A coil of cross-sectional area  \(A\) having \(n\)  turns is placed in a uniform magnetic field \(B.\)  When it is rotated with an angular velocity \(\omega ,\)  the maximum \(e.m.f.\)  induced in the coil will be

A person lives in a high-rise building on the bank of a river \(50\, m\) wide. Across the river is a well lit tower of height \(40\, m\). When the person, who is at a height of \(10\, m\), looks through a polarizer at an appropriate angle at light of the tower reflecting from the river surface, he notes that intensity of light coming from distance \(X\) from his building is the least and this corresponds to the light coming from light bulbs at height \('Y'\) on the tower. The values of \(X\) and \(Y\) are respectively close to (refractive index of water \(  \simeq  \frac{4}{3})\)

Consider two charged metallic spheres \(S_{1}\) and \(\mathrm{S}_{2}\) of radii \(\mathrm{R}_{1}\) and \(\mathrm{R}_{2},\) respectively. The electric \(\left.\text { fields }\left.\mathrm{E}_{1} \text { (on } \mathrm{S}_{1}\right) \text { and } \mathrm{E}_{2} \text { (on } \mathrm{S}_{2}\right)\) on their surfaces are such that \(\mathrm{E}_{1} / \mathrm{E}_{2}=\mathrm{R}_{1} / \mathrm{R}_{2} .\) Then the ratio \(\left.\mathrm{V}_{1}\left(\mathrm{on}\; \mathrm{S}_{1}\right) / \mathrm{V}_{2} \text { (on } \mathrm{S}_{2}\right)\) of the electrostatic potentials on each sphere is 

The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is \(40\,cm.\) The area of the image is \(9\,times\) that of the square. The focal length of the lens is........\(cm\)

A guitar string of length \(90\,cm\) vibrates with a fundamental frequency of \(120\,Hz.\) The length of the string producing a fundamental frequency of \(180\,Hz\) will be \(...........cm\).

Train A is moving along two parallel rail tracks towards north with speed \(72 \mathrm{~km} / \mathrm{h}\) and train B is moving towards south with speed \(108 \mathrm{~km} / \mathrm{h}\). Velocity of train \(B\) with respect to \(A\) and velocity of ground with respect to \(B\) are _______ (in \(\mathrm{ms}^{-1}\) ).

The least count of the main scale of a screw gauge is \(1\, mm\). The minimum number of divisions on its circular scale required to measure \(5\,\mu m\) diameter of a wire is

The heat extracted out of \(x\) gram of water initially at \(50°C\) to cool it down to \(0°C\) is sufficient to evaporate \((1000 - x)\) gram of water also initially at \(50°C\). The value of \(x\) (closest integer) is _______.
(Take latent heat of water \(2256\text{ kJ/kg.K}\), specific heat capacity of water \(4200\text{ J/kg.K}\))

\(\mathrm{N}\) moles of a polyatomic gas \((f=6)\) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of \(\mathrm{N}\) is _______.

A body of mass \(10 kg\) is projected at an angle of \(45^{\circ}\) with the horizontal. The trajectory of the body is observed to pass through a point \((20,10)\). If \(T\) is the time of flight, then its momentum vector, at time \(t =\frac{ T }{\sqrt{2}}\), is. \(\left[\right.\) Take \(\left.g=10 m / s ^{2}\right]\)

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of \(100 \mathrm{~cm}^2\) with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density \(1.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3\). What force one needs to apply on the hinged door so that it does not get opened ?
(Acceleration due to gravity \(=10 \mathrm{~m} / \mathrm{s}^2\))