Board Paper of Class 12-Science 2023 Physics Delhi(Set 1) - Solutions

General Instructions:

Read the following instructions very carefully and follow them:

(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
μ_o = 4π × 10^–7 T m A^–1
ε₀ = 8.854 × 10^–12 C² N^–1 m^–2

$fraction numerator 1 over denominator 4 pi epsilon subscript 0 end fraction$ = 9 × 10⁹ N m² C^–2
Mass of electron (m_e) = 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 $2 \times 10^{5}$ N/C. It the dipole experiences a torque of $8 \times 10^{- 3}$ 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 long parallel wires kept 2 m apart carry 3A current each, in the same direction. The force per unit length on one wire due to the other is
(A) 4.5 × 10^–5, attractive
(B) 4.5 × 10^–7, N/m, repulsive
(C) 9 × 10^–7, N/m, repulsive
(D) 9 × 10^–5 N/m, attractive VIEW SOLUTION

Question 3
Which of the following has its permeability less than that of free space?
(A) Copper
(B) Aluminium
(C) Copper chloride
(D) Nickel 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
The energy of a photon of wavelength λ is
(A) hc λ
(B) hc/λ
(C) λ/hc
(D) λh/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
During the formation of a p-n junction:
(A) diffusion current keeps increasing.
(B) drift current remains constant.
(C) both the diffusion current and drift current remain constant.
(D) diffusion current remains almost constant but drift current increases till both currents become equal. 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
Which of the following statements about a series LCR circuit connected to an ac source is correct?
(A) If the frequency of the source is increased, the impedance of the circuit first decreases and then increases.
(B) If the net reactance (X_L − X_C) of circuit becomes equal to its resistance, then the current leads the voltage by 45°.
(C) At resonance, the voltage drop across the inductor is more than that across the capacitor.
(D) At resonance, the voltage drop across the capacitor is more than that across the inductor. VIEW SOLUTION

Question 14
According to Huygens principle, the amplitude of secondary wavelets is
(A) equal in both the forward and the backward directions.
(B) maximum in the forward direction and zero in the backward direction.
(C) large in the forward direction and small in the backward direction.
(D) small in the forward direction and large in the backward direction. VIEW SOLUTION

Question 15
The radius of the n^th orbit in Bohr model of hydrogen atom is proportional to
(A) n²
(B) $\frac{1}{n^{2}}$
(C) n
(D) $\frac{1}{n}$ 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 equivalent resistance between points A and B in the given network is 2R.
Reason (R) : All the resistors are connected in parallel.

(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 $\vec{m}$ in a magnetic field $\vec{B}$ is given by the dot product of $\vec{m}$ and $\vec{B}$ .
(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
Draw a graph showing the variation of potential energy of a pair of nucleons as a function of their separation. Indicate the region in which the nuclear force is (a) attractive and (b) repulsive. 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
Identify the electromagnetic wave whose wavelengths range is from about
(a) 10⁻¹² m to about 10⁻⁸m.
(b) 10⁻³ m to about 10⁻¹ m.
Write one use of each. VIEW SOLUTION

Question 22
Depiet the orientation of an electric dipole in (a) stable and (b) unstable equilibrium in an external uniform electric field.
Write the potential energy of the dipole in each case. VIEW SOLUTION

Question 23
Write the expression for the Lorentz force on a particle of charge q moving with a velocity $\vec{v}$ in a magnetic field $\vec{B} .$ When is the magnitude of this force maximum? Show that no work is done by this force on the particle during its motion from a point ${\vec{r}}_{1}$ to point ${\vec{r}}_{2} .$
OR

A long straight wire AB carries a current I. A particle (mass m and charge q) moves with a velocity $\vec{v}$ , parallel to the wire, at a distance d from it as shown in the figure. Obtain the expression for the force experienced by the particle and mention its directions.
VIEW SOLUTION

Question 24
The potential difference applied across a given conductor is doubled. How will this affect (i) the mobility of electrons and (ii) the current density in the conductor.? Justify your answers. VIEW SOLUTION

Question 25
Two coils C₁ and C₂ are placed close to each other. The magnetic flux $ϕ$ 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 $(\frac{{dI}_{1}}{dt})$ 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 $' μ_{1}'$ is incident on a plane surface making an angle of incidence (i). It enters into a medium of refractive index $μ_{2} (μ_{2} > μ_{1}) .$
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 voltage of 220 V is applied across a device X. A current of 0.22 A flows in the circuit and it lags behind the applied voltage in phase by $π / 2$ radian. When the same voltage is applied across another device Y, the current in the circuit remains the same and it is in phase with the applied voltage.
(i) Name the devices X and Y and,
(ii) Calculate the current flowing in the circuit when the same voltage is applied across the series combination of X and Y. 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 I_g. 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
(i) Differentiate between 'distance of closest approach' and 'impact parameter'.
(ii) Determine the distance of closest approach when an alpha particle of kinetic energy 3.95 MeV approaches a nucleus of Z = 79, stops and reverses its directions.
OR

(i) State three postulates of Bohr's theory of hydrogen atom.
(ii) Find the angular momentum of an electron revolving in the second orbit in Bohr's hydrogen atom. VIEW SOLUTION

Question 31
(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 32
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 33
(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 34
Note : Questions number 34 and 35 are Case Study based questions.
Read the following paragraph and answer the 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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