The equation of the electric field of an electromagnetic wave propagating through free space is given by :
E \(=\sqrt{377} \sin \left(6.27 \times 10^3 t -2.09 \times 10^{-5} x \right)\) N/C
he average power of the electromagnetic wave is\(\left(\frac{1}{\alpha}\right) W / m ^2\). The value of \(\alpha\) is ___________
\(\left(\right.\) Take \(\sqrt{\frac{\mu_0}{\varepsilon_0}}=377\) in SI units \()\)

In the given figure, two wheels \(P\) and \(Q\) are connected by a belt \(B\). The radius of \(P\) is three times as that of \(Q\). In case of same rotational kinetic energy, the ratio of rotational inertias \(\left(\frac{{I}_{1}}{{I}_{2}}\right)\) will be \({x}: 1\). The value of \({x}\) will be \(.....\, .\)

A long conducting wire having a current \(I\) flowing through it, is bent into a circular coil of \(N\) turns.Then it is bent into a circular coil of \(n\) tums. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is:

A mirror is used to produce an image with magnification of \(\frac{1}{4}\). If the distance between object and its image is 40 cm , then the focal length of the mirror is ________

In photoelectric effect, the stopping potential \(\left(\mathrm{V}_0\right) \mathrm{v} / \mathrm{s}\) frequency \((\nu)\) curve is plotted.
( h is the Planck's constant and \(\phi_0\) is work function of metal )
(A) \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) is linear.
(B) The slope of \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) curve \(=\frac{\phi_0}{\mathrm{~h}}\)
(C) h constant is related to the slope of \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) line.
(D) The value of electric charge of electron is not required to determine \(h\) using the \(V_0 \mathrm{v} / \mathrm{s} \nu\) curve.
(E) The work function can be estimated without knowing the value of \(h\).
Choose the correct answer from the options given below :

A thin lens made of glass (refractive index \(= 1.5\)) of focal length \(f=16\; \mathrm{cm}\) is immersed in a liquid of refractive index \(1.42 .\) If its focal length in liquid is \(f_{l},\) then the ratio \(f_{l} /f\) is closest to the integer

Two carnot engines \(A\) and \(B\) operate in series such that engine \(A\) absorbs heat at \(T_{1}\) and rejects heat to a sink at temperature \(T\). Engine \(B\) absorbs half of the heat rejected by engine \(A\) and rejects heat to the sink at \({T}_{3}\). When workdone in both the cases is equal, the value of \({T}\) is 

The function of time representing a simple harmonic motion with a period of \(\frac{\pi}{\omega}\) is :

In a \(\Delta ABC,\frac{a}{b} = 2 + \sqrt 3 \) and \(\angle C\, = \,{60^o}.\) Then the ordered pair \((\angle A,\angle B)\) is equal to

The fractional change in the magnetic field intensity at a distance \('r'\) from centre on the axis of current carrying coil of radius \('a'\) to the magnetic field intensity at the centre of the same coil is : (Take \(r << a )\)

An astronaut of mass \(m\) is working on a satellite or biting the earth at a distance \(h\) from the earth's surface. The radius of the earth is \(R\), while its mass is \(M\). The gravitational pull \(F_G\) on the astronaut is

Which of the following is not a dimensionless quantity?

The total number of positive integral solutions \(( x , y , z )\) such that \(xyz =24\) is