7 moles of a tetra-atomic non-linear gas A at 10 atm and T K are mixed with 6 moles of another gas B at T/3K and 5atm in a closed, rigid vessel without energy transfer with surroundings. If final temperature of mixture was 5T/6K, then atomcity of gas B is (Assuming all modes of energy are active)

1) 1
2) 4
3) 2
4) 3

In a good conductor the energy gap between the conduction band and valence band is:

(1) Wide
(2) Infinite
(3) Zero
(4) Narrow

The maximum speed at which a car can turn around a curve of 20m radius on a level road if the coefficient of friction between the tyres and the road is 0.4, is

1) 10.26 m/s
2) 8.85 m/s
3) 9.16 m/s
4) 11.22 m/s

Two solid spheres of iron have their radii in the ratio 2:1 . Then ratio of the moments of inertia about their diameters is :

1) 4:1
2) 8:1
3) 16:1
4) 32:1

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R ? 

$$\begin{array}{1 1} (1)\;\large\frac{5GmM}{6R}\\ (2)\;\large\frac{2GmM}{3R} \\ (3)\;\large\frac{GmM}{2R}\\ (4)\;\large\frac{GmM}{3R}\end {array}$$

The magnification of an object placed in front of a convex lens of focal length 20 cm is is +2. To obtain a magnification of -2, The object has to be moved a distance equal to:

1) 10 cm
2) 20 cm
3) 30 cm
4) 40 cm

A bus moving on a level road with a velocity $$V$$ can be stopped at a distance of $$x$$, by the application of a retarding force $$F$$. The load on the bus is increased by $$25\%$$ by boarding the passengers. Now, if the bus is moving with the same speed and if the same retarding force is applied, the distance travelled by the bus before it stops is:

1) x
2) 1.25x
3) 5x
4) 2.5x

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)$$\displaystyle zero$$

The 6563 ?A Hα line emitted by hydrogen in a star is found to be red-shifted by 15 A?. Estimate the speed with which the star is receding from the Earth.

1) 68.6×10⁵ms−1
2) 2.86×10⁵ms⁻¹
3) 6.86×10⁵ms−1
4) 1.86×10⁵ms−1

 A uniform ladder in static equilibrium leans against a frictionless wall. The ladder has length L and mass M. Given that the angle between the ladder and floor is 30^o degrees, what would be the value of the coefficient of static friction (µs) between the ladder and the ground?

1) µs ≥ 1/ Ö3

2) µs ≥ 2/ Ö3

3) µs ≥  Ö3 / 2

4) µs ≥  1/ 2