If a radioactive element having half-life of \(30\,min\) is undergoing beta decay, the fraction of radioactive element remains undecayed after \(90\,min\). will be :

Distance between an object and three times magnified real image is 40 cm . The focal length of the mirror used is _________ cm .

When one light ray is reflected from a plane mirror with \(30^{\circ}\) angle of reflection, the angle of deviation of the ray after reflection is \(.....^{\circ}\)

In a parallel plate capacitor set up, the plate area of capacitor is \(2 \,m ^{2}\) and the plates are separated by \(1\, m\). If the space between the plates are filled with a dielectric material of thickness \(0.5\, m\) and area \(2\, m ^{2}\) (see \(fig.\)) the capacitance of the set-up will be \(.........\, \varepsilon_{0}\) (Dielectric constant of the material \(=3.2\) ) and (Round off to the Nearest Integer)

From the circuit given below, the capacitance between terminals \(A\) and \(B\) shown in the circuit is ______ \(\mu\)F.
(take \(C_1=C_2=C_3=1\) \(\mu\)F and \(C_4=2\) \(\mu\)F.)

A sample contains \(10^{-2}\, kg\) each of two substances A and \(B\) with half lives \(4 \,s\) and \(8 \,s\) respectively. The ratio of then atomic weights is \(1: 2\) The ratio of the amounts of \(A\) and \(B\) after \(16 \,s\) is \(\frac{x}{100}\). the value of \(x\) is........

A thin disc of mass \(M\) and radius \(R\) has mass per unit area \(\sigma (r) = kr^2\) where \(r\) is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is

A block of mass \(m\) slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given \({m}=8 \,{kg}, {M}=16\, {kg}\) Assume all the surfaces shown in the figure to be frictionless.

A plane electromagnetic wave travels in a medium of relative permeability \(1.61\) and relative permittivity \(6.44\). If magnitude of magnetic intensity is \(4.5 \times 10^{-2} \;Am ^{-1}\) at a point, what will be the approximate magnitude of electric field intensity at that point\(?\) (Given : permeability of free space \(\mu_{0}=4 \pi \times 10^{-7}\;NA ^{-2}\), speed of light in vacuum \(c =3 \times 10^{8} \;ms ^{-1}\) )

Equivalent resistance between the adjacent corners of a regular \(n\)-sided polygon of uniform wire of resistance \(R\) would be:

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency \(10\ GHz\). What is the frequency of the microwave measured by the observer?.......\(GHz\) ( speed of light \(= 3 \times  10^8 \) \(ms^{-1}\))