A beam of light travelling along \(X\)-axis is described by the electric field \(E _{ y }=900 \sin \omega( t - x / c )\). The ratio of electric force to magnetic force on a charge \(q\) moving along \(Y\)-axis with a speed of \(3 \times 10^{7}\,ms ^{-1}\) will be. [Given speed of light \(=3 \times 10^{8}\,ms ^{-1}\) ]

An astronaut takes a ball of mass \(m\) from earth to space. He throws the ball into a circular orbit about earth at an altitude of \(318.5 \mathrm{~km}\). From earth's surface to the orbit, the change in total mechanical energy of the ball is \(x \frac{\mathrm{GM}_e \mathrm{~m}}{21 R_e}\). The value of \(x\) is _______. (take \(R_{\mathrm{e}}=6370 \mathrm{~km}\) )

Two small equal point charges of magnitude \(q\) are suspended from a common point on the ceiling by insulating mass less strings of equal lengths. They come to equilibrium with each string making angle \(\theta \) from the vertical. If the mass of each charge is \(m,\) then the electrostatic potential at the centre of line joining them will be \(\left( {\frac{1}{{4\pi { \in _0}}} = k} \right).\)

A particle performs simple harmonic motion with a period of \(2\) second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is \(\frac{1}{ a } s .\) The value of \('a'\) to the nearest integer is.........

Which one of the following is not a measurable quantity ?

A spherical ball of mass \(2\) kg falls from a height of \(10\) m and is brought to rest after penetrating \(10\) cm into sand. The average force exerted by sand on the ball is _______ N. (Take \(g = 10\) m/s\(^2\))

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The density of the copper \(\left({ }_{29}^{64} \mathrm{Cu}\right)\) nucleus is greater than that of the carbon \(\left({ }_6^{12} \mathrm{C}\right)\) nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to \(\mathrm{A}^{1 / 3}\).
In the light of the above statements, choose the most appropriate answer from the options given below :

A hollow spherical shell at outer radius \(R\) floats just submerged under the water surface. The inner radius of the shell is \(r\). If the specific gravity of the shell material is \(\frac{27}{8}\) \(w.r.t.\) water, the value of \(r\) is\(......R\)

A particle is rotating in a circular path and at any instant its motion can be described as \(\theta = \dfrac{5t^4}{40} - \dfrac{t^3}{3}\). The angular acceleration of the particle after \(10\) seconds is _______ rad/s\(^2\).

A alternating current at any instant is given by \(i=\left[6+\sqrt{56} \sin \left(100 \pi t+\frac{\pi}{3}\right)\right] A\). The rms value of the current is _________ A.

Match the LIST-I with LIST-II

LIST-I		LIST-II
A.	Pressure varies inversely with volume of an ideal gas	I.	Adiabatic process
B.	Heat absorbed goes partly to increase internal energy and partly to do work	II.	Isochoric process
C.	Heat is neither absorbed nor released by a system	III.	Isothermal process
D.	No work is done on or by a gas	IV.	Isobaric process

Choose the correct answer from the options given below: