31.

Four point charge -Q,-q,2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is

• Q= -q

• Q=-1/q

• Q=q

• Q=q

In the circuit shown the cells A and B have negligible resistances. For V_A = 12V, R₁ = 500Ω and R = 100Ω the galvanometer (G) shows no deflection. The value of V_B is

• 4V

• 2V

• 12 V

• 12 V

The current (I) in the inductance is varying with time according to the plot shown in a figure.

An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle θ with the direction of the field. Assuming that the potential energy of the dipole to be zero when θ =90^o, the torque and the potential energy of the dipole will respectively be

• pE sin θ, pE cos θ

• pE sin θ,-2pE cos θ

• pE sin θ, 2 pE cos θ

• pE sin θ, 2 pE cos θ

An electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths λ₁:λ₂ emitted in the two cases is

• 7/5

• 27/20

• 27/5

• 27/5

In a CE transistor amplifier, the audio signal voltage across the collector resistance of 2kΩ is 2V. If the base resistance is 1kΩ and the current amplification of the transistor is 100, the input signal voltage is

• 0.1 V

• 1.0 V

• 1 mV

• 1 mV

If the nuclear radius of²⁷ Al is 3.6 Fermi, the approximate nuclear radius of ⁶⁴Cu in Fermi is

• 2.4

• 1.2

• 4.8

• 4.8

When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index

• equal to that of glass

• less than one

• greater than that of glass

• greater than that of glass

A mixture consists of two radioactive materials A₁ and A₂ with half-lives of 20 s and 10 s respectively. Initially, the mixture has 40 g of A₁ and 160 g of A₂. The amount of the two in the mixture will become equal after

• 60 s

• 80 s

• 20 s

• 20 s

C and si both have a same lattice structure, having 4 bonding electrons in each. However, C is insulator whereas Si is an intrinsic semiconductor. This is because

• in the case of C, the valence band is not completely filled at absolute zero temperature

• in a case C, the conduction band is partly filled even at absolute zero temperature

• the four bonding electrons in the case of C lie in the second orbit, whereas in case of Si they lie in the third

• the four bonding electrons in the case of C lie in the second orbit, whereas in case of Si they lie in the third