The distance between Sun and Earth is \(R.\) The duration of year if the distance between Sun and Earth becomes \(3R\) will be 

A particle executes simple harmonic motion represented by displacement function as \(x(t)=A \sin (\omega t+\phi)\) If the position and velocity of the particle at \(t=0\, {s}\) are \(2\, {cm}\) and \(2\, \omega \,{cm} \,{s}^{-1}\) respectively, then its amplitude is \(x \sqrt{2} \,{cm}\) where the value of \(x\) is ..... .

A monoatomic gas at pressure \(P\) and volume \(V\) is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be \(.....P\)

The root mean square speed of molecules of nitrogen gas at \(27^{\circ} C\) is approximately\(.......m/s\)(Given mass of a nitrogen molecule \(=4.6 \times 10^{-26}\,kg\) and take Boltzmann constant  \(k _{ B }=1.4 \times 10^{-23}\,JK ^{-1}\) )

A wire of length 25 m and cross-sectional area \(5 \mathrm{~mm}^2\) having resistivity of \(2 \times 10^{-6} \Omega \mathrm{~m}\) is bent into a complete circle. The resistance between diametrically opposite points will be:

The entropy of any system is given by \({S}=\alpha^{2} \beta \ln \left[\frac{\mu {kR}}{J \beta^{2}}+3\right]\) Where \(\alpha\) and \(\beta\) are the constants. \(\mu, J, K\) and \(R\) are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant repectively. [Take \({S}=\frac{{dQ}}{{T}}\) ] Choose the incorrect option from the following:

A thin rod of mass \(0.9\, kg\) and length \(1 \,m\) is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move \(0.1\, kg\) moving in a straight line with velocity \(80\,m / s\) hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in \(rad/s\)) of the rod immediately after the collision will be

Consider a modified Bernoulli equation.
\(\left( P +\frac{ A }{ Bt ^2}\right)+\rho g ( h + Bt )+\frac{1}{2} \rho V^2=\) constant
If \(t\) has the dimension of time then the dimensions of A and B are _________ , _________ respectively.

In a Young's double slit experiment with light of wavelength \(\lambda \) the separation of slits is \(d\) and distance of screen is \(D\) such that \(D >> d >> \lambda \). If the fringe width is \(\beta \). the distance from point of maximum intensity to the point where intensity falls to half of maximum intensity on either side is

The current gain of a common emitter amplifier is \(69\). If the emitter current is \(7.0\,mA\), collector current is.....\(mA\)

By what percentage will the illumination of the lamp decrease if the current drops by \(20 \%\) ?