A radioactive sample has a half-life of \(10 \mathrm{~min}\). If 64 nuclei are contained in the sample the number of nuclei that would decay after, \(50 \mathrm{~min}\) is

An ideal gas is expanding such that \(P T^2=\) constant. The coefficient of volume expansion of the gas is

In a single slit diffraction experiment, for slit width '\(\alpha\)' the width of the central maxima is '\(\beta\)'. If we double the slit width then the corresponding width of the central maxima will be:

A proton is moving along negative X axis. If a uniform magnetic field is applied parallel to the positive Z axis, then choose the correct answer from the following options;
1. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XY plane
2. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XY plane
3. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XZ plane
4. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XZ plane

Blowing air with open mouth is an example of

In the energy band diagram of a material shown below, open circles and filled circles denote holes and electrons respectively. The material is a

For a paramagnetic material, the dependence of the magnetic susceptibility \(\chi\) on the absolute temperature is given as

A pan filled with hot food cools from \(94^{\circ} \mathrm{C}\) to \(86^{\circ} \mathrm{C}\) in \(2 \mathrm{~min}\), when the room temperature is \(20^{\circ} \mathrm{C}\). The time taken for the food to cool from \(86^{\circ} \mathrm{C}\) to \(74^{\circ} \mathrm{C}\) will be

The line joining two points \(A(2,0) B(3,1)\) is rotated about \(A\) in anticlockwise direction through an angle of \(15^{\circ}\). If \(B\) goes to \(C\) in the new position, then the coordinates of \(C\) is

Three long straight wires \(A, B\) and \(C\) are carrying currents as shown in figure, then the resultant force on \(B\) is directed

\(\int \sqrt{x} e^{\sqrt{x}} d x\) is equal to

A charge \(10 \mathrm{nC}\) is situated in a medium of relative permittivity 10 . The potential due to this charge at a distance of \(0.1 \mathrm{~m}\) is

Find the geometric progression for which the sum of the first two terms is -4, the fifth term is four times the third term and common ratio is less than zero