A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by \(52\, K\), its efficiency is doubled. The temperature in Kelvin of the source will be ...... .

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area \('a'\) is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is \((a\,<\,<\,A)\)

Shown in the figure is rigid and uniform one meter long rod \(AB\) held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass \('m'\) and has another weight of mass \(2m\) hung at a distance of \(75\, cm\) from \(A\). The tension in the string at \(A\) is\(....mg\)

An electron, moving along the \(x-\) axis with an initial energy of \(100\, eV\), enters a region of magnetic field \(\vec B = (1.5\times10^{-3}T)\hat k\) at \(S\) (See figure). The field extends between \(x = 0\) and \(x = 2\, cm\). The electron is detected at the point \(Q\) on a screen placed \(8\, cm\) away from the point \(S\). The distance \(d\) between \(P\) and \(Q\) (on the screen) is :......\(cm\) (electron's charge \(= 1.6\times10^{-19}\, C\), mass of electron \(= 9.1\times10^{-31}\, kg\))

The increase in pressure required to decrease the volume of a water sample by \(0.2 \%\) is \(\mathrm{P} \times 10^5 \mathrm{Nm}^{-2}\). Bulk modulus of water is \(2.15 \times 10^9 \mathrm{Nm}^{-2}\). The value of P is ________.

For extrinsic semiconductors; when doping level is increased;

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of \(3\), keeping the number of turns of the coil per unit length of the frame the same, then self inductance of the coil

In a screw gauge when the circular scale is given five complete rotations it moves linearly by \(2.5\) mm. If the circular scale has \(100\) divisions, the least count of screw gauge is _____ mm.

An ac circuit has an inductor and a resistor of resistance \({R}\) in series, such that \({X}_{{L}}=3 {R}\). Now, a capacitor is added in series such that \({X}_{{C}}=2 {R}\). The ratio of new power factor with the old power factor of the circuit is \(\sqrt{5}: {x}\). The value of \({x}\) is ...... .

A new unit \((\alpha)\) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of \(\alpha\) units if light takes \(6\) min. \(40\) s to cover this distance?

A charge of \(4\,\mu C\) is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be.