All electromagnetic wave is transporting energy in the negative \(z\) direction. At a certain point and certain time the direction of electric field of the wave is along positive y direction. What will be the direction of the magnetic field of the wave at that point and instant?

Four identical solid spheres each of mass \('m'\) and radius \('a'\) are placed with their centres on the four corners of a square of side \('b'\). The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is

A particle of mass \(m\) moves in a circular orbit in a central potential field \(U ( r )= U _{0} r ^{4}\). If Bohr's quantization conditions are applied, radii of possible orbitals \(r _{ n }\) vary with \(n ^{1 / \alpha}\), where \(\alpha\) is ....... .

Some distant star is to be observed by some telescope of diameter of objective lens \(a\), at an angular resolution of \(3.0\times 10^{-7}\) radian. If the wavelength of light from the star reaching the telescope is \(500\) nm, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)

A balloon is moving up in air vertically above a point \(A\) on the ground. When it is at a height \(h _{1},\) a girl standing at a distance \(d\) (point \(B\) ) from \(A\) (see figure) sees it at an angle \(45^{\circ}\) with respect to the vertical. When the balloon climbs up a further height \(h _{2},\) it is seen at an angle \(60^{\circ}\) with respect to the vertical if the girl moves further by a distance \(2.464\, d\) (point \(C\) ). Then the height \(h _{2}\) is (given tan \(\left.30^{\circ}=0.5774\right)\)\(.......\)

If the wavelength of the first member of Lyman series of hydrogen is \(\lambda\). The wavelength of the second member will be _______.

The specific heat of water \(=4200\, J\, kg ^{-1}\, K ^{-1}\) and the latent heat of ice \(=3.4 \times 10^{5}\, J\, kg ^{-1}.\) \(100\) grams of ice at \(0^{\circ} C\) is placed in \(200\, g\) of water at \(25^{\circ} C\). The amount of ice that will melt as the temperature of water reaches \(0^{\circ} C\) is close to (in \(grams\)) 

A uniform wire (Young's modulus \(2 \times 10^{11}\, Nm^{-2}\) ) is subjected to longitudinal tensile stress of \(5 \times 10^7\,Nm^{-2}\) . If the over all volume change in the wire is \(0.02\%,\) the fractional decrease in the radius of the wire is close to

If Surface tension \((S)\), Moment of Inertia \((I)\) and Planck’s constant \((h)\), were to be taken as the fundamental units, the dimensional formula for linear momentum would be

One end of a straight uniform \(1\; \mathrm{m}\) long bar is pivoted on horizontal table. It is released from rest when it makes an angle \(30^{\circ}\) from the horizontal (see figure). Its angular speed when it hits the table is given as \(\sqrt{\mathrm{n}}\; \mathrm{s}^{-1},\) where \(\mathrm{n}\) is an integer. The value of \(n\) is

The force of interaction between two atoms is given by \(F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);\) where \(x\) is the distance, \(k\) is the Boltzmann constant and \(T\) is temperature and \(\alpha \) and \(\beta \) are two constants. The dimension of \(\beta \) is

A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If \(r_{d}\) and \(r_{p}\) are the radii of their circular paths respectively, then the ratio \(\frac{r_{d}}{r_{p}}\) will be \(\sqrt{ x }: 1\) where \(x\) is ..........