For \(a\) gas \(C_{p}-C_{V}=R\) in a state \(P\) and \(C_{p}-C_{V}=1.10 R\) in a state \(Q, T_{p}\) and \(T_{Q}\) are the temperatures in two different states \(P\) and \(Q\) respectively. Then

An object is placed at a distance of \(12\,cm\) in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by \(4\,cm\) towards the stationary object. The distance by which the position of image would be shifted, will be:

A travelling harmonic wave is represented by the equation \(y(x, t) = 10^{-3}\,sin\,(50t + 2x)\), where \(x\) and \(y\) are in meter and \(t\) is in seconds. Which of the following is a correct statement about the wave?

An observer looks at a distant tree of height \(10\ m\) with a telescope of magnifying power of \(20\). To the observer the tree appears :

If the distance of the earth from Sun is \(1.5 \times 10^6\,km\). Then the distance of an imaginary planet from Sun, if its period of revolution is \(2.83\) years is \(.............\times 10^6\,km\)

The angular momentum of a planet of mass \(M\) moving around the sun in an elliptical orbit is \(\overrightarrow{ L }\). The magnitude of the areal velocity of the planet is:

Given below are two statements: Statements \(I:\) The temperature of a gas is \(-73^{\circ}\,C\). When the gas is heated to \(527^{\circ}\,C\), the root mean square speed of the molecules is doubled. Statement \(II:\) The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below :

Two projectiles are projected with the same initial velocities at the \(15^\circ\) and \(30^\circ\) with respect to the horizontal. The ratio of their ranges is \(1:x\). The value of \(x\) is:

Seawater at a frequency \(f =9 \times 10^{2} \,Hz ,\) has permittivity \(\varepsilon=80\, \varepsilon_{0}\) and resistivity \(\rho=0.25\, \Omega m.\) Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source \(V ( t )= V _{0} \sin (2 \pi ft ) .\) Then the conduction current density becomes \(10^{x}\) times the displacement current density after time \(t =\frac{1}{800} \,s\). The value of \(x\) is ......... .
\(\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}\right)\)

Two vectors \(\overrightarrow{{X}}\) and \(\overrightarrow{{Y}}\) have equal magnitude. The magnitude of \((\overrightarrow{{X}}-\overrightarrow{{Y}})\) is \({n}\) times the magnitude of \((\overrightarrow{{X}}+\overrightarrow{{Y}})\). The angle between \(\overrightarrow{{X}}\) and \(\overrightarrow{{Y}}\) is -

Given below are two statements :- Statement \(I\) : Davisson-Germer experiment establishes the wave nature of electrons. Statement \(II\) : If electrons have wave nature, they can interfere and show diffraction. In the light of the above statements choose the correct answer from the options given below

A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be

\(ABC\) is a plane lamina of the shape of an equilateral triagnle. \(D,\) \(E\) are mid points of \(AB\), \(AC\) and \(G\) is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through \(G\) and perpendicular to the plane \(ABC\) is \(I _{0} .\) If part \(ADE\) is removed, the moment of inertia of the remaining part about the same axis is \(\frac{ NI _{0}}{16}\) where \(N\) is an integer. Value of \(N\) is