A Carnot engine has efficiency of \(50 \%\). If the temperature of sink is reduced by \(40^{\circ} C\), its efficiency increases by \(30 \%\). The temperature of the source will be\(....K\)

The oscillating magnetic field in a plane electromagnetic wave is given by \(B _{ y }=5 \times 10^{-6} \sin\) \(1000\,\pi\left(5 x -4 \times 10^{8} t \right) T\). The amplitude of electric field will be.

A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is \(91.6 \%\), then the loss of power in units of \(\mathrm{cal} / \mathrm{s}\) is

The maximum velocity of the photoelectrons emitted from the surface is \(v\) when light of frequency \(n\) falls on a metal surface. If the incident frequency is increased to \(3n\) , the maximum velocity of the ejected photoelectrons will be 

A ball is dropped from the top of a \(100\; m\) high tower on a planet. In the last \(\frac{1}{2}\;s \) before hitting the ground, it covers a distance of \(19\; \mathrm{m}\). Acceleration due to gravity (in \(\mathrm{ms}^{-2}\) ) near the surface on that planet is

\(300 \,cal\). of heat is given to a heat engine and it rejects \(225 \,cal\). of heat. If source temperature is \(227^{\circ} C\), then the temperature of sink will be____\({ }^{\circ} C\).

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 \(.....P\)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion-(A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer.
Reason-(R) : The speed of light reduces in an optically denser medium than air while its frequency does not change.
In the light of the above statements, choose the most appropriate answer from the options given below :

Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area \(0.5 \mathrm{~m}^2\). It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)\)

In the given circuit, \(C _1=2\,\mu F , C _2=0.2\,\mu F\), \(C _3=2\,\mu F , C _4=4\,\mu F,\) \(C _5=2\,\mu F , C _6=2\,\mu F\), the charge stored on capacitor \(C _4\) is \(.....\mu C\).

A wire of resistance \(R_{1}\) is drawn out so that its length is increased by twice of its original length.The ratio of new resistance to original resistance is.