An \(\alpha\) particle and a proton are accelerated from rest by a potential difference of \(200\, V\). After this, their de Broglie wavelengths are \(\lambda_{\alpha}\) and \(\lambda_{p}\) respectively. The ratio \(\frac{\lambda_{p}}{\lambda_{a}}\) is

Given below are two statements : Statement \((I)\) : The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement \((II)\) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas. In the light of the above statements, choose the correct answer from the option given below:

For the given circuit, in the steady state, \(\left| V _{ B }- V _{ D }\right|=.......V.\)

If an electron is moving in the \(n ^{\text {th }}\) orbit of the hydrogen atom, then its velocity \(\left( v _{ n }\right)\) for the \(n ^{\text {th }}\) orbit is given as

A ring is hung on a nail. It can oscillate, without slipping or sliding \((i)\) in its plane with a time period \(T_{1}\) and, \((ii)\) back and forth in a direction perpendicular to its plane, with a period \(T _{2}\). the ratio \(\frac{ T _{1}}{ T _{2}}\) will be 

Conductor wire ABCDE with each \(\operatorname{arm} 10 \mathrm{~cm}\) in length is placed in magnetic field of \(\frac{1}{\sqrt{2}}\) Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of \(10 \mathrm{~cm} / \mathrm{s}\), induced emf between points A and E is _____ mV.

An \(NPN\) transistor is used in common emitter configuration as an amplifier with \(1\,k\Omega \) load resistance. Signal voltage of \(10\,mV\) is applied across the base emitter. This produces a \(3\,mA\) change in the collector current and \(15\,\mu A\) change in the base current of the amplifier. The input resistance and voltage gain are

In a typical combustion engine the work done by a gas molecule is given \(W =\alpha^{2} \beta e ^{\frac{-\beta x ^{2}}{ KT }}\), where \(x\) is the displacement, \(k\) is the Boltzmann constant and \(T\) is the temperature. If \(\alpha\) and \(\beta\) are constants, dimensions of \(\alpha\) will be

A car is moving on a horizontal curved road with radius \(50\,m\). The approximate maximum speed of car will be \(............\,ms^{-1}\), if friction between tyres and road is \(0.34.\left[\right.\) Take \(\left.g =10 ms ^{-2}\right]\)

A car is moving with speed of \(150\,km / h\) and after applying the brake it will move \(27\,m\) before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling \(....m\) distance.