A cylinder of fixed capacity of \(44.8 \,litres\) contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by \(20.0^{\circ} C\) will be ..............  \(J\)(Given gas constant \(R =8.3 \,JK ^{-1}- moI ^{-1}\) )

A paramagnetic sample shows a net magnetisation of \(6 \,A / m\) when it is placed in an external magnetic field of \(0.4 \,T\) at a temperature of \(4\, K\). When the sample is placed in an external magnetic field of \(0.3\, T\) at a temperature of \(24\, K\), then the magnetisation will be\(......A/m\)

The percentage errors in quantities \(P, Q, R\)  and \(S\)  are \(0.5\%,\,1\%,\,3\%\)  and  \(1 .5\%\) respectively in the  measurement of a physical quantity \(A\, = \,\frac{{{P^3}{Q^2}}}{{\sqrt {R}\,S }}\) . the maximum percentage error in the value of \(A\)  will be ........... \(\%\)

When the position vector \(\overrightarrow{ r }=x \hat{ i }+y \hat{ j }+z \hat{ k }\) changes sign as \(-\overrightarrow{ r }\), which one of the following vector will not flip under sign change ?

In Young's double slit experiment, the distance between slits and the screen is \(1 .0\,\,m\) and monochromatic light of \(600\,\,nm\)  is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance \(d_0\) between the slits . If the angular resolution of the eye is \(\frac {1}{60}^o,\) the value of \(d_0\)  is close to......\(mm\)

Escape velocity of a body from earth is \(11.2 \mathrm{~km} / \mathrm{s}\). If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is _______.

An ideal gas is expanding such that \({PT}^{3}=\) constant. The coefficient of volume expansion of the gas is:

Consider a block kept on an inclined plane (inclined at \(45^{\circ}\) ) as shown in the figure. If the force required to just push it up the incline is \(2\) times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane \((\mu)\) is equal to

The energy required to ionise a hydrogen like ion in its ground state is \(9\) Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state ?  ........\(nm\)

A compass needle of oscillation magnetometer oscillates \(20\) times per minute at a place \(P\) of dip \(30^{\circ}\). The number of oscillations per minute become \(10\) at another place \(Q\) of \(60^{\circ} dip\). The ratio of the total magnetic field at the two places \(\left(B_{Q}: B_{p}\right)\) is.

A vernier callipers has \(20\) divisions on the vernier scale, which coincides with \(19^{\text {th }}\) division on the main scale. The least count of the instrument is \(0.1 \mathrm{~mm}\). One main scale division is equal to _______ \(\mathrm{mm}\).

A metallic conductor of length \(1\; m\) rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity \(5 \;rad / s\). If the horizontal component of earth's magnetic field is \(0.2 \times 10^{-4} \;T\), then emf induced between the two ends of the conductor is .............

A force of \(40\, N\) acts on a point \(B\) at the end of an \(L-\) shaped object, as shown in the figure. The angle \(\theta\) that will produce maximum moment of the force about point \(A\) is given by