A parallel-plate capacitor of area A, plate
separation d and capacitance C is filled with four
dielectric materials having dielectric constants k1,
k2, k3 and k4 as shown in the figure below. If a single
dielectric material is to be used to have the same
capacitance C in this capacitor, then its dielectric
constant k is given by :-

(1)``\frac 2k``= ``\frac{3}{k_1 + k_2 + k_3}`` + ``\frac{1}{k_4}``
(2)``\frac 1k``= ``\frac{1}{k_1}`` + ``\frac{1}{k_2}`` + ``\frac{1}{k_3}`` + ``\frac{3}{2k_4}``
(3)`` k = k_1 + k_2 + k_3 + 3k_4``
(4) `` k =\frac 23`` ``( k_1 + k_2 + k_3 )+ 2k_4``

The potential difference (``V_A - V_B``) between the points
A and B in the given figure is :-

(1) + 6 V
(2) + 9 V
(3) - 3 V
(4) + 3 V

A filament bulb (500 W, 100 V) is to be used in a
230 V main supply. When a resistance R is
connected in series, it works perfectly and the bulb
consumes 500 W. The value of R is :-
(1) 26 ``\Omega``
(2) 13 ``\Omega``
(3) 230 ``\Omega``
(4) 46 ``\Omega``

A long wire carrying a steady current is bent into
a circular loop of one turn. The magnetic field at
the centre of the loop is B. It is then bent into a
circular coil of n turns. The magnetic field at the
centre of this coil of n turns will be :-
(1) 2nB
(2) ``2n^2B``
(3) nB
(4) ``n^2B``

A bar magnet is hung by a thin cotton thread in a
uniform horizontal magnetic field and is in
equilibrium state. The energy required to rotate it
by 60° is W. Now the torque required to keep the
magnet in this new position is :-
(1)``\frac{\sqrt3 W}{2}``
(2) ``\frac{2W}{\sqrt3 }``
(3)``\frac{W}{\sqrt3 }``
(4) ``\sqrt3 ``W

An electron is moving in a circular path under the
influence of a transverse magnetic field of
3.57 ``10^{-2}`` T. If the value of e/m is
1.76 X ``10^{11}`` C/kg, the frequency of revolution of
the electron is :-
(1) 62.8 MHz
(2) 6.28 MHz
(3) 1 GHz
(4) 100 MHz

Which of the following combinations should be
selected for better tuning of an L-C-R circuit used
for communication ?
(1) R = 15 ``\Omega``, L = 3.5 H, C = 30 ``\mu``F
(2) R = 25 ``\Omega``, L = 1.5 H, C = 45 ``\mu``F
(3) R = 20 ``\Omega``, L = 1.5 H, C = 35 ``\mu``F
(4) R = 25 ``\Omega``, L = 2.5 H, C = 45 ``\mu``F

A uniform magnetic field is restricted within a region
of radius r. The magnetic field changes with time
at a rate ``\frac {\vec {db}}{dt}``. Loop 1 of radius R > r encloses the
region r and loop 2 of radius R is outside the region
of magnetic field as shown in the figure below. Then
the e.m.f. generated is :-

(1)``-\frac {\vec {db}}{dt}````\pi R^2`` in loop 1 and zero in loop 2
(2) ``-\frac {\vec {db}}{dt}````\pi r^2`` in loop 1 and zero in loop 2
(3) Zero in loop 1 and zero in loop 2
(4) ``-\frac {\vec {db}}{dt}````\pi r^2`` in loop 1 and ``-\frac {\vec {db}}{dt}````\pi r^2`` in loop 2.

The potential differences across the resistance,
capacitance and inductance are 80 V, 40 V and
100 V respectively in an L-C-R circuit. The power
factor of this circuit is :-
(1) 0.8
(2) 1.0
(3) 0.4
(4) 0.5

A 100 ``\Omega`` resistance and a capacitor of 100 ``\Omega``
reactance are connected in series across a 220 V
source. When the capacitor is 50% charged, the
peak value of the displacement current is :-
(1) 4.4 A
(2) 11 2 A
(3) 2.2 A
(4) 11 A

Two identical glass (``\mu_g``= 3/2) equiconvex lenses of
focal length f each are kept in contact. The space
between the two lenses is filled with water
(``\mu_w`` = 4 / 3). The focal length of the combination
is :-
(1) ``\frac {4f}{3}``
(2) ``\frac {3f}{4}``
(3) ``\frac {f}{3}``
(4) f

An air bubble in a glass slab with refractive index
1.5 (near normal incidence) is 5 cm deep when
viewed from one surface and 3 cm deep when
viewed from the opposite face. The thickness (in cm)
of the slab is :-
(1) 12
(2) 16
(3) 8
(4) 10

The interference pattern is obtained with two
coherent light sources of intensity ratio n. In the
interference pattern, the ratio ``\frac {I_{max} - i_{min}}{I_{max} + i_{min}}`` will be :-
(1)``\frac {\sqrt n}{(n+1)^2}``
(2)``\frac {2\sqrt n}{(n+1)^2}``
(3)``\frac {\sqrt n}{(n+1)}``
(4)``\frac {2\sqrt n}{(n+1)}``

A person can see clearly objects only when they lie
between 50 cm and 400 cm from his eyes. In order
to increase the maximum distance of distinct vision
to infinity, the type and power of the correcting lens,
the person has to use, will be :-
(1) concave, - 0.2 diopter
(2) convex, + 0.15 diopter
(3) convex, + 2.25 diopter
(4) concave, - 0.25 diopter