The workdone in an adiabatic change in an ideal gas depends upon only :

An inductor of reactance \(100 \Omega\), a capacitor of reactance \(50 \Omega\), and a resistor of resistance \(50 \Omega\) are connected in series with an AC source of 10 V , 50 Hz. Average power dissipated by the circuit is ________ W.

A balloon is moving up in air vertically above a point \(A\) on the ground. When it is at a height \(h _{1},\) a girl standing at a distance \(d\) (point \(B\) ) from \(A\) (see figure) sees it at an angle \(45^{\circ}\) with respect to the vertical. When the balloon climbs up a further height \(h _{2},\) it is seen at an angle \(60^{\circ}\) with respect to the vertical if the girl moves further by a distance \(2.464\, d\) (point \(C\) ). Then the height \(h _{2}\) is (given tan \(\left.30^{\circ}=0.5774\right)\)\(.......\)

In the given circuit, rms value of current \(\left( I _{ rms }\right)\) through the resistor \(R\) is :\(..........\,A\)

If mass is written as \(\mathrm{m}=\mathrm{kc}^{\mathrm{p}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}\) then the value of \(P\) will be _______. (Constants have their usual meaning with \(\mathrm{k}\) a dimensionless constant)

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm , at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :

The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of \(176 rad / s\). The frequency of this simple harmonic oscillator is _________ Hz. \(\left[\right.\) take \(\left.\pi=\frac{22}{7}\right]\)

Match Column\(-I\) with Column\(-II :\) Choose the correct answer from the options given below:

Two ideal electric dipoles \(A\) and \(B\) having their dipole moment \(p_{1}\) and \(p_{2}\) respectively are placed on a plane with their centres at \(O\) as shown in the figure. At point \(C\) on the axis of dipole \(A\), the resultant electric field is making an angle of \(37^{\circ}\) with the axis. The ratio of the dipole moment of \(A\) and \(B, \frac{P_{1}}{P_{2}}\) is \(....\) (take \(\left.\sin 37^{\circ}=\frac{3}{5}\right)\)

A ball is dropped from the top of a \(100\; m\) high tower on a planet. In the last \(\frac{1}{2}\;s \) before hitting the ground, it covers a distance of \(19\; \mathrm{m}\). Acceleration due to gravity (in \(\mathrm{ms}^{-2}\) ) near the surface on that planet is

A mixture of carbon dioxide and oxygen has volume \(8310\) cm\(^3\), temperature \(300\) K, pressure \(100\) kPa and mass \(13.2\) g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are _______.
(Assume both carbon dioxide and oxygen gases behave like ideal gases) \([R = 8.31\) J/mol.K\(]\)

\(UV\) light of \(4.13 \mathrm{eV}\) is incident on a photosensitive metal surface having work function \(3.13 \mathrm{eV}\). The maximum kinetic energy of ejected photoelectrons will be _______.

In a photoelectric effect experiment a light of frequency \(1.5\) times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons emitted will be _______.