If the refractive index of the material of a prism is \(\cot \left(\frac{A}{2}\right)\), where \(A\) is the angle of prism then the angle of minimum deviation will be

\(7\) mole of certain monoatomic ideal gas undergoes a temperature increase of \(40 K\) at constant pressure. The increase in the internal energy of the gas in this process is\(....J\) (Given \(R =8.3 JK ^{-1} mol ^{-1}\) )

The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2 m away from it, is :

Two concentric circular coils, \(C _{1}\) and \(C _{2}\), are placed in the \(XY\) plane. \(C _{1}\) has \(500\) turns, and a radius of \(1\; cm . C _{2}\) has \(200\) turns and radius of \(20\, cm . C _{2}\) carries a time dependent current \(I(t)=\left(5 t^{2}-2 t+3\right) \;A\) where \(t\) is in \(s\). The \(emf\) nduced in \(C _{1}\) (in \(mV\) ), at the instant \(t =1\; s\) is \(\frac{4}{ x }\). The value of \(x\) is

Two spherical balls having equal masses with radius of \(5\, {cm}\) each are thrown upwards along the same vertical direction at an interval of \(3\, {s}\) with the same initial velocity of \(35 \,{m} / {s}\), then these balls collide at a height of \(\ldots \ldots \ldots . {m}\). (Take \({g}=10 \,{m} / {s}^{2}\) )

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from \(27^{\circ} C\) to \(87^{\circ} C\).
The rate of consumption of the gas is ___________ \(g / s\).
(Take heat of combustion of gas \(=5.0 \times 10^4 J / g\) ) specific heat capacity of water \(=4200 J / kg.~{ }^{\circ} C\)

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is \(\sqrt{\frac{2}{x}}\). The value of \(x\) is \(.......\)

In a Young's double slit experiment, the distance between the two identical slits is \(6.1\) times larger than the slit width. Then the number of intensity maxima observed with in the central maximum of the single slit diffraction pattern is

Two narrow bores of diameter \(5.0\, {mm}\) and \(8.0\, {mm}\) are joined together to form a \(U-\)shaped tube open at both ends. If this \({U}\)-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water \({T}=7.3 \times 10^{-2} \, {Nm}^{-1}\), angle of contact \(=0, {g}=10\, {ms}^{-2}\) and density of water \(\left.=1.0 \times 10^{3} \,{kg} \,{m}^{-3}\right]\) (in \(mm\))

An electric dipole is formed by two equal and opposite charges \(q\) with separation \(d\). The charges the same mass \(m\). It is kept in a uniform electric field \(E\). If it slightly rotated from its equilibrium orientation, then its angular frequency \(\omega \) is

The \(K_{\alpha}\; X-\)ray of molybdenum has wavelength \(0.071\, {nm}\). If the energy of a molybdenum atoms with a \(K\) electron knocked out is \(27.5\, {keV}\), the energy of this atom when an \(L\) electron is knocked out will be \(....\,keV.\) (Round off to the nearest integer) \(\left[{h}=4.14 \times 10^{-15} \,{eVs}, {c}=3 \times 10^{8}\, {ms}^{-1}\right.]\)

A \(70\, kg\) man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force \(F\) to raise himself The center of gravity rises by \(0.5\, m\) before he leaps. After the leap the \(c.g.\) rises by another \(1\, m\). The maximum power delivered by the muscles is : (Take \(g\, = 10\, ms^{-2}\))

An object is placed at a distance of \(12 \,{cm}\) from a convex lens. A convex mirror of focal length \(15 \,{cm}\) is placed on other side of lens at \(8 \,{cm}\) as shown in the figure. Image of object coincides with the object.When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be ..... \((cm)\)