A particle starts from the origin at time \(t = 0\) and moves along the positive \(x-\) axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time \(t = 5\,s\) ?.........\(m\)

A soap bubble of radius \(3\, {cm}\) is formed inside the another soap bubble of radius \(6\, {cm}\). The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is .......... \({cm}\) 

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy \(3\, {eV}\). The proton captures the electrons and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength \(4000\, \mathring {{A}}\). What is the maximum kinetic energy of the emitted photoelectron ? (In \({eV}\))

If Surface tension \((S)\), Moment of Inertia \((I)\) and Planck’s constant \((h)\), were to be taken as the fundamental units, the dimensional formula for linear momentum would be

A hemispherical vessel is completely filled with a liquid of refractive index \(\mu\). A small coin is kept at the lowest point \((\mathrm{O})\) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is _______.

The value closest to the thermal velocity of a Helium atom at room temperature \((300\,K)\)in \(ms^{-1}\) is \([k_B\, = 1 .4\times10^{-23}\,J/K;\, m_{He}\, = 7\times10^{-27}\,kg]\)

A bar magnet with a magnetic moment \(5.0\,Am ^2\) is placed in parallel position relative to a magnetic field of \(0.4\,T\). The amount of required work done in turning the magnet form parallel to antiparallel position relative to the field direction is \(.........\,J\)

Match List \(I\) with List \(II\) :

List \(I\) (Physical Quantity)	List \(II\) (Dimensional Formula)
\((A)\) Pressure gradient	\((I)\) \(\left[ M ^0 L ^2 T ^{-2}\right]\)
\((B)\) Energy density	\((II)\) \(\left[ M ^1 L ^{-1} T ^{-2}\right]\)
\((C)\) Electric Field	\((III)\) \(\left[ M ^1 L ^{-2} T ^{-2}\right]\)
\((D)\) Latent heat	\((IV)\) \(\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]\)

Choose the correct answer from the options given below:

An \(HCl\) molecule has rotational, translational and vibrational motions. If the \(rms\) velocity of \(HCl\) molecules in its gaseous phase is \(\bar v ,\,m\) is its mass and \(k_B\) is Boltzmann constant, then its temperature will be

Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\).

In young's double slit experiment, the fringe width is \(12\,mm\). If the entire arrangement is placed in water of refractive index \(\frac{4}{3}\), then the fringe width becomes \((in\,mm)\)

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as \(100\) Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by \(30^{\circ}\) in clockwise direction, the intensity of emerging light will be .......... Lumens.

A particle of mass \({m}\) is suspended from a ceiling through a string of length \(L\). The particle moves in a horizontal circle of radius \(r\) such that \({r}=\frac{{L}}{\sqrt{2}}\). The speed of particle will be: