Find the value of the angle of emergence from the prism. Refractive index of the glass is `` \sqrt{3} `` .

(A) `` 60^{\circ} ``
(B) `` 30^{\circ} ``
(C) `` 45^{\circ} ``
(D) `` 90^{\circ} ``

The equivalent capacitance of the combination shown in the figure is :

(A)3 C
(B)2 C
(C)C/2
(D)3C/2

If force `` [ F ] `` , acceleration `` [ A ] `` and time `` [ T ] `` are chosen as the fundamental physical quantities. Find the dimensions of energy.
(A) `` [ F ][ A ][ T ] ``
(B) `` [ F ][ A ]\left[ T ^{2}\right] ``
(C) `` [ F ][ A ]\left[ T ^{-1}\right] ``
(D) `` [ F ]\left[ A ^{-1}\right][ T ] ``

A cup of coffee cools from `` 90^{\circ} C `` to `` 80^{\circ} C `` in t minutes, when the room temperature is `` 20^{\circ} C `` . The time taken by a similar cup of coffee to cool from `` 80^{\circ} C `` to `` 60^{\circ} C `` at a room temperature same at `` 20^{\circ} C `` is :
(A) `` \frac{13}{10} t ``
(B) `` \frac{13}{5} t ``
(C) `` \frac{10}{13} t ``
(D) `` \frac{5}{13} t ``

The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is `` 0.25\, \Omega `` . What will be the effective resistance if they are connected in series?
(A) `` 0.25\, \Omega ``
(B) `` 0.5\, \Omega ``
(C) `` 1\, \Omega ``
(D) `` 4\, \Omega ``

The number of photons per second on an average emitted by the source of monochromatic light of wavelength `` 600\, nm `` , when it delivers the power of `` 3.3 \times 10^{-3} `` watt will be : `` \left( h =6.6 \times 10^{-34} Js \right) ``
(A) `` 10^{18} ``
(B) `` 10^{17} ``
(C) `` 10^{16} ``
(D) `` 10^{15} ``

Three resistors having resistances `` r _{1}, r _{2} `` and `` r _{3} `` are connected as shown in the given circuit. The ratio `` \frac{i_{3}}{i_{1}} `` of currents in terms of resistances used in the circuit is :

(A) `` \frac{ r _{1}}{ r _{2}+ r _{3}} ``
(B) `` \frac{ r _{2}}{ r _{2}+ r _{3}} ``
(C) `` \frac{r_{1}}{r_{1}+r_{2}} ``
(D) `` \frac{ r _{2}}{ r _{1}+ r _{3}} ``

A point object is placed at a distance of `` 60\, cm `` from a convex lens of focal length `` 30\, cm `` . If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of `` 40\, cm `` from it, the final image would be formed at a distance of :

(A)20 cm from the lens, it would be a real image.
(B)30 cm from the lens, it would be a real image.
(C)30 cm from the plane mirror, it would be a virtual image.
(D)20 cm from the plane mirror, it would be a virtual image.

For the given circuit, the input digital signals are applied at the terminals A, B and C. What would be the output at the terminal `` y `` ?


(A)

(B)

(C)

(D)

A step down transformer connected to an ac mains supply of `` 220\, V `` is made to operate at `` 11\, V,\, 44\, W `` lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?
(A)0.2 A
(B)0.4 A
(C)2 A
(D)4 A

A uniform conducting wire of length `` 12\, a `` and resistance `` ' R ' `` is wound up as a current carrying coil in the shape of,
(i) an equilateral triangle of side `` 'a' `` .
(ii) a square of side `` 'a' `` .
The magnetic dipole moments of the coil in each case respectively are:
(A) `` \sqrt{3} Ia ^{2} `` and `` 3\, Ia ^{2} ``
(B) `` 3\, Ia ^{2} `` and `` Ia ^{2} ``
(C) `` 3\, Ia ^{2} `` and `` 4\, Ia ^{2} ``
(D) `` 4\, Ia ^{2} `` and `` 3\, Ia ^{2} ``

In the product
`` \vec{ F } = q (\vec{v} \times \vec{ B }) ``
`` = q \vec{v} \times\left( B \hat{i}+ B \hat{j}+ B _{0} \hat{k}\right) ``
For `` q =1 `` and `` \vec{v}=2 \hat{i}+4 \hat{j}+6 \hat{k} `` and
`` \vec{ F }=4 \hat{i}-20 \hat{j}+12 \hat{k} ``
What will be the complete expression for `` \vec{ B } `` ?
(A) `` -8 \hat{i}-8 \hat{j}-6 \hat{k} ``
(B) `` -6 \hat{i}-6 \hat{j}-8 \hat{k} ``
(C) `` 8 \hat{i}+8 \hat{j}-6 \hat{k} ``
(D) `` 6 \hat{i}+6 \hat{j}-8 \hat{k} ``

`` A `` particle moving in a circle of radius `` R `` with a uniform speed takes a time `` T `` to complete one revolution.
If this particle were projected with the same speed at an angle ' `` \theta `` ' to the horizontal, the maximum height attained by it equals `` 4 R `` . The angle of projection, `` \theta `` , is then given by :
(A) `` \theta=\cos ^{-1}\left(\frac{ gT ^{2}}{\pi^{2} R }\right)^{1 / 2} ``
(B) `` \theta=\cos ^{-1}\left(\frac{\pi^{2} R}{g T^{2}}\right)^{1 / 2} ``
(C) `` \theta=\sin ^{-1}\left(\frac{\pi^{2} R}{ g T ^{2}}\right)^{1 / 2} ``
(D) `` \theta=\sin ^{-1}\left(\frac{2 gT ^{2}}{\pi^{2} R }\right)^{1 / 2} ``

A series LCR circuit containing `` 5.0\, H `` inductor, `` 80\, \mu F `` capacitor and `` 40\, \Omega `` resistor is connected to `` 230\, V `` variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:
(A) `` 25\, rad / s `` and `` 75\, rad / s ``
(B) `` 50\, rad / s `` and `` 25\, rad / s ``
(C) `` 46\, rad / s `` and `` 54\, rad / s ``
(D) `` 42\, rad / s `` and `` 58\, rad / s ``

From a circular ring of mass `` 'M' `` and radius `` 'R' `` an arc corresponding to a `` 90^{\circ} `` sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is `` 'K' `` times ' `` MR^{2} `` '. Then the value of `` 'K' `` is :
(A) `` \frac{3}{4} ``
(B) `` \frac{7}{8} ``
(C) `` \frac{1}{4} ``
(D) `` \frac{1}{8} ``