The length of a metallic wire is increased by \(20 \%\) and its area of cross section is reduced by \(4 \%\). The percentage change in resistance of the metallic wire is \(.......\)

A zener diode of power rating \(2\, {W}\) is to be used as a voltage regulator. If the zener diode has a breakdown of \(10 \,{V}\) and it has to regulate voltage fluctuated between \(6\, {V}\) and \(14\, {V}\), the value of \({R}_{{s}}\) for safe operation should be \(....\Omega\)

A light beam of wavelength \(500\, {nm}\) is incident on a metal having work function of \(1.25\, {eV}\), placed in a magnetic field of intensity \(B\). The electrons emitted perpendicular to the magnetic field \(B\), with maximum kinetic energy are bent into circular arc of radius \(30\, {cm}\). The value of \(B\) is \(....\,\times 10^{-7} \,{T}\). Given \({hc}=20 \times 10^{-26}\, {J}-{m}\), mass of electron \(=9 \times 10^{-31} \,{kg}\)

Two radioactive substances A and B of mass numbers \(200\) and \(212\) respectively, shows spontaneous \(\alpha\)-decay with same \(Q\) value of \(1\) MeV. The ratio of energies of \(\alpha\)-rays produced by A and B is ________.

A particle of mass \(0.50 \mathrm{~kg}\) executes simple harmonic motion under force \(\mathrm{F}=-50\left(\mathrm{Nm}^{-1}\right) \mathrm{x}\). The time period of oscillation is \(\frac{x}{35} s\). The value of \(x\) is _______. (Given \(\pi=\frac{22}{7}\) )

A circular disc of radius \(b\) has a hole of radius \(a\) at its centre (see figure). If the mass per unit area of the disc varies as \(\left( {\frac{{{\sigma _0}}}{r}} \right)\), then the radius of gyration of the disc about its axis passing through the centre is

An massless equilateral triangle \(EFG\) of side \('a'\) (As shown in figure) has three particles of mass \(m\) situated at its vertices. The moment of intertia of the system about the line \(EX\) perpendicular to \(EG\) in the plane of \(EFG\) is \(\frac{ N }{20}\, ma ^{2}\) where \(N\) is an integer. The value of \(N\) is

A body having specific charge \(8\,\mu {C} / {g}\) is resting on a frictionless plane at a distance \(10\, {cm}\) from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of \(100 \,{V} / {m}\) is applied horizontally toward the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be \(....\, S.\)

Light wave traveling in air along \(x\)-direction is given by \(E _{ y }=540 \sin \pi \times 10^{4}( x - ct ) Vm ^{-1}\). Then, the peak value of magnetic field of wave will be \(\dots \times 10^{-7}\,T\) (Given \(c =3 \times 10^{8}\,ms ^{-1}\) )

During the propagation of electromagnetic waves in a medium

Given below are two statements: one is labelled as Assertion\((A)\) and the other is labelled as Reason \((R).\) \(Assertion\) \((A)\) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. \(Reason\) \((R)\) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below :

A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm , respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be _______.

The position vector of a moving body at any instant of time is given as \(\vec{r}=\left(5 t^2 \hat{i}-5 t \hat{j}\right) \mathrm{m}\). The magnitude and direction of velocity at \(t=2 \mathrm{~s}\) is,