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Gives insight on set theory and calculations.
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Time Allowed : 2½ Hours] [Maximum Marks : 150 Number of Pages in this Booklet : 20 Number of Questions in this Booklet : 75
Signature and Name of Invigilator
Seat No. (In figures as in Admit Card) Seat No. .............................................................. (In words) OMR Sheet No. (To be filled by the Candidate)
Test Booklet No.
A B D
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equation. 2 2 2 0
d y dy (^) y dx^ −^ dx +^ = One solution of this equation is A ex. The second linearly independent solution is : (A) e – x (B) xex (C) xe–x (D) x^2 + x
of f ( z ) over a contour comprising the real axis a semi-circle of infinite radius in the upper half plane is :
(A) (^2) a^ π
(B) (^2) a^ π i
(C) (^) a^ π
(D) zero
(A) T^ =^12 ml^2
(B) T = mgl cosθ
(C) T^ =^12 ml^2 θ&^2
(D) T^ =^12 m θ&^2
collide elastically with each other
and scatter off, then the following
statement is correct in the center of
mass frame :
(A) the velocities of the two particles
are interchanged after the
collision
(B) the magnitudes of the velocities
of the two particles are
unchanged by the collision
(C) the two particles move off
together after the collision
(D) the particle with the larger
velocity comes to a rest,
whereas the other particle
stays in motion
the action of a gravitational potential
V( ) MG r = − (^) R , then the following
statement is correct :
(A) The motion of the system is
confined to a plane
(B) The energy of the system is the
only conserved quantity
(C) The motion of the particle is
always bounded
(D) There are no initial conditions
for which the particle can be
execute uniform circular
motion
in quantum mechanics is : (A) (^) i h (B) zero (C) 3 i h
(D) ^ ∂∂ x +^ ∂∂ y + ∂∂ z
quantum mechanical system is
always :
(A) Suppressed (lowered) due to second order perturbation
(B) Suppressed (lowered) due to first order perturbation
(C) Raised due to second order perturbation
(D) Raised due to first order perturbation
operator h i^ ∂^ ∂ x , such that it describes a particle moving in free space in the direction of negative x -axis, with zero uncertainty in the linear momentum? (A) cos kx (B) eikx (C) ekx (D) e – ikx
particles is symmetric under particle interchange. Which of the following is a consequence of this property? (A) Pauli-Exclusion principle (B) Bose-Einstein condensation (C) Heisenberg uncertainty principle (D) Bohr-correspondence principle
of 2R from the centre of a grounded conducting sphere of radius R. The image charge and its distance from the centre are respectively :
(A) −^ q and^ R 2
(B) − 2^ q and R 2
(C) −^ q and^ R 4
(D) − 2^ q and R 4
(A) E 0 B 0 =^ ω k (B) E 0 B 0 = ω k (C) E 0 K = B 0 ω (D) E 0 ω = B 0 k
~
R 1
R 2
C 1
RE C 2
C 3
560 Ω
6.8 kΩ
22 kΩ RC^ = 1 kΩ Vout
(B) 1.42 mF (C) 1.42 μF (D) 1.42 PF
(A) I c = 5.17 mA V c = 0 V (B) I c = 98 μA V c = 392 mV (C) I c = 4 mA V c = 16 V (D) I c = 4 mA V c = 4.7 V
R 1 = 10 kΩ (^) R f = 12 kΩ R 2 = 10 kΩ R 3 = 10 kΩ –
Vout
(A) NAND gate (B) NOR gate (C) AND gate (D) OR gate
(A) 8208 Å
(B) 8028 Å
(C) 8828 Å
(D) 8820 Å
energy level E, when E – EF = k T,
is :
(A) 0.
edge of 3.6Å. How many unit cells
are present in a lump of 1cm^3?
(A) truncated octahedron
(B) rhombohedron
(C) tetrahedron
(D) rhombic dodecahedron
(A) behaves linearly as a function of the applied field (^) H , up to a critical field H c
(B) vanishes identically upto the critical field H c
(C) is a non-zero constant below H c
(D) shows parabolic behaviour below H c and a gap above H c
ferromagnetic material exhibits
B-H curve in the form of :
(A) B–H loop
(B) Straight line
(C) Circle
(D) Ellipse
a junction formed by sandwiching a
thin layer of insulator between two
superconductors causes rf current
oscillations of a frequency of :
(A) 48.36 MHz
(B) 4836.00 MHz
(C) 4.836 MHz
(D) 483.6 MHz
(A) near the top of the valence band
(B) near the bottom of the conduction band
(C) midway between valence and conduction bands
(D) below the valence band
(A) 168 O
(B) 5626 Fe
(C) 20882 Pb
(D) 23592 U
is true for a compound nuclear reaction? (A) The formation of the compound nucleus and its break-up are independent (B) The break-up of compound nucleus is instantaneous (very short life time) (C) The break-up of a compound nucleus depends on the channel of its formation (D) The Q-value of compound nuclear reaction is always negative
the surface energy part is proportional to : (A) A2/ (B) A1/ (C) A (D) A^2
Spin -I and its Z-component I 3 for
the following system of a particle
π_^ + p
(B) UdU
(D) ddd