A linear aperture whose width is 0.02 cm is placed
immediately in front of a lens of focal length 60 cm.
The aperture is illuminated normally by a parallel
beam of wavelength 5 X ``10^{-5}`` cm. The distance of
the first dark band of the diffraction pattern from
the centre of the screen is :-
(1) 0.20 cm
(2) 0.15 cm
(3) 0.10 cm
(4) 0.25 cm

Electrons of mass m with de-Broglie wavelength ``\lambda``
fall on the target in an X-ray tube. The cutoff
wavelength (``\lambda_0``) of the emitted X-ray is :-
(1)``\lambda_0``= ``\frac {2m^2c^2\lambda^3}{h^2}``
(2) ``\lambda_0``= ``\lambda``
(3)``\lambda_0``= ``\frac {2mc\lambda^2}{h}``
(4) ``\lambda_0``= ``\frac {2h}{mc}``

Photons with energy 5 eV are incident on a
cathode C in a photoelectric cell. The maximum
energy of emitted photoelectrons is 2 eV. When
photons of energy 6 eV are incident on C, no
photoelectrons will reach the anode A, if the
stopping potential of A relative to C is :-
(1) - 1 V
(2) - 3 V
(3) + 3 V
(4) + 4 V

If an electron in a hydrogen atom jumps from the
3rd orbit to the 2nd orbit, it emits a photon of
wavelength ``\lambda``. When it jumps from the 4th orbit to
the 3rd orbit, the corresponding wavelength of the
photon will be :-
(1)20/7 ``\lambda``
(2)20/13 ``\lambda``
(3)16/25 ``\lambda``
(4)9/16 ``\lambda``

The half-life of a radioactive substance is 30 minutes.
The time (in minutes) taken between 40% decay and
85% decay of the same radioactive substance is :-
(1) 45
(2) 60
(3) 15
(4) 30

For CE transistor amplifier, the audio signal voltage
across the collector resistance of 2 k``\Omega`` is 4 V. If the
current amplification factor of the transistor is
100 and the base resistance is 1 k``\Omega``, then the input
signal voltage is :-
(1) 30 mV
(2) 15 mV
(3) 10 mV
(4) 20 mV

The given circuit has two ideal diodes connected as
shown in the figure below. The current flowing
through the resistance ``R_``1 will be :-

(1) 1.43 A
(2) 3.13 A
(3) 2.5 A
(4) 10.0 A

What is the output Y in the following circuit, when
all the three inputs A,B,C are first 0 and then 1 ?

(1) 1,0
(2) 1,1
(3) 0,1
(4) 0.0

Planck's constant (h), speed of light in vacuum
and Newton's gravitational constant (G) are three
fundamental constants. Which of the following
combinations of these has the dimension of length?
(1)``\sqrt \frac {hc}{(G)}``
(2) ``\sqrt \frac {Gc}{(h^\frac 32)}``
(3) ``\sqrt \frac {Gh}{(c^\frac 32)}``
(4)``\sqrt \frac {Gh}{(c^\frac 52)}``

Two cars P and Q start from a point at the same
time in a straight line and their positions are
represented by ``x_p(t) = at + bt^2`` and ``x_Q (t) = ft - t^2``.
At what time do the cars have the same velocity ?
(1)``\frac {a+ f}{2(1+ b)}``
(2)``\frac { f -a}{2(1+ b)}``
(3)``\frac {a- f}{(1+ b)}``
(4)``\frac {a+ f}{2(b - 1)}``

In the given figure, a = 15 ``\frac {m}{s^2}`` represents the total
acceleration of a particle moving in the clockwise
direction in a circle of radius R = 2.5 m at a given
instant of time. The speed of the particle is :-

(1) 5.7 m/s
(2) 6.2 m/s
(3) 4.5 m/s
(4) 5.0 m/s

A rigid ball of mass m strikes a rigid wall at 60° and
gets reflected without loss of speed as shown in the
figure below. The value of impulse imparted by the
wall on the ball will be :-

(1)mV/2
(2)mV/3
(3) mV
(4) 2mV

A bullet of mass 10g moving horizontally with a
velocity of 400 ``ms^{-1}`` strikes a wooden block of mass
2 kg which is suspended by a light inextensible string
of length 5 m. As a result, the centre of gravity of
the block is found to rise a vertical distance of
10 cm. The speed of the bullet after it emerges out
horizontally from the block will be :-
(1) 120 ``ms^{-1}``
(2) 160 ``ms^{-1}``
(3) 100 ``ms^{-1}``
(4) 80 ``ms^{-1}``

Two identical balls A and B having velocities of
0.5 m/s and -0.3 m/s respectively collide elastically
in one dimension. The velocities of B and A after
the collision respectively will be :-
(1) -0.3 m/s and 0.5 m/s
(2) 0.3 m/s and 0.5 m/s
(3) -0.5 m/s and 0.3 m/s
(4) 0.5 m/s and -0.3 m/s

A particle moves from a point ``(-2\hat{i} + 5\hat{j})`` to
+ ``(4\hat{j} + 3\hat{k})`` when a force of ``(4\hat{i} + 3\hat{j})`` N is applied.
How much work has been done by the force ?
(1) 5 J
(2) 2 J
(3) 8 J
(4) 11 J