If one mole of the polyatomic gas is having two vibrational modes and \(\beta\) is the ratio of molar specific heats for polyatomic gas \(\left(\beta=\frac{ C _{ P }}{ C _{ v }}\right)\) then the value of \(\beta\) is:

Two resistors \(2 \Omega\) and \(3 \Omega\) are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire XY . When an unknown resistor is connected in parallel with \(3 \Omega\) resistor, the null point is shifted by 22.5 cm toward Y . The resistance of unknown resistor is _________ \(\Omega\).

A convex lens of focal length \(20\, cm\) produces images of the same magnification \(2\) when an object is kept at two distances \(x_1\) and \(x_2\) \((x_1 > x_2)\) from the lens. The ratio of \(x_1\) and \(x_2\) is

Match List - I with List - II.

List - I	List - II
(A) Magnetic induction	(I) Ampere meter2
(B) Magnetic intensity	(II) Weber
(C) Magnetic flux	(III) Gauss
(D) Magnetic moment	(IV) Ampere meter

Choose the correct answer from the options given below :

In an open organ pipe \(v_3\) and \(v_6\) are \(3^{\text {rd }}\) and \(6^{\text {th }}\) harmonic frequencies, respectively.
If \(v_6-v_3=2200 \) Hz then length of the pipe is ______ mm.
(Take velocity of sound in air is 330 m/s.)

An \(LCR\) circuit contains resistance of \(110 \, \Omega\) and a supply of \(220\, V\) at \(300 \,rad / s\) angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by \(45^{\circ}\). If on the other hand, only inductor is removed the current leads by \(45^{\circ}\) with the applied voltage. The rms current flowing in the circuit will be ...... \(A\)

A sand dropper drops sand of mass \(m(t)\) on a conveyer belt at a rate proportional to the square root of speed \((v)\) of the belt, i.e. \(\frac{\mathrm{dm}}{\mathrm{dt}} \propto \sqrt{v}\). If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

A point charge of \(10^{-8} C\) is placed at origin. The work done in moving a point charge \(2 \mu C\) from point \(A (4,4,2) m\) to \(B (2,2,1) m\) is _________ J.

If \(\epsilon_0\) denotes the permittivity of free space and \(\Phi_{\mathrm{E}}\) is the flux of the electric field through the area bounded by the closed surface, then dimension of \(\left(\epsilon_0 \frac{\mathrm{~d} \phi_{\mathrm{E}}}{\mathrm{dt}}\right)\) are that of :

In a car race on straight road, car \(A\) takes a time \(t\) less than car \(B\) at the finish and passes finishing point with a speed \(v\) more than that of car \(B.\) Both the cars start from rest and travel with constant acceleration \(a_1\) and \(a_2\) respectively. Then \(v\) is equal to