An electric field \(\overrightarrow{\mathrm{E}}=(2 \mathrm{xi}) \mathrm{NC}^{-1}\) exists in space. \(\mathrm{A}\) cube of side \(2 \mathrm{~m}\) is placed in the space as per figure given below. The electric flux through the cube is _______ \(\mathrm{Nm}^2 / \mathrm{C}\)

A square aluminium (shear modulus is \(25 \times 10^{9}\,Nm ^{-2}\) ) slab of side \(60\,cm\) and thickness \(15\,cm\) is subjected to a shearing force (on its narrow face) of \(18.0 \times 10^{4}\,N\). The lower edge is riveted to the floor. The displacement of the upper edge is \(.......\mu\,m\).

A uniform cylinder of mass \(M\) and radius \(R\) is to be pulled over a step of height \(a (a < R\)) by applying a force \(F\) at its centre \('O'\) perpendicular to the plane through the axes of the cylinder on the edge of the step ( see figure). The minimum value of \(F\) required is 

Two immiscible liquids of refractive indices \(\frac{8}{5}\) and \(\frac{3}{2}\) respectively are put in a beaker as shown in the figure. The height of each column is \(6 \mathrm{~cm}\). A coin is placed at the bottom of the beaker. For near normal vision, the apparent depth of the coin is \(\frac{\alpha}{4} \mathrm{~cm}\). The value of \(\alpha\) is__________.

In a meter bridge experiment null point is obtained at \(40\, cm\) from one end of the wire when resistance \(X\) is balanced against another resistance \(Y\). If \(X < Y\), then the new position of the null point from the same end, if one decides to balance a resistance of \(3X\) against \(Y\), will be close to .............. \(cm\)

The logic gate equivalent to the given circuit diagram is:

A plane electromagnetic wave of frequency \(100\, MHz\) is travelling in vacuum along the \(x -\) direction. At a particular point in space and time, \(\overrightarrow{ B }=2.0 \times 10^{-8} \hat{ k } T\). (where, \(\hat{ k }\) is unit vector along \(z-\)direction) What is \(\overrightarrow{ E }\) at this point ?

During the melting of a slab of ice at 273 K at atmospheric pressure :

A roller is mad e by joining  together two cones at their vertices \(O\). It is kept on two rails \(AB\) and \(CD\), which are placed asymmetrically (see figure) , with its axis perpendicular to \(CD  \) and its centre \(O\) at the centre ofline joining \(AB\) and \(CD\) (see figure) . It is given a light push so that it \(A\) starts rolling with its centre \(O\) moving parallel to \(CD\) in the direction shown. As it moves, the roller will tend to

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

Monochromatic light of wavelength \(500 \mathrm{~nm}\) is used in Young's double slit experiment. An interference pattern is obtained on a screen When one of the slits is covered with a very thin glass plate (refractive index \(=1.5\) ), the central maximum is shifted to a position previously occupied by the \(4^{\text {th }}\) bright fringe. The thickness of the glass-plate is _______\(\mu \mathrm{m}\).

The magnetic field associated with a light wave is given, at the origin, by \(B = B_0 [sin\,(3.14 \times 10^7)\,ct\,+\,sin\,(6.28 \times 10^7)\,ct]\) If this light falls on a silver plate having a work function of \(4.7\,eV,\) what will be the maximum kinetic energy of the photo electrons? .............. \(eV\)

A thin prism \(\mathrm{P}_1\) with angle \(4^{\circ}\) made of glass having refractive index 1.54 , is combined with another thin prism \(\mathrm{P}_2\) made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism \(P_2\) in degrees is _______.