A batsman hits back a ball of mass \(0.4 \; kg\) straight in the direction of the bowler without changing its initial speed of \(15 \; ms ^{-1}\). The impulse imparted to the ball is \(\dots \; Ns\)

A steel rod with \({y}=2.0 \times 10^{11} \,{Nm}^{-2}\) and \(\alpha=10^{-5}{ }^{\circ} {C}^{-1}\) of length \(4\, {m}\) and area of cross-section \(10\, {cm}^{2}\) is heated from \(0^{\circ} {C}\) to \(400^{\circ} {C}\) without being allowed to extend. The tension produced in the rod is \({x} \times 10^{5} \, {N}\) where the value of \({x}\) is ....... .

The acceleration due to gravity on the earth's surface at the poles is \(g\) and angular velocity of the earth about the axis passing through the pole is \(\omega .\) An object is weighed at the equator and at a height \(h\) above the poles by using a spring balance. If the weights are found to be same, then \(h\) is \(:( h << R ,\) where \(R\) is the radius of the earth)

A straight wire \(AB\) of mass \(40\,g\) and length \(50\,cm\) is suspended by a pair of flexible leads in uniform magnetic field of magnitude \(0.40\,T\) as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ...........\(A\). (Take \(g=10\,ms ^{-2}\) ).

The average kinetic energy of a molecule of the gas is

A point light source emits E.M. waves in free space. A detector, placed at a distance of \(L\) m, measures the intensity as \(I_o\). The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as \(45°\). The measured intensity at new location will be _______.

The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is \(915\)\(A\). The longest wavelength of spectral lines in the Balmer series will be _______ \(A\).

When a dc voltage of \(100 \mathrm{~V}\) is applied to an inductor, a dc current of \(5 \mathrm{~A}\) flows through \(1\) . When an ac voltage of \(200 \mathrm{~V}\) peak value is connected to inductor, its inductive reactance is found to be \(20 \sqrt{3} \Omega\). The power dissipated in the circuit is _______\(W\).

Two sides of a parallelogram are along the lines, \(x + y = 3\) and \(x -y + 3 = 0\). If its diagonals intersect at \((2, 4)\), then one of its vertex is

A value of \(x\) for which \(\sin \,\left( {{{\cot }^{ - 1}}\,\left( {1 + x} \right)} \right) = \cos \,\left( {{{\tan }^{ - 1}}\,x} \right)\), is

Suppose \(f ( x )\) is a polynomial of degree four, having critical points at \(-1,0,1\) . If \(T =\{ x \in R \mid f ( x )= f (0)\},\) then the sum of squares of all the elements of \(T\) is

In a Vernier Calipers. \(10\) divisions of Vernier scale is equal to the \(9\) divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of \(zero\) of the main scale and \(4^{\text {th }}\) Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to \(1\,mm\). While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between \(30\) and \(31\) divisions of main scale reading and \(6^{\text {th }}\) Vernier scale division exactly. coincides with the main scale reading. The diameter of the spherical body will be \(.......cm\)

A sample of gas with \(\gamma=1.5\) is taken through an adiabatic process in which the volume is compressed from \(1200\, {cm}^{3}\) to \(300\, {cm}^{3}\). If the initial pressure is \(200\, {kPa}\). The absolute value of the workdone by the gas in the process \(= \,..... J.\)