A reversible engine has an efficiency of \(\frac{1}{4}\). If the temperature of the sink is reduced by \(58^{\circ} {C}\), its efficiency becomes double. Calculate the temperature of the sink. (In \(^{\circ} {C}\))

The acceptor level of a p-type semiconductor is \(6 \mathrm{eV}\). The maximum wavelength of light which can create a hole would be _______. (Given hc \(=1242 \mathrm{eV} \mathrm{nm}\).)

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed \(v\). The sphere and the cylinder reaches upto maximum heights \(h_1\) and \(h_2\), respectively, above the initial level. The ratio \(h_1: h_2\) is \(\frac{n}{10}\). The value of \(\mathrm{n}\) is __________.

Two identical capacitors \(\mathrm{A}\) and \(\mathrm{B}\), charged to the same potential \(5\; \mathrm{V}\) are connected in two different circuits as shown below at time \(\mathrm{t}=0\) If the charge on capacitors \(A\) and \(B\) at time \(\mathrm{t}=\mathrm{CR}\) is \(\mathrm{Q}_{\mathrm{A}}\) and \(\mathrm{Q}_{\mathrm{B}}\) respectively, then (Here \(e\) is the base of natural logarithm)

If a radioactive element having half-life of \(30\,min\) is undergoing beta decay, the fraction of radioactive element remains undecayed after \(90\,min\). will be :

A body of mass \(0.5\, kg\) travels on straight line path with velocity \(v =\left(3 x ^{2}+4\right) m / s\). The net workdone by the force during its displacement from \(x =0\) to \(x =2\, m\) is\(.......J\)

A simple pendulum doing small oscillations at a place \(\mathrm{R}\) height above earth surface has time period of \(T_1=4 \mathrm{~s}\). \(T_2\) would be it's time period if it is brought to a point which is at a height \(2 R\) from earth surface. Choose the correct relation. \([R=\) radius of Earth]:

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy \(3\, {eV}\). The proton captures the electrons and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength \(4000\, \mathring {{A}}\). What is the maximum kinetic energy of the emitted photoelectron ? (In \({eV}\))

A particle is moving in a circular path of radius \(a,\) with a constant velocity \(v\) as shown in the figure.The centre of circle is marked by \('C'\). The angular momentum from the origin \(O\) can be written as

A player caught a cricket ball of mass \(150 \mathrm{~g}\) moving at a speed of \(20 \mathrm{~m} / \mathrm{s}\). If the catching process is completed in \(0.1 \mathrm{~s}\), the magnitude of force exerted by the ball on the hand of the player is _______.

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) The escape velocities of planet \(A\) and \(B\) are same. But \(A\) and \(B\) are of unequal mass. Reason \(R :\) The product of their mass and radius must be same, \(M _{1} R _{1}= M _{2} R _{2}\) In the light of the above statements, choose the most appropriate answer from the options given below

Two stars of masses \(m\) and \(2\, m\) at a distance \(d\) rotate about their common centre of mass in free space. The period of revolution is