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1. If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

(1). [F ] [A] [T ]

(2). [F ] [A] [T 2]

(3). [F ] [A] [T −1]

(4). [F ] [A−1] [T ]

2. If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of

(1). [M2] [L−1] [T 0]

(2). [M ] [L−1] [T −1]

(3). [M ] [L0] [T 0]

(4). [M2] [L−2] [T −1]

3. A screw gauge gives the following readings when used to measure the diameter of a wire
Main scale reading : 0 mm
Circular scale reading : 52 divisions
Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is

(1). 0.52 cm

(2). 0.026 cm

(3). 0.26 cm

(4). 0.052 cm

4. A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let Sn be the distance travelled by the block in the interval t = n − 1 to t = n. Then, the ratio Sn/Sn+ 1 is

(1). 2n − 1/2n

(2). 2n − 1/2n + 1

(3). 2n + 1/2n − 1

(4). 2n/2n − 1

5. A car starts from rest and accelerates at 5 m/s2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s?(Take g = 10 m/s2)

(1). 20 m/s, 5 m/s2

(2). 20 m/s, 0

(3). 20√2 m/s, 0

(4). 20√2 m/s, 10 m/s2

6. A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ' θ ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, θ, is then given by:

(1). \( \theta = {\cos^{-1} \left( \frac{gT^2}{\pi^2 R} \right)}^{1 / 2} \)

(2). \( \theta = {\cos^{-1} \left( \frac{\pi ^2R}{gT^2} \right)}^{1 / 2} \)

(3). \( \theta = {\sin^{-1} \left( \frac{\pi ^2R}{gT^2} \right)}^{1 / 2} \)

(4). \( \theta = {\sin^{-1} \left( \frac{2gT^2}{\pi^2 R} \right)}^{1 / 2} \)

7. A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height.The magnitude of impulse imparted to the ball is (g = 10 m/s2) nearly

(1). 0 kg m/s

(2). 4.2 kg m/s

(3). 2.1 kg m/s

(4). 1.4 kg m/s

8. A uniform rod of length 200 cm and mass 500 g is balanced on a wedgeplaced at 40 cm mark. A mass of 2 kg is suspended from the rod at 20cm and another unknown mass 'm' is suspended from the rod at 160 cmmark as shown in the figure. Find the value of 'm' such that the rod is inequilibrium. (g = 10 m/s2)

(1). 1 / 2 kg

(2). 1 / 3 kg

(3). 1 / 6 kg

(4). 1 / 12 kg

9. A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at thatinstant are respectively

(1). \(\frac{S}{4}\), \(\frac{3gS}{2}\)

(2). \(\frac{S}{4}\),\(\frac{\sqrt{3gs}}{2}\)

(3). \(\frac{S}{2}\),\(\frac{\sqrt{3gs}}{2}\)

(4). \(\frac{S}{4}\),\(\sqrt{\frac{3gs}{2}}\)

10. Water falls from a height of 60 m at the rate of 15 kg/s to operate aturbine. The losses due to frictional force are 10% of the input energy.How much power is generated by the turbine?(g = 10 m/s2 )

(1). 10.2 kW

(2). 8.1 kW

(3). 12.3 kW

(4). 7.0 kW

11. From a circular ring of mass ' M and radius ' R ' an arc correspondingto a 90° sector is removed. The moment of inertia of the remaining partof the ring about an axis passing through the centre of the ring andperpendicular to the plane of the ring is ' K times ′M R2'. Then thevalue of ' K is

(1). \(\frac{3}{4}\)

(2). \(\frac{7}{8}\)

(3). \(\frac{1}{4}\)

(4). \(\frac{1}{8}\)

12. The velocity of a small ball of mass M and density d , when dropped in acontainer filled with glycerine becomes constant after some time. If thedensity of glycerine is \(\frac{d}{2}\), then the viscous force acting on the ball will be

(1). \(\frac{Mg}{2}\)

(2). \(Mg\)

(3). \(\frac{3}{2}Mg\)

(4). \(2Mg\)

13. A body is executing simple harmonic motion with frequency\(\, 'n'\), thefrequency of its potential energy is

(1). \(n\)

(2). \(2n\)

(3). \(3n\)

(4). \(4n\)

14. A thick current carrying cable of radius 'R' carries current 'I' uniformlydistributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by

(1).

(2).

(3).

(4).

15. An infinitely long straight conductor carries a current of 5A as shown. An electron is moving with a speed of 105 m ∕ s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

(1). 4 × 10−20 N

(2). 8π × 10−20 N

(3). 4π × 10−20 N

(4). 8 × 10−20 N

16. In the product \(\vec{F} = q \left(\vec{v} × \vec{B}\right) = q\vec{V} × \left( B\hat{i} + B\hat{j} + B_0\hat{k}\right)\) For q = 1 and \(\vec{V} = 2\hat{i} + 4\hat{j} + 6\hat{k}\) and \(\vec{F} = 4|hat{i} - 20\hat{j} + 12\hat{k}\) What will be the complete expression for \(\vec{B}\)

(1). \(-8\hat{i} - 8\hat{j} - 6\hat{k}\)

(2). \(-6\hat{i} - 6\hat{j} - 8\hat{k}\)

(3). \(8\hat{i} + 8\hat{j} - 6\hat{k}\)

(4). \(6\hat{i} + 6\hat{j} - 8\hat{k}\)

17. The escape velocity from the Earth's surface is \(v\). The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is

(1). \(v\)

(2). \(2v\)

(3). \(3v\)

(4). \(4v\)

18. A particle of mass \(' m '\) is projected with a velocity \(v = kV_e\left(k < 1\right)\) from the surface of the earth.(\(V_e = escape\, velocity\)) The maximum height above the surface reached by the particle is

(1). \(R\left(\frac{k}{1 − k}\right)^2\)

(2). \(R\left(\frac{k}{1 + k}\right)^2\)

(3). \(\frac{R^2k}{1 + k}\)

(4). \(\frac{Rk^2}{1 - k^2}\)

19. Match Column l with Column ll andchoose the correct match fromthegiven choices.

(1). A-3, B-1, C-4, D-2

(2). A-2, B-3, C-4, D-1

(3). A-2, B-1, C-4, D-3

(4). A-3, B-2, C-1, D-4

20. A dipole is placed in an electric field as shown. In which direction will it move?

(1). Towards the left as its potential energy will increase

(2). Towards the right as its potentialenergy will decrease

(3). Towards the left as its potentialenergy will decrease

(4). Towards the right as its potentialenergy will increase

21. Polar molecules are the molecules

(1). having zero dipole moment

(2). acquire a dipole moment only in the presence of electric field due to displacement of charges.

(3). acquire a dipole moment only when magnetic field is absent

(4). having a permanent electric dipole moment

22. An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance ' R ' are connected in series to an ac source of potential difference 'V' volts as shown in figure. Potential difference across L, C and R is 40V , 10 V and 40V ,respectively. The amplitude of current flowing through C R series circuit is 10√2A. The impedance of the circuit is

(1). 4√2Ω

(2). 5√2Ω

(3). 4Ω

(4). 5Ω

23. A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?

(1). 0.2 A

(2). 0.4 A

(3). 2 A

(4). 4 A

24. A series LCR circuit containing 5.0 H inductor, 80 μF capacitor and 40 resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be

(1). 25 rad/s and 75 rad/s

(2). 50 rad/s and 25 rad/s

(3). 46 rad/s and 54 rad/s

(4). 42 rad/s and 58 rad/s

25. Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 > R2, the mutual inductance M between them will be directly proportional to

(1). \(\frac{R_1}{R_2}\)

(2). \(\frac{R_2}{R_1}\)

(3). \(\frac{R_1^2}{R_2}\)

(4). \(\frac{R_2^2}{R_1}\)

26. A dipole is placed in an electric field as shown. In which direction will it move?

(1). Towards the left as its potential energy will increase.

(2). Towards the right as its potential energy willdecrease.

(3). Towards the left as its potential energy will decrease.

(4). Towards the right as its potential energy will increase.

27. The equivalent capacitance of the combination shown in the figure is

(1). 3C

(2). 2C

(3). \(\frac{C}{2}\)

(4). \(\frac{3C}{2}\)

28. Two charged spherical conductors of radius R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres (σ1/σ2) is

(1). \(\frac{R_1}{R_2}\)

(2). \(\frac{R_2}{R_1}\)

(3). \(\sqrt{\frac{R_!}{R_2}}\)

(4). \(\frac{R_1^2}{R_2^2}\)

29. A parallel plate capacitor has a uniform electric field ' \(\vec{F}\) ' in the space between the plates. If the distance between the plates is ' d ' and the area of each plate is ' A ', the energy stored in the capacitor is ( ε0 = permittivity of free space)

(1). \(\frac{1}{2}ε_0E^2\)

(2). \(ε_0E Ad\)

(3). \(\frac{1}{2}ε_0E^2Ad\)

(4). \(\frac{E^2Ad}{ε_0}\)

30. Polar molecules are the molecules

(1). Having zero dipole moment

(2). Acquire a dipole moment only in the presence of electric field due to displacement of charges

(3). Acquire a dipole moment only when magnetic field is absent

(4). Having a permanent electric dipole moment

31. Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

(1). 660 V

(2). 1320 V

(3). 1520 V

(4). 1980 V

32. A radioactive nucleus \({}^{A}_{z}X\) undergoes spontaneous decay inthe sequence
\({}^{A}_{z}X \, \rightarrow \, {}_{z-1}B \, \rightarrow \, {}_{z-3}C \, \rightarrow \, {}_{z-2}D\) where Z is the atomic number of element X. The possible decay particles in the sequence are

(1). \(\alpha,\, \beta^-,\, \beta^+\)

(2). \(\alpha,\, \beta^+,\, \beta^-\)

(3). \(\beta^+,\, \alpha,\, \beta^-\)

(4). \(\beta^-,\, \alpha,\, \beta^+\)

33. The half-life of a radioactive nuclide is 100 h. The fraction of original activity that will remainafter 150 h would be

(1). \(\displaystyle \frac{1}{2}\)

(2). \(\displaystyle \frac{1}{2 \sqrt{2}}\)

(3). \(\displaystyle \frac{2}{3}\)

(4). \(\displaystyle \frac{2}{3 \sqrt{2}}\)

34. A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the binding energyin the process is

(1). 0.9 MeV

(2). 9.4 MeV

(3). 804 MeV

(4). 216 MeV

35. A cup of coffee cools from \(90^\circ C\) to \(80^\circ C\) in t minutes, when the room temperature is \(20^\circ C\). The time taken by a similar cup of coffee to cool from \(80^\circ C\) to \(60^\circ C\) at a room temperature same at \(20^\circ C\) is

(1). \(\displaystyle \frac{5}{13}\, t\)

(2). \(\displaystyle \frac{13}{10}\, t\)

(3). \(\displaystyle \frac{13}{5}\, t\)

(4). \(\displaystyle \frac{10}{13}\, t\)

36. A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 Kg is suspended by it is

(1). 0.628 S

(2). 0.0628 S

(3). 6.28 S

(4). 3.14 S