In a vernier callipers, each \(cm\) on the main scale is divided into \(20\) equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be \(\dots \; \times 10^{-2} \;mm\)

The length of a seconds pendulum at a height \(h=2 R\) from earth surface will be _______. (Given: \(R =\) Radius of earth and acceleration due to gravity at the surface of earth \(g =\pi^{2}\,m / s ^{-2}\) )

Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the \(n^{th}\) orbital will therefore be proportional to

The half life period of radioactive element \({x}\) is same as the mean life time of another radioactive element \(y.\) Initially they have the same number of atoms. Then:

A bus moving along a straight highway with speed of \(72 \mathrm{~km} / \mathrm{h}\) is brought to halt within \(4 \mathrm{~s}\) after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is __________\(\mathrm{m}\).

A person is swimming with a speed of \(10\, m /s\) s at an angle of \(120^{\circ}\) with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is \('x'\) \(m / s\). The value of \('x'\) to the nearest integer is ..............

A transformer consisting of \(300\) turns in the primary and \(150\) turns in the secondary gives output power of \(2.2\, kW\). If the current in the secondary coils is \(10\, A\), then the input voltage and current in the primary coil are

A wire of length \(10 \mathrm{~cm}\) and radius \(\sqrt{7} \times 10^{-4} \mathrm{~m}\) connected across the right gap of a meter bridge. When a resistance of \(4.5 \ \Omega\) is connected on the left gap by using a resistance box, the balance length is found to be at \(60 \mathrm{~cm}\) from the left end. If the resistivity of the wire is \(\mathrm{R} \times 10^{-7} \Omega \mathrm{m}\), then value of \(\mathrm{R}\) is :

The first three spectral lines of \(H\) -atom in the Balmer series are given \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) considering the Bohr atomic model, the wave lengths of first and third spectral lines \(\left(\frac{\lambda_{1}}{\lambda_{3}}\right)\) are related by a factor of approximately 'x' \(\times 10^{-1}\). The value of \(x\), to the nearest integer, is

The electric potential at the centre of two concentric half rings of radii \(R_1\) and \(R_2\), having same linear charge density \(\lambda\) is

A convex lens of focal length \(40 \mathrm{~cm}\) forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length \(20 \mathrm{~cm}\). The photoelectric current now is: