DELHI PUBLIC SCHOOL, GURGAON

PRE-BOARD I EXAMINATION (2025-26)

SUBJECT: PHYSICS (042)
CLASS: XII ( )
SET B

Time Allowed: 3 hours Maximum Marks: 70

General Instructions:

1. There are 33 questions in all. All questions are compulsory.

2. This question paper has five sections: Section A, Section B, Section C, Section D and Section E.
3. All the sections are compulsory.

4. Section A contains sixteen questions, twelve MCQ and four Assertion Reasoning based of 1 mark each, Section B

contains five questions of two marks each, Section C contains seven questions of three marks each, Section D

contains two case study based questions of four marks each and Section E contains three long answer questions of

five marks each.

5. There is no overall choice. However, an internal choice has been provided in one question in Section B, one

question in Section C, one question in each CBQ in Section D and all three questions in Section E. You have to

attempt only one of the choices in such questions.

6. Use of calculators is not allowed.

7. You may use the following values of physical constants where ever necessary

i. c = 3 x 108 m/s

ii. me = 9.1 x10-31 kg

iii. e = 1.6 x 10-19 C

iv. μ0 = 4π x 10-7 Tm𝑨−𝑨

v. h = 6.63 x10-34 Js

vi. ε0 = 8.854 x 10-12 𝑨𝑨𝑨−𝑨𝑨−𝑨

vii. Avogadro’s number = 6.023 X 𝑨𝑨𝑨𝑨 per gram mole

Section A

1. Pure silicon at 300 K has equal electron (ne) and hole (nh) concentrations of 1.5 × 1016 m-3. Doping by indium [1]

increases nh to 4.5 × 1022 m-3 . The ne in the doped silicon is

a) 3 × 1019 m-3 b) 9 × 10-5 m-3

c) 2.25 × 1011 m-3 d) 5 × 109 m-3

2. If 2% of the main current is to be passed through the galvanometer of resistance G, the resistance of shunt [1]
required is

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 G
a) 50G b)
49
G
c) 50 d) 49G
3. In two positions concave mirror produces magnified image of given object The positions are [1]

a) (i) Beyond C, (ii) Between P and F b) (i) At C, (ii) at F

c) (i) At C, (ii) between P and F d) (i) Between F and C, (ii) Between P and F
4. A frog can be levitated in a magnetic field produced by a current in a vertical solenoid placed below the frog. [1]
This is possible, because the body of the frog behaves as

a) paramagnetic b) ferromagnetic

c) anti-ferromagnetic d) diamagnetic
5. Potential energy of two equal positive charges 1μC each held 1m apart in air is [1]

a) Zero b) 1 J

c) 9 × 10-3 J d) 9 × 10-3 eV

6. A proton and an α-particle follow the same circular path in a transverse magnetic field. Their kinetic energies [1]
are in the ratio:

a) 1 : 4 b) 1 : √2

c) 1 : 1 d) 1 : 2
7. A planar loop is rotated in a magnetic field about an axis perpendicular to the field. The polarity of induced emf [1]
changes once in each:

a) 1 revolution b) ( 43 ) revolution
c) ( 1 ) revolution d) ( 1 ) revolution
4 2
8. Two bar magnets having same geometry with magnetic moments M and 2M are firstly placed in such a way that [1]
their similar poles are on the same side and its period of oscillation is T1. Now the polarity of one of the magnets
is reversed and its time period becomes T2. Then,

a) T1 = T2 b) T2 = ∞

c) T1 > T2 d) T1 < T2

9. A plane wavefront is incident on a concave mirror of radius of curvature R. The radius of the refracted [1]
wavefront will be:

a) 2R b) R
R R
c) 2 d) 4
10. The dimensional formula of electric charge is: [1]

a) [M0L0T1A-1] b) [M0L0T-1A1]

c) [M0L0T-1 A-1] d) [M0L0T1A1]

11. In the given figure, a diode D is connected to an external resistance R = 100Ω and an emf of 3.5 V. If the barrier [1]
potential developed across the diode is 0.5 V, the current in the circuit will be

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 a) 40 mA b) 30 mA

c) 35 mA d) 20 mA
12. Magnifying power of a compound microscope is high if [1]

a) the objective has a short focal length and the b) the objective has a long focal length and
eye-piece has a long focal eye-piece has a short focal

c) both objective and eye-piece have long focal d) both objective and eye-piece have short
lengths focal lengths
13. Assertion (A): The photoelectrons produced by a monochromatic light beam incident on a metal surface, have a [1]
spread in their kinetic energies.
Reason (R): The work function of the metal varies as a function of depth from the surface.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

14. Assertion (A): All the charge in a conductor gets distributed on the whole of its outer surface. [1]
Reason (R): In a dynamic system, charges try to keep their potential energy minimum.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

15. Assertion (A): For identical coherent waves, the maximum intensity is four times the intensity due to each wave [1]
Reason (R): Intensity is proportional to the square of amplitude.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

16. Assertion: The resistance offered by an inductor in a DC circuit is always constant. [1]
Reason: The resistance of the inductor in steady-state is zero.

a) Both A and R are true and R is the correct b) Both A and R are true but R is NOT the
explanation of A correct explanation of A

c) A is true but R is false d) A is false and R is also false

Section B
17. i. How are microwaves produced? [2]
ii. Write two important uses of infrared waves.
18. Three identical specimens of magnetic materials Nickel, Antimony, Aluminium are kept in a uniform magnetic [2]
field. Draw the modification in the field lines in each case. Justify your answer.
19. The V-I characteristic of a silicon diode is given in the figure. [2]

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 Calculate the diode resistance in:
i. forward bias at V = ±2 V and V = + 1 V, and
ii. reverse bias V = - 1 V and - 2 V
o [2]
20. The wavelength of the first member of Lyman series is 1216A. Calculate the wavelength of second member of
Balmer series.
21. a. State Ampere's circuital law connecting the line integral of B over a closed path to the net current crossing [2]
the area bounded by the path.
b. Use Ampere's law to derive the formula for the magnetic field due to an infinitely long straight current
carrying wire.
OR
a. A point charge q moving with speed v v enters a uniform magnetic field B that is acting into the plane of the
paper as shown. What is the path followed by the charge q and in which plane does it move?

b. How does the path followed by the charge get affected if its velocity has a component parallel to B?
Section C
22. A battery if 24 cells each of emf 1.5 V and internal resistance, 2Ω is to be connected in order to send the [3]
maximum current through a 12Ω resistor. How are they to be connected? Find the current in each cell and the
potential difference across the external resistance.
23. a. Draw V-I characteristics of a p-n Junction diode. [3]
b. Differentiate between the threshold voltage and the breakdown voltage for a diode.
c. Write the property of a junction diode which makes it suitable for rectification of ac voltages.

24. When light of frequency v1 is incident on a photosensitive surface, the stopping potential is V1. If the frequency [3]
v1
of incident radiation becomes , the stopping potential changes to V 2. Find out the expression for the threshold
2
frequency for the surface in terms of V1 and V2.
If the frequency of incident radiation is doubled, will the maximum kinetic energy of the photoelectrons also be
doubled? Give reason.
25. Write symbolically the nuclear β+ decay process of 11 C . Is the decayed product X an isotope or isobar of 11 C? [3]
6 6

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 Given the mass values m (11
6
C) = 11.011434 u and m(X) = 11.009305 u. Estimate the Q-value in this process.
o o
26. A hydrogen atom in its excited state emits radiations of wavelengths 1218 A and 974.3 A when it finally comes [3]

to the ground state. Identify the energy levels from where transitions occur. Given Rydberg constant R = 1.1 ×
107 m-1. Also specify the spectral series to which these lines belong.
27. How is the spacing between fringes in a double slit experiment affected if: [3]
a. the slits separation is increased,
b. the colour of light used is changed from red to blue,
c. the whole apparatus is submerged in a oil of refractive index 1.2?
Justify your anwer in each case.
28. i. Define the term self-inductance and write its S.I. unit. [3]
ii. Obtain the expression for the mutual inductance of two long co-axial solenoids S1 and S2 wound one over
the other, each of length L and radii r1 and r2 and n1 and n2 number of turns per unit length, when a current I
is set up in the outer solenoid S2.

OR
a. Define mutual inductance and write its S.I. unit.
b. A square loop of side a carrying a current I2 is kept at distance x from an infinitely long straight wire carrying a
current I1 as shown in the figure. Obtain the expression for the resultant force acting on the loop.

Section D
29. Read the text carefully and answer the questions: [4]
Maxwell showed that the speed of an electromagnetic wave depends on the permeability and permittivity of the
medium through which it travels. The speed of an electromagnetic wave in free space is given by c = 1 . The
√μ0 ε0
fact led Maxwell to predict that light is an electromagnetic wave. The emergence of the speed of light from
purely electromagnetic considerations is the crowning achievement of Maxwell’s electromagnetic theory. The
speed of an electromagnetic wave in any medium of permeability μ and permittivity ε will be c
where K is
√Kμr
the dielectric constant of the medium and μr is the relative permeability.
1
(a) The dimensions of ε E2
2 0
(ε0 : permittivity of free space; E = electric field) is

a) MLT-1 b) ML-1T-2

c) ML2T-2 d) ML2 T-1

(b) Let [ε0] denote the dimensional formula of the permittivity of the vacuum. If M = mass, L = length, T =
time and A = electric current, then

a) [ε0] = ML2T-1 b) [ε0] = MLT-2A-2

c) [ε0] = M-1L-3T4A2 d) [ε0] = M-1L-3T2A

(c) An electromagnetic wave of frequency 3 MHz passes from vacuum into a dielectric medium with

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 permittivity ε = 4. Then

a) wavelength is halved and the frequency b) wavelength and frequency both remain
remains unchanged. unchanged

c) wavelength is doubled and the d) wavelength is doubled and the

frequency remains unchanged frequency becomes half
OR
The electromagnetic waves travel with

a) the speed of light c = 3 × 108 m s-1 in b) the speed of light c = 3 × 10 m s -1 in

fluid medium. solid medium

c) the speed of light c = 3 × 108 m s-1 in d) the same speed in all media

free space
(d) Which of the following are not electromagnetic waves?
cosmic rays, γ-rays, β-rays, X-rays

a) β-rays b) X-rays

c) γ-rays d) cosmic rays

30. Read the text carefully and answer the questions: [4]
In 1909, Robert Millikan was the first to find the charge of an electron in his now-famous oil-drop experiment.
In that experiment, tiny oil drops were sprayed into a uniform electric field between a horizontal pair of
oppositely charged plates. The drops were observed with a magnifying eyepiece, and the electric field was
adjusted so that the upward force on some negatively charged oil drops was just sufficient to balance the
downward force of gravity. That is, when suspended, upward force qE just equaled Mg. Millikan accurately
measured the charges on many oil drops and found the values to be whole number multiples of 1.6 × 10-19 C
the charge of the electron. For this, he won the Nobel prize.

(a) If a drop of mass 1.08 × 10-14 kg remains stationary in an electric field of 1.68 × 105 NC-1 , then the
charge of this drop is

a) 6.40 × 10-19 C b) 4.8 × 10-19 C

c) 3.2 × 10-19 C d) 1.6 × 10-19 C

(b) Extra electrons on this particular oil drop (given the presently known charge of the electron) are

a) 4 b) 5

c) 8 d) 3
(c) A negatively charged oil drop is prevented from falling under gravity by applying a vertical electric field

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 100 V m-1. If the mass of the drop is 1.6 × 10-3 g, the number of electrons carried by the drop is (g = 10
ms-2)

a) 109 b) 1018

c) 1012 d) 1015

(d) The important conclusion given by Millikan's experiment about the charge is

a) charge has no definite value b) charge is quantized

c) charge is never quantized d) charge on oil drop always increases

OR
If in Millikan's oil drop experiment, charges on drops are found to be 8μC, 12μC, 20μC, then quanta of
charge is

a) 20μC b) 12μC

c) 8μC d) 4μC
Section E
31. i. Draw a labelled ray diagram of a compound microscope showing image formation at least distance of [5]
distinct vision. Derive an expression for its magnifying power.
ii. A telescope consists of two lenses of focal length 100 cm and 5 cm. Find the magnifying power when the
final image is formed at infinity.
OR
a. Draw a diagram showing the Young's arrangement' for producing a sustained interference pattern. Hence obtain
the expression for the width of the interference fringes obtained in this pattern.
b. If the principal source point S were to be moved a little upwards, towards the slit S1 from its usual symmetrical
position, with respect to the two slits S1 and S2, discuss how the interference pattern, obtained on the screen,
would get affected.

32. a. If two similar large plates, each of area A having surface charge densities +σ and - σ are separated by a [5]
distance d in air, then find the expression for
i. the field at points between the two plates and on the outer side of the plates. Specify the direction of the
field in each case.
ii. the potential difference between the plates.
iii. the capacitance of the capacitor so formed.
b. Two metallic spheres of radii R and 2R are charged so that both of these have the same surface charge
density σ. If they are connected to each other with a conducting wire, in which direction will the charge flow
and why?
OR

i. Derive an expression for potential energy of an electric dipole p 𝑨in an external uniform electric field E𝑨. When
is the potential energy of the dipole (1) maximum, and (2) minimum?
ii. An electric dipole consists of point charges -1.0 pC and +1.0 pC located at (0, 0) and (3 mm, 4 mm) respectively
in x - y plane. An electric field E𝑨 = ( m V ) i is switched on in the region. Find the torque τ 𝑨acting on the
1000

dipole.

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33. i. Draw a labelled diagram of a step-up transformer and describe its working principle. Explain any three [5]
causes for energy losses in a real transformer.
ii. A step-up transformer converts a low voltage into high voltage. Does it violate the principle of conservation
of energy? Explain.
iii. A step-up transformer has 200 and 3000 turns in its primary and secondary coils respectively. The input
voltage given to the primary coil is 90 V. Calculate:
1. The output voltage across the secondary coil
2. The current in the primary coil if the current in the
secondary coil is 2.0 A.
OR
i. The figure shows the variation of resistance and reactance versus angular frequency. Identify the curve which
corresponds to inductive reactance and resistance.

ii. Show that series LCR circuit at resonance behaves as a purely resistive circuit. Compare the phase relation
between current and voltage in series LCR circuit for (i) XL > XC, (ii) XL = XC using phasor diagrams.
iii. What is an acceptor circuit and where it is used?

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