A vessel contains \(16 \,g\) of hydrogen and \(128 \,g\) of oxygen at standard temperature and pressure. The volume of the vessel in \(cm ^{3}\) is

If a source of electromagnetic radiation having power \(15 kW\) produces \(10^{16}\) photons per second, the radiation belongs to a part of spectrum is.(Take Planck constant \(h =6 \times 10^{-34}\,Js\) )

A disc is rolling without slipping on a surface. The radius of the disc is \(R\). At \(t=0\), the top most point on the disc is \(A\) as shown in figure. When the disc completes half of its rotation, the displacement of point \(A\) from its initial position is

A helicopter is flying horizontally with a speed \('v'\) at an altitude \('{h}'\) has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

The position vector of a moving body at any instant of time is given as \(\vec{r}=\left(5 t^2 \hat{i}-5 t \hat{j}\right) \mathrm{m}\). The magnitude and direction of velocity at \(t=2 \mathrm{~s}\) is,

A square aluminium (shear modulus is \(25 \times 10^{9}\,Nm ^{-2}\) ) slab of side \(60\,cm\) and thickness \(15\,cm\) is subjected to a shearing force (on its narrow face) of \(18.0 \times 10^{4}\,N\). The lower edge is riveted to the floor. The displacement of the upper edge is \(.......\mu\,m\).

Following figure shows two processes \(A\) and \(B\) for a gas. If \(\Delta Q_A\) and \(\Delta Q_B\) are the amount of heat absorbed by the system in two cases, and \(\Delta U_A\) and \(\Delta U_B\) are changes in internal energies, respectively, then

As shown in the figure. a configuration of two equal point charges \(\left( q _0=+2 \mu C \right)\) is placed on an inclined plane. Mass of each point charge is \(20\,g\). Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height \(h = x \times 10^{-3}\,m\) The value of \(x\) is \(..........\).(Take \(\left.\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\,Nm ^2 C ^{-2}, g=10\,ms ^{-1}\right)\)

In the below circuit the current in each resistance is

When a certain photosensitive surface is illuminated with monochromatic light of frequency \(v\) , the stopping potential for the photo current is \(-V_0/2.\) When the surface is illuminated by monochromatic light of frequency \(v/2,\) the stopping potential is \(-V_0.\) The threshold frequency for photoelectric emission is

Given below are two statement  Statement \(-I\) : What \(\mu\) amount of an ideal gas undergoes adiabatic change from state \(\left( P _{1}, V _{1}, T _{1}\right)\) to state \(\left( P _{2}, V _{2}, T _{2}\right)\), the work done is \(W =\frac{1 R \left( T _{2}- T _{1}\right)}{1-\gamma}\), where \(\gamma=\frac{ C _{ P }}{ C _{ V }}\) and \(R =\) universal gas constant, Statement \(-II\) : In the above case. when work is done on the gas. the temperature of the gas would rise. Choose the correct answer from the options given below