Physics · Sample Paper 1

General instructions

Section A · Class 11 syllabus

1. Question 14 marks

   The dimensional formula of Planck's constant is

   1. A.$[ML^2T^{-1}]$
   2. B.$[MLT^{-1}]$
   3. C.$[ML^2T^{-2}]$
   4. D.$[M^0L^0T^0]$
2. Question 24 marks

   The percentage errors in measuring mass and speed are 2% and 3%. The maximum percentage error in kinetic energy is

   1. A.5%
   2. B.8%
   3. C.11%
   4. D.1%
3. Question 34 marks

   A ball is dropped from a height of 45 m. The time taken to reach the ground is

   1. A.2 s
   2. B.3 s
   3. C.4.5 s
   4. D.9 s
4. Question 44 marks

   The velocity of a particle is $v = 3t^2 - 2t$ (SI units). Its acceleration at $t = 2$ s is

   1. A.$8\ \text{m s}^{-2}$
   2. B.$10\ \text{m s}^{-2}$
   3. C.$12\ \text{m s}^{-2}$
   4. D.$6\ \text{m s}^{-2}$
5. Question 54 marks

   A projectile is thrown with speed $20\ \text{m s}^{-1}$ at $30^\circ$ to the horizontal. Its maximum height is

   1. A.5 m
   2. B.10 m
   3. C.15 m
   4. D.20 m
6. Question 64 marks

   A body moves in a circle of radius 2 m at a constant speed of $4\ \text{m s}^{-1}$. Its centripetal acceleration is

   1. A.$2\ \text{m s}^{-2}$
   2. B.$4\ \text{m s}^{-2}$
   3. C.$8\ \text{m s}^{-2}$
   4. D.$16\ \text{m s}^{-2}$
7. Question 74 marks

   Two blocks of 2 kg and 3 kg on a smooth surface are pushed by a 10 N force applied to the 2 kg block. The force exerted by the 2 kg block on the 3 kg block is

   1. A.4 N
   2. B.6 N
   3. C.10 N
   4. D.2 N
8. Question 84 marks

   A block rests on a rough incline. It just begins to slide when the angle is $30^\circ$. The coefficient of static friction is

   1. A.$\tfrac12$
   2. B.$\tfrac{1}{\sqrt3}$
   3. C.$\sqrt3$
   4. D.$\tfrac{\sqrt3}{2}$
9. Question 94 marks

   A 2 kg body falls freely from 10 m. Its kinetic energy just before hitting the ground is

   1. A.20 J
   2. B.100 J
   3. C.200 J
   4. D.400 J
10. Question 104 marks

    A body of mass m moving with speed v collides with an identical body at rest and they stick together. The fraction of kinetic energy lost is

    1. A.$\tfrac14$
    2. B.$\tfrac12$
    3. C.$\tfrac34$
    4. D.0
11. Question 114 marks

    The moment of inertia of a solid sphere of mass M and radius R about a tangent is

    1. A.$\tfrac25MR^2$
    2. B.$\tfrac75MR^2$
    3. C.$\tfrac35MR^2$
    4. D.$MR^2$
12. Question 124 marks

    A solid cylinder rolls without slipping. The fraction of its total kinetic energy that is rotational is

    1. A.$\tfrac12$
    2. B.$\tfrac13$
    3. C.$\tfrac23$
    4. D.$\tfrac14$
13. Question 134 marks

    If the radius of the Earth shrank by 1% with its mass unchanged, g at the surface would

    1. A.decrease by 1%
    2. B.increase by 1%
    3. C.increase by 2%
    4. D.decrease by 2%
14. Question 144 marks

    The time period of a satellite close to the Earth's surface is about

    1. A.24 h
    2. B.84 min
    3. C.12 h
    4. D.30 min
15. Question 154 marks

    Two wires of the same material have lengths in the ratio 1 : 2 and diameters in the ratio 2 : 1. Under the same load, their extensions are in the ratio

    1. A.1 : 8
    2. B.1 : 4
    3. C.8 : 1
    4. D.2 : 1
16. Question 164 marks

    A water drop of radius 1 mm has surface tension $0.07\ \text{N m}^{-1}$. The excess pressure inside it is

    1. A.70 Pa
    2. B.140 Pa
    3. C.35 Pa
    4. D.280 Pa
17. Question 174 marks

    A black body's temperature is doubled. Its rate of radiation becomes

    1. A.2 times
    2. B.4 times
    3. C.8 times
    4. D.16 times
18. Question 184 marks

    A Carnot engine works between $327^\circ$C and $27^\circ$C. Its efficiency is

    1. A.25%
    2. B.50%
    3. C.75%
    4. D.92%
19. Question 194 marks

    In an adiabatic expansion of an ideal gas,

    1. A.temperature rises
    2. B.temperature falls
    3. C.internal energy stays constant
    4. D.heat is absorbed
20. Question 204 marks

    The ratio $C_p/C_v$ for a diatomic gas (rigid molecules) is

    1. A.$\tfrac53$
    2. B.$\tfrac75$
    3. C.$\tfrac43$
    4. D.$\tfrac32$
21. Question 214 marks

    A mass on a spring oscillates with a period of 2 s. If the mass is made four times, the period becomes

    1. A.1 s
    2. B.2 s
    3. C.4 s
    4. D.8 s
22. Question 224 marks

    An organ pipe closed at one end is 85 cm long. If the speed of sound is 340 m/s, its fundamental frequency is

    1. A.100 Hz
    2. B.200 Hz
    3. C.50 Hz
    4. D.400 Hz

Section B · Class 12 syllabus

1. Question 234 marks

   The electric flux through a closed surface enclosing a charge q is

   1. A.$q\varepsilon_0$
   2. B.$q/\varepsilon_0$
   3. C.zero
   4. D.$q/4\pi\varepsilon_0$
2. Question 244 marks

   Two equal charges repel each other with force F. If the distance between them is halved, the force becomes

   1. A.F/2
   2. B.2F
   3. C.4F
   4. D.F/4
3. Question 254 marks

   Three capacitors of 6 μF each are connected in series. The equivalent capacitance is

   1. A.18 μF
   2. B.2 μF
   3. C.3 μF
   4. D.6 μF
4. Question 264 marks

   A parallel-plate capacitor is charged and disconnected. A dielectric of constant K is then inserted. The energy stored

   1. A.increases K times
   2. B.decreases K times
   3. C.is unchanged
   4. D.becomes zero
5. Question 274 marks

   A 4 Ω and a 12 Ω resistor are connected in parallel across a 6 V battery of negligible internal resistance. The total current is

   1. A.0.5 A
   2. B.1 A
   3. C.2 A
   4. D.1.5 A
6. Question 284 marks

   A wire of resistance R is cut into four equal parts, which are joined in parallel. The new resistance is

   1. A.R/4
   2. B.R/16
   3. C.4R
   4. D.R
7. Question 294 marks

   The magnetic field at the centre of a circular loop of radius 0.1 m carrying 1 A is ($\mu_0 = 4\pi\times10^{-7}$)

   1. A.$2\pi\times10^{-6}$ T
   2. B.$4\pi\times10^{-6}$ T
   3. C.$\pi\times10^{-6}$ T
   4. D.$2\times10^{-6}$ T
8. Question 304 marks

   A galvanometer is converted into an ammeter by connecting

   1. A.a high resistance in series
   2. B.a low resistance in parallel
   3. C.a high resistance in parallel
   4. D.a low resistance in series
9. Question 314 marks

   The magnetic susceptibility of a superconductor is

   1. A.+1
   2. B.0
   3. C.−1
   4. D.∞
10. Question 324 marks

    The magnetic flux through a coil changes from 0.5 Wb to 0.1 Wb in 0.2 s. The average induced emf is

    1. A.2 V
    2. B.0.4 V
    3. C.4 V
    4. D.0.08 V
11. Question 334 marks

    The rms value of an AC voltage with peak 311 V is about

    1. A.311 V
    2. B.220 V
    3. C.155 V
    4. D.440 V
12. Question 344 marks

    In a series LCR circuit, $R = 30\ \Omega$, $X_L = 60\ \Omega$ and $X_C = 20\ \Omega$. The power factor is

    1. A.0.6
    2. B.0.8
    3. C.0.5
    4. D.1
13. Question 354 marks

    Which of these has the longest wavelength?

    1. A.X-rays
    2. B.infrared
    3. C.ultraviolet
    4. D.microwaves
14. Question 364 marks

    A convex lens of focal length 20 cm forms a real image of the same size as the object. The object distance is

    1. A.10 cm
    2. B.20 cm
    3. C.40 cm
    4. D.80 cm
15. Question 374 marks

    The critical angle for glass of refractive index √2 is

    1. A.$30^\circ$
    2. B.$45^\circ$
    3. C.$60^\circ$
    4. D.$90^\circ$
16. Question 384 marks

    In Young's double-slit experiment, the whole apparatus is immersed in water (μ = 4/3). The fringe width

    1. A.increases by 4/3
    2. B.decreases to 3/4 of its value
    3. C.is unchanged
    4. D.becomes zero
17. Question 394 marks

    Unpolarised light passes through two polaroids with axes at 60°. The fraction of the original intensity transmitted is

    1. A.1/2
    2. B.1/4
    3. C.1/8
    4. D.3/8
18. Question 404 marks

    The work function of a metal is 2 eV and light of 5 eV falls on it. The stopping potential is

    1. A.2 V
    2. B.3 V
    3. C.5 V
    4. D.7 V
19. Question 414 marks

    An electron and a proton have the same de Broglie wavelength. Which has more kinetic energy?

    1. A.electron
    2. B.proton
    3. C.both equal
    4. D.can't say
20. Question 424 marks

    The ionisation energy of a hydrogen atom in its first excited state is

    1. A.13.6 eV
    2. B.3.4 eV
    3. C.1.51 eV
    4. D.10.2 eV
21. Question 434 marks

    The half-life of a radioactive sample is 10 days. The fraction remaining after 30 days is

    1. A.1/3
    2. B.1/6
    3. C.1/8
    4. D.1/9
22. Question 444 marks

    The nuclear radius of $^{27}$Al is $3.6$ fm. The radius of $^{125}$Te is about

    1. A.4 fm
    2. B.5 fm
    3. C.6 fm
    4. D.8 fm
23. Question 454 marks

    In an n-type semiconductor, the majority charge carriers are

    1. A.holes
    2. B.electrons
    3. C.protons
    4. D.positive ions