21.

As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge -Q from the point A [coordinates (O, a)] to another point B [coordinates (a, O)] along the straight path AB is

• zero

• $\left(\frac{-\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}} \frac{1}{{\mathrm{a}}^2}\right) \sqrt{2}\mathrm{a}$

• $\left(\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}} \frac{1}{{\mathrm{a}}^2}\right)$

• $\left(\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}} \frac{1}{{\mathrm{a}}^2}\right)\sqrt{2}\mathrm{a}$

For the network shown in the figure, the value of the current i is

• $\frac{9 \mathrm{V}}{35}$

• $\frac{5 \mathrm{V}}{18}$

• $\frac{5 \mathrm{V}}{9}$

• $\frac{18 \mathrm{V}}{5}$

If the magnetic dipole moment of an atom of diamagnetic material, paramagnetic material and ferromagnetic material are denoted by ${\mathrm{\mu }}_{ \mathrm{d} }, {\mathrm{\mu }}_{ \mathrm{p}} \mathrm{and} {\mathrm{\mu }}_{ \mathrm{f}}$  respectively, then

• ${\mathrm{\mu }}_{ \mathrm{d}} \ne 0 \mathrm{and} {\mathrm{\mu }}_{ \mathrm{f} }\ne 0$

• ${\mathrm{\mu }}_{\mathrm{p}}= 0 \mathrm{and} {\mathrm{\mu }}_{ \mathrm{f}} \ne 0$

• ${\mathrm{\mu }}_{ \mathrm{d}} = 0 \mathrm{and} {\mathrm{\mu }}_{ \mathrm{p}} \ne 0$

• ${\mathrm{\mu }}_{ \mathrm{d} }\ne 0, {\mathrm{\mu }}_{ \mathrm{p}} = 0$

In a circuit, L, C and R are connected in series with an alternating voltage source of frequency f. The current leads the voltage by 45°. The value of C is

• $\frac{1}{2\mathrm{\pi f} \left(2\mathrm{\pi f} \mathrm{L} + \mathrm{R}\right)}$

• $\frac{1}{\mathrm{\pi f} \left(2\mathrm{\pi f} \mathrm{L} + \mathrm{R}\right)}$

• $\frac{1}{2\mathrm{\pi f} \left(2\mathrm{\pi f} \mathrm{L} - \mathrm{R}\right)}$

• $\frac{1}{\mathrm{\pi f} \left(2\mathrm{\pi f} \mathrm{L} - \mathrm{R}\right)}$

When a wire of uniform cross-section a, length land resistance R is bent into a complete circle, resistance between two of dimetrically opposite points will be

• $\frac{\mathrm{R}}{4}$

• $\frac{\mathrm{R}}{8}$

• 4R

• $\frac{\mathrm{R}}{2}$

If  ${\mathrm{\lambda }}_{\mathrm{\nu }}, {\mathrm{\lambda }}_{\mathrm{x}} \mathrm{and} {\mathrm{\lambda }}_{\mathrm{m}}$represent the wavelengths of visible light, X-rays and microwaves respectively, then

• ${\mathrm{\lambda }}_{ \mathrm{m}} > {\mathrm{\lambda }}_{ \mathrm{x}} > {\mathrm{\lambda }}_{ \mathrm{\nu }}$

• ${\mathrm{\lambda }}_{\mathrm{v}} >{\mathrm{\lambda }}_{\mathrm{m}} > {\mathrm{\lambda }}_{\mathrm{x}}$

• ${\mathrm{\lambda }}_{\mathrm{m}}> {\mathrm{\lambda }}_{\mathrm{v}} > {\mathrm{\lambda }}_{\mathrm{x}}$

• ${\mathrm{\lambda }}_{\mathrm{v}} > {\mathrm{\lambda }}_{\mathrm{x}} > {\mathrm{\lambda }}_{\mathrm{m}}$

An electron moves in a circular orbit with a uniform speed v. It produces a magnetic field B at the centre of the circle. The radius of the circle is proportional, to

• B/v

• v/B

• √v/B

• √B/v

In the reaction,${}_1{}^2\mathrm{H} +{}_1{}^3\mathrm{H} \to {}_2{}^4\mathrm{He} + {}_0{}^1\mathrm{n}$ if the binding energies of ${}_1{}^2\mathrm{H}, {}_1{}^3 \mathrm{H} \mathrm{and} {}_2{}^4\mathrm{He}$ are respectively a, b and c (in MeV), then the energy in this reaction is released in this reaction is

• c + a - b

• c - a - b

• a + b + c

• a +b - c

The work functions for metals A, B and C are respectively 1.92 eV, 2.0 eV and 5 eV. According to Einstein's equation, the metals which will emit photoelectrons for a radiation length 4100 A^o is /are 

• none

• A only

• A and B only

• all the three metals

 The nuclei of which one of the following pairs
of nuclei are isotones ?

• ${}_{34}\mathrm{Se}^{ 74}, {}_{31}\mathrm{Ga}^{ 71}$

• ${}_{42}\mathrm{Mo}^{ 92}, {}_{40}\mathrm{Zr}^{ 92}$

• ${}_{38}\mathrm{Sr}^{ 84}, {}_{38}\mathrm{Sr}^{ 86}$

• ${}_{20}\mathrm{Ca}^{40}, {}_{16}\mathrm{S}^{ 32}$