A uniform wire of resistance 12Ω  is bent in the form of a square. A cell of emf 6 V having negligible internal resistance connected across the diagonal of the square. The magnetic induction at its centre is (in T)

1) 0
2) 10^−7?
3) 5×10⁻⁷
4) $$\dfrac{\mu _{0}}{4\pi }\times 5\times 10^{-7}$$

In the basic $$\displaystyle CsCl$$ crystal structure, $$\displaystyle { Cs }^{ + }$$ and $$\displaystyle { Cl }^{ - }$$ ions are arranged in a bcc configuration as shown in the figure. The net electrostatic force exerted by the eight $$\displaystyle { Cs }^{ + }$$ ions on the $$\displaystyle { Cl }^{ - }$$ ion is : 

1) $$\displaystyle \frac { 1 }{ 4\pi { \varepsilon }_{ 0 } } \frac { 4{ e }^{ 2 } }{ 3{ a }^{ 2 } } $$

2) $$\displaystyle \frac { 1 }{ 4\pi { \varepsilon }_{ 0 } } \frac { 16{ e }^{ 2 } }{ 3{ a }^{ 2 } } $$

3) $$\displaystyle \frac { 1 }{ 4\pi { \varepsilon }_{ 0 } } \frac { 32{ e }^{ 2 } }{ 3{ a }^{ 2 } } $$

4)$$\displaystyle zero$$

An open container has net 10 gm mass of a radioactive material. The net mass in the container after two mean lives is approximately:

1) 1.35 gm
2) 2.5 gm
3) 10 gm
4) 5 gm

 Two satellites A and B of the same mass are going around the earth in concentric orbits. The distance of satellite B from earth’s center is twice that of satellite A. What is the ratio of the speed of B to that of A?

1. ½

2. 1/Ö2

A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the  cylinder above the piston is ?1, and that below the piston is ?2 , such that ?1 > ?2 . Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, mm, will be given by :

(R is universal gas constant and g is the acceleration due to gravity)

1) $$\dfrac{nRT}{g} \left[\dfrac{1}{\ell_2} + \dfrac{1}{\ell_1}\right]$$
2) $$\dfrac{nRT}{g} \left[\dfrac{\ell_1 - \ell_2}{\ell_1\ell_2} \right]$$
3) $$\dfrac{RT}{g} \left[\dfrac{2\ell_1 + \ell_2}{\ell_1\ell_2} \right]$$
4) $$\dfrac{RT}{g} \left[\dfrac{\ell_1 - 3\ell_2}{\ell_1\ell_2} \right]$$

A transmitter transmits at a wavelength of 300m A condenser of capacitance 2.4μF is being used. The value of the inductance for the resonant circuit is approximately

1) 10⁻⁴ H
2) 10⁻⁶ H
3) 10⁻⁸ H
4) 10⁻¹⁰ H

If the ratio of amplitude of two superposed waves is 2:1, then the ratio of maximum intensity and minimum intensity is

1) 9:1
2) 1:9
3) 4:1
4) 1:4

In Young's double slit experiment, the fringe width is $$1\times 10^{-4}m$$, if the distance between the slit and screen is doubled and the distance between two slits is reduced to half and the wavelength is changed from $$6.4\times 10^{-7}m$$ to $$4.0\times 10^{-7}m$$, then the value of new fringe width will be

1) $$2.5\times 10^{-4} m$$
2) $$2.0\times 10^{-4} m$$
3) $$1\times 10^{-4} m$$
4) $$0.5\times 10^{-4} m$$

The hydrostatic pressure on the dam wall at the bottom of a deep reservoir depends upon the
 
 (1) Depth of the water
 (2) Surface area of the water
 (3) Length of the reservoir
 (4) Thickness of the wall

In terms of Rydberg constant R, the shortest wavelength in Balmer series of hydrogen atom spectrum will have wavelength:

(1) 3/2 R
(2) 9/4 R
(3) 1/R
(4) 4/R