. This formula helps us obtain a relation between u, v and f for a lens. Lenses form images of objects and they are used in a number of optical devices, for example microscopes and telescopes.

(i) An object AB is kept in front of a composite convex lens, as shown in figure. Will the lens produce one image ? If not, explain. (ii) A real image of an object formed by a convex lens is observed on a screen. If the screen is removed, will the image still be formed ? Explain.

(iii) A double convex lens is made of glass of refractive index 1.55 with both faces of the same radius of curvature. Find the radius of curvature required if focal length is 20 cm.

OR

(iii) Two convex lenses A and B of focal lengths 15 cm and 10 cm respectively are placed coaxially 'd' distance apart. A point object is kept at a distance of 30 cm in front of lens A. Find the value of 'd' so that the rays emerging from lens B are parallel to its principal axis. VIEW SOLUTION

• Question 35
A capacitor is a system of two conductors separated by an insulator. The two conductors have equal and opposite charges with a potential difference between them. The capacitance of a capacitor depends on the geometrical configuration (shape, Size and separation) of the system and also on the nature of the insulator separating the two conductors. They are used to store charges. Like resistors, capacitors can be arranged in series or parallel or a combination of both to obtain desired value of capacitance.

(i) Find the equivalent capacitance between points A and B in the given diagram. (ii) A dielectric slab is inserted between the plates of a parallel plate capacitor. The electric field between the plates decreases. Explain.
(iii) A capacitor A of capacitance C, having charge Q is connected across another uncharged capacitor B of capacitance 2C. Find an expression for
(a) the potential difference across the combination and
(b) the charge lost by capacitor A.

OR

(iii) Two slabs of dielectric constants 2K and K fill the space between the plates of a parallel plate capacitor of plate area A and plate separation d as shown in figure. Find an expression for capacitance of the system. VIEW SOLUTION
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