The ratio of average electric energy density and total average energy density of electromagnetic wave is:

A vector has magnitude same as that of \(\overrightarrow{\mathrm{A}}-=3 \hat{\mathrm{j}}+4 \hat{\mathrm{j}}\) and is parallel to \(\overrightarrow{\mathrm{B}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}\). The \(\mathrm{x}\) and \(y\) components of this vector in first quadrant are \(\mathrm{x}\) and \(3\) respectively where  \(x\)= _______.

Substance \(A\) has atomic mass number \(16\) and half life of \(1\) day. Another substance \(B\) has atomic mass number \(32\) and half life of \(\frac{1}{2}\) day. If both \(A\) and \(B\) simultaneously start undergo radio activity at the same time with initial mass \(320\,g\) each, how many total atoms of \(A\) and \(B\) combined would be left after \(2\) days \(.........\times 10^{24}\)

A force \(\overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{b} \hat{j}+\hat{k}\) is applied on a particle and it undergoes a displacement \(\hat{i}-2 \hat{j}-\hat{k}\). What will be the value of \(b\), if work done on the particle is zero.

A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by 30° from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop is ________ mm. (Take \( \pi=22/7 \))

In the given circuit, rms value of current \(\left( I _{ rms }\right)\) through the resistor \(R\) is :\(..........\,A\)

\(10\) divisions on the main scale of a Vernier calliper coincide with \(11\) divisions on the Vernier scale. If each division on the main scale is of \(5\) units, the least count of the instrument is _______.

A beaker contains a fluid of density \(\rho \, kg / m^3\), specific heat \(S\, J / kg\,^oC\) and viscosity \(\eta \). The beaker is filled upto height \(h\). To estimate the rate of heat transfer per unit area \((Q / A)\) by convection when beaker is put on a hot plate, a student proposes that it should depend on \(\eta \,,\,\left( {\frac{{S\Delta \theta }}{h}} \right)\) and \(\left( {\frac{1}{{\rho g}}} \right)\) when \(\Delta \theta \) (in \(^oC\)) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for \((Q / A)\) is

An electromagnetic wave of frequency \(5\, GHz ,\) is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are \(2 .\) Its velocity in this medium is \(\times 10^{7}\, m / s\)

Suppose that intensity of a laser is \(\left(\frac{315}{\pi}\right)\, W / m ^{2} .\) The \(rms\) electric field, in units of \(V / m\) associated with this source is close to the nearest integer is \(\left(\epsilon_{0}=8.86 \times 10^{-12} C ^{2} Nm ^{-2} ; c =3 \times 10^{8} ms ^{-1}\right)\)

Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths \(\lambda _N,\,\lambda _A\)  respectively. The ratio \(\frac{{{\lambda _N}}}{{{\lambda _A}}}\)  is closest to

Consider following statements for refraction of light through prism, when angle of deviation is minimum.
(A) The refracted ray inside prism becomes parallel to the base.
(B) Larger angle prisms provide smaller angle of minimum deviation.
(C) Angle of incidence and angle of emergence becomes equal.
(D) There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.
(E) Angle of refraction becomes double of prism angle.
Choose the correct answer from the options given below.

A gas has \(n\) degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be.