An ideal gas is expanding such that \({PT}^{3}=\) constant. The coefficient of volume expansion of the gas is:

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is \(R_0= 10\, m\). What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity \(v = 20\, m/s\), on a horizontal surface ......... \(^o.\) \((g = 10\, m/s^2)\)

In the given figure, the \(emf\) of the cell is \(2.2\, {V}\) and if internal resistance is \(0.6\, \Omega\). Calculate the power dissipated in the whole circuit: (in \(W\))

Match the List-I with List-II

	List-I		List-II
A.	Magnetic induction	I.	\(M L T ^{-2} A^{-2}\)
B.	Magnetic flux	II.	\(ML ^2 T^{-2} A^{-2}\)
C.	Magnetic permeability	III.	\(ML ^0 T^{-2} A^{-1}\)
D.	Self inductance	IV.	\(ML ^2 T^{-2} A^{-1}\)

Choose the correct answer from the options given below:

A stone tide to a string of length \(L\) is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed \(u\). The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is \(\sqrt{ x \left( u ^{2}- gL \right)}\). The value of \(x\) is .............

Two \(4\) bits binary numbers, \(A = 1101\) and \(B = 1010\) are given in the inputs of a logic circuit shown in figure below. The output \((Y)\) will be:

Which one of the following is the correct dimensional formula for the capacitance in F ? \(\mathrm{M}, \mathrm{L}, \mathrm{T}\) and C stand for unit of mass, length, time and charge,

The stream of a river is flowing with a speed of \(2\,km/h.\) A swimmer can swim at a speed of \(4\,km/h.\) ....... \(^o\) should be the direction of the swimmer with respect to the flow of the river to cross the river straight .

Match the List-I with List-II

List - I	List - II
(A) Triatomic rigid gas	(I) \(\frac{C_P}{C_V} = \frac{5}{3}\)
(B) Diatomic non-rigid gas	(II) \(\frac{C_P}{C_V} = \frac{7}{5}\)
(C) Monoatomic gas	(III) \(\frac{C_P}{C_V} = \frac{4}{3}\)
(D) Diatomic rigid ga	(IV) \(\frac{C_P}{C_V} = \frac{9}{7}\)

Choose the correct answer from the options given below :

A 4 kg mass moves under the influence of a force \(\vec{F}=\left(4 t^3 \hat{i}-3 t \hat{j}\right) N\) where \(t\) is the time in second. If mass starts from origin at \(t=0\), the velocity and position after \(t=2 s\) will be :

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal place: \((i)\) a ring of radius \(R,\,(ii)\) a solid cylinder of radius \(\frac {R}{2}\)  nd \((iii)\) a solid sphere of radius \(\frac {R}{4}.\) If, in each case, the speed of the center of mass at bottom of the incline is same, the ratio of the maximum heights they climb is