Let \(\eta_{1}\) is the efficiency of an engine at \(T _{1}=447^{\circ}\,C\) and \(T _{2}=147^{\circ}\,C\) while \(\eta_{2}\) is the efficiency at \(T _{1}=947^{\circ}\,C\) and \(T _{2}=47^{\circ}\,C\). The ratio \(\frac{\eta_{1}}{\eta_{2}}\) will be.

A printed page is pressed by a glass of water. The refractive index of the glass and water is \(1.5\) and \(1.33\), respectively. If the thickness of the bottom of glass is \(1\, cm\) and depth of water is \(5\, cm\) , how much the page will appear to be shifted if viewed from the top ?

A girl standing on road holds her umbrella at \(45^{\circ}\) with the vertical to keep the rain away. If she starts running without umbrella with a speed of \(15 \sqrt{2} \; kmh ^{-1}\), the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is ...........  \(kmh ^{-1}\)

The Young's modulus of a steel wire of length \(6\,m\) and cross-sectional area \(3\,mm ^2\), is \(2 \times 11^{11}\,N / m ^2\). The wire is suspended from its support on a given planet. A block of mass \(4\,kg\) is attached to the free end of the wire. The acceleration due to gravity on the planet is \(\frac{1}{4}\) of its value on the earth. The elongation of wire is  (Take \(g\) on the earth \(=10\) \(\left.m / s ^2\right):\)

A copper ball of mass \(100\ gm\) is at a temperature \(T\). It is dropped in a copper calorimeter of mass \(100\ gm\), filled with \(170\  gm\) of water at room temperature. Subsequently, the temperature of the system is found to be \(75^o C\). \(T\) is given by......\(^oC\) (Given : room temperature \(= 30^o  C\), specific heat of copper \(=\) \(0.1\) \(cal/gm^o C\))

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.
In the light of the above statements, choose the most appropriate answer from the options given below :

In an \(n-p-n\) common emitter (\(CE\)) transistor the collector current changes from \(5\,mA\) to \(16\,mA\) for the change in base current from \(100\,\mu A\) and \(200\,\mu A\), respectively. The current gain of transistor is

\(UV\) light of \(4.13 \mathrm{eV}\) is incident on a photosensitive metal surface having work function \(3.13 \mathrm{eV}\). The maximum kinetic energy of ejected photoelectrons will be _______.