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1. Dimensions of stress are :

(1). [M L2 T −2]

(2). [M L0 T −2]

(3). [M L−1 T −2]

(4). [M L T −2]

2. Taking into account of the significant figures, what is the value of 9.99 m − 0.0099 ?

(1). 9.98 m

(2). 9.980 m

(3). 9.9 m

(4). 9.9801 m

3. A screw gauge has least count of 0.01 mathrm mm and there are 50 divisions in its circular scale. Thepitch of the screw gauge is :

(1). 0.25mm

(2). 0.5mm

(3). 1.0mm

(4). 0.01mm

4. A ball is thrown vertically downward with a velocity of 20m ∕ s from the top of a tower. It hits the ground after some time with a velocity of 80m ∕ s The height of the tower is : (g = 10m ∕ s2)

(1). 340m

(2). 320m

(3). 300m

(4). 360m

5. A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L1 when mass M is suspended from its free end. The expression for Young's modulus is :

(1). \(\frac{M g\left(L_1 - L\right)}{AL}\)

(2). \(\frac{MgL}{AL_1}\)

(3). \(\frac{M gL}{A\left(L_1 - L\right)}\)

(4). \(\frac{MgL_1}{AL}\)

6. A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :

(1). 5.0 g

(2). 10.0 g

(3). 20.0 g

(4). 2.5 g

7. A wire of length L, area of cross-section A is hanging from a fixed support. The length of the wire changes to L1 when mass M is suspended from its free end. The expression for Young’s modulus is

(1). \(\frac{Mg\left(L_1 - L\right)}{AL}\)

(2). \(\frac{MgL}{AL_1}\)

(3). \(\frac{MgL}{A\left(L_1-L\right)}\)

(4). \(\frac{MgL_1}{AL}\)

8. The phase difference between displacement and acceleration of aparticle in a simple harmonic motion is:

(1). \(\frac{3π}{2}\) rad

(2). \(\frac{π}{2}\) rad

(3). \(zero\)

(4). \(π\, rad\)

9. In a guitar, two strings \(A\) and \(B\) made of same material are slightly out of tune and produce beats of frequency \(6\,Hz\). When tension in \(B\) is slightly decreased, the beat frequency increases to \(7\,Hz\). If the frequency of \(A\) is \(530\,Hz\), the original frequency of \(B\) will be

(1). \(524\,Hz\)

(2). \(536\,Hz\)

(3). \(537\,Hz\)

(4). \(523\,Hz\)

10. A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is: (µ0 = 4π × 10−7T mA−1)

(1). 3.14 × 10−4T

(2). 6.28 × 10−5T

(3). 3.14 × 10−5T

(4). 6.28 × 10−4T

11. A body weighs \(72\,N\) on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

(1). \(32\,N\)

(2). \(30\,N\)

(3). \(24\,N\)

(4). \(48\,N\)

12. A 40μ F capacitor is connected to a 200V , 50H z ac supply. The rms value of the current in the circuit is, nearly:

(1). 2.05A

(2). 2.5A

(3). 25.1A

(4). 1.7A

13. A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is π/3. If instead C is removed from the circuit, the phase difference is again π/3 between current and voltage. The power factor of the circuit is:

(1). 0.5

(2). 1.0

(3). -1.0

(4). zero

14. A spherical conductor of radius 10 cm has a charge of \(3.2 × 10_{−7} C\) distributed uniformly. What is the magnitude of electric field at a point 15cm from the centre of the sphere? ( \(1 ∕ 4π \epsilon_0 = 9 × 10^9 N m^2/C^2\))

(1). \(1.28 × 10^5\,N ∕ C \)

(2). \(1.28 × 10^6\, N ∕ C \)

(3). \(1.28 × 10^7\, N ∕ C \)

(4). \(1.28 × 10^4\ ,N ∕ C \)

15. In a certain region of space with volume 0.2 m3, the electric potential is found to be 5V throughout. The magnitude of electric field in this region is:

(1). 0.5N ∕ C

(2). 1N ∕ C

(3). 5N ∕ C

(4). zero

16. A short electric dipole has a dipole moment of 16 × 10−9Cm. The electric potential due to the dipole at a point at a distance of 0.6m from the centre of the dipole, situated on a line making an angle of \(60^\circ\) with the dipole axis is : \(\left(\frac{1}{4πϵ0} = 9 × 10^9 Nm^2/C^2\right)\)

(1). 200V

(2). 400V

(3). zero

(4). 50V

17. The capacitance of a parallel plate capacitor with air as medium is 6µF . With the introduction of a dielectric medium, the capacitance becomes 30µF. The permittivity of the medium is:
(\(E_0 = 8.85 × 10^{−12}\,C^2N^{−1}m^{−2}\))

(1). \( 1.77×10^{−12}\, C^2N^{−1}m^{−2}\)

(2). \(0.44×10^{−10}\, C^2N^{−1}m^{−2}\)

(3). \(5.00\, C^2 N^{−1}m^{−2}\)

(4). \(0.44×10^{−13}\, C^2N^{−1}m^{−2}\)

18. Assume that light of wavelength 600 nm is coming from a star. The limit of resolution of telescope whose objective has a diameter of 2 m is

(1). \(1.83 \times 10^{-7}\) rad

(2). \(7.32 \times 10^{-7}\) rad

(3). \(6.00 \times 10^{-7}\) rad

(4). \(3.66 \times 10^{-7}\) rad

19. A ray is incident at an angle of incidence i on one surface of a small angle prism (with angle of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is \(\mu\), then the angle of incidence is nearly equal to

(1). \(\displaystyle \frac{2\, \text{A}}{\mu}\)

(2). \(\mu \text{A}\)

(3). \(\displaystyle \frac{\mu \, \text{A}}{2}\)

(4). \(\displaystyle \frac{\text{A}}{2\,\mu}\)

20. Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass.The centre of mass of the system from the 5 kg particle is nearly at a distance of

(1). 50 cm

(2). 67 cm

(3). 80 cm

(4). 33 cm

21. Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is

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

(2). \(\displaystyle \frac{g}{5}\)

(3). \(\displaystyle \frac{g}{10}\)

(4). \(g\)

22. In Young's double slit experiment, if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes

(1). half

(2). four times

(3). one-fourth

(4). double

23. Light with an average flux of \(20\, \text{W}/cm^2\) falls on a non-reflecting surface at normal incidence having surface area \(20\,cm^2\). The energy recieved by the surface during time span of 1 minute is

(1). \(12 \times\ 10^3\) J

(2). \(24 \times\ 10^3\) J

(3). \(48 \times\ 10^3\) J

(4). \(10 \times\ 10^3\) J

24. The quantities of heat required to raise the temperarture of two solid copper spheres of radii \(r_1\) and \(r_2\) (\(r_1\,=\,1.5\,r_2\)) through 1 K are in the ratio

(1). 9/5

(2). 3/2

(3). 5/3

(4). 27/8

25. Find the torque about the origin when a force of \(3\, \hat{j}\, \text{N}\) acts on a particle whose position vector is \(2\, \hat{k}\, m\).

(1). \(6\, \hat{j}\, \text{Nm}\)

(2). \(-6\, \hat{i}\, \text{Nm}\)

(3). \(6\, \hat{k}\, \text{Nm}\)

(4). \(6\, \hat{i}\, \text{Nm}\)

26. The Brewsters angle \(i_b\) for an interface should be

(1). \(30^\circ\, <\, i_b\, <\, 45^\circ\)

(2). \(45^\circ\, <\, i_b\, <\, 90^\circ\)

(3). \( i_b\, =\, 90^\circ\)

(4). \(0^\circ\, <\, i_b\, <\, 30^\circ\)

27. The energy required to break one bond in DNA is \(10^{-20}\, \text{J}\). This value in eV is nearly

(1). 0.6

(2). 0.06

(3). 0.006

(4). 6