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1 [P.T.O.
- The trace of an antisymmetric
matrix is :
(A) real
(B) zero
(C) pure imaginary
(D) unity
- What is the volume of a
parallelopiped spanned by the
vectors :
( i ˆ^^ +^ ˆ j^^ ) ,^ ( ˆ j^^ +^ k ˆ^ )^ ,^ ( k ˆ^ + i ˆ)?
(A) zero
(B) 1
(C) 2
(D) 3
Physics
Paper II
Time Allowed : 75 Minutes] [Maximum Marks : 100 Note : This paper contains Fifty (50) multiple choice questions, each question carrying Two (2) marks. All questions are compulsory.
- In an X-ray diffraction experiment the incident radiation has a linewidth of 0.1%. Assuming ideal situation what will be the angular width δθ of a diffraction line at a scattering angle of π/2? (A) 0.001 rad (B) 0.01 rad (C) 0.005 rad (D) 0.002 rad
- An experiment involves measurement of two random variables A and B. The measurement error in A is 0.1% and that in B is 0.2%. The error in measurement of (A + B) will then be : (A) 0.1% (B) 0.2% (C) 0.03% (D) 0.0225%
- The step function
u u u
^ >
θ = (^) <
is given by the integral
C
e^ izu
π i ∫ z dz
when the contour C is :
(A) circle of radius a with origin as centre
(B) a semicircle comprising real axis and half the arc of circle above the real axis
(C) a semicircle as in (B) above but avoiding the origin by indenting the real axis by a semicircle of radius ε above the real axis
(D) a semicircle comprising the imaginary axis and an infinite arc of circle on the right side of origin
- The value of ∇( r^2 ) is :
(A) (^) r ˆ
(B) 2 r %
(C) 2| r % |
(D) zero
- The value of ∇^2 (1/ r ) is :
(A) −^1 r^2
(B) –4πδ( r )
(C) 4 π
(D) zero
- If A is an antisymmetric matrix of
odd order n , then the determinant of A is :
(A) positive real number
(B) negative real number
(C) zero
(D) real number (–1)( n^ + 1)/
- The stationary eigenfunction for
Hamiltonian of a particle of mass m in one-dimensional potential V( x ) is given to be : ψ( x ) = A exp(– bx^2 /2), where A and b are real positive constants. It follows that : (A) V( x ) = constant (B) V( x ) ∝ 1/ x (C) V( x ) ∝ x^2 (D) V( x ) ∝ x^3
- If the φ dependent part of an
eigenfunction of an electron in a hydrogen atom e^2 i φ, then the minimum principal and minimum orbital angular momentum quantum numbers n and l respectively for this eigenfunction will be : (A) n = 3, l = 2 (B) n = 2, l = 2 (C) n = 2, l = 1 (D) n = 1, l = 2
- The wave function of a particle
moving in one-dimensional time
independent potential V( x ) is
represented by ψ( x ) = e–iax + b , where
a and b are real constants. This
means that the potential V( x ) is of
the form :
(A) V( x ) ∝ x
(B) V( x ) ∝ x^2
(C) V( x ) = constant
(D) V( x ) = e–ax^ + b
- The eigenvalues of a Hermitian
operator must be :
(A) Complex
(B) Real
(C) Positive
(D) Negative
5 [P.T.O.
- If the Q factor of a coil which is W 0 L/R is measured as a function of frequency, then : (A) the plot between Q and frequency is linear (B) the value of Q initially decreases with increase in frequency and afterwards increases with increase in frequency (C) the value of Q initially increases with increase in frequency and afterwards decreases with increase in frequency (D) the Q factor remains constant irrespective of the value of frequency
- In a Millikan oil drop experiment, one of the drop falls at speed V without field and rises at speed 2 V with field E applied. If the field is made E/2, the drop will : (A) fall with speed V/ (B) rise with speed V/ (C) rise with speed 3V/ (D) remain steady
- It is required to operate a proportional counter with a maximum radial field of 107 Vm–1. The applied voltage required if the radii of the wire and tube are 0.002 cm and 1 cm respectively is :
(A) 107 Volts
(B) 1242 Volts
(C) 1242 × 10^7 Volts
(D) 12 Volts
- A pressure sensor measures the systolic blood pressure of a human body which is 120 mm of Hg. It means :
(A) Pressure is only 120 mm of Hg
(B) Pressure is 120 mm of Hg above atmospheric pressure
(C) Pressure is 120 mm of Hg below atmospheric pressure
(D) It is noway related to atmospheric pressure
7 [P.T.O.
- In the figure a frictionless, massless pulley is fixed to the edge of a frictionless table. The two blocks of mass 10 kg and 5 kg are connected by a weightless string passing over the pulley. Is the tension in the string : (A) Greater than (B) Less than (C) Equal to (D) Square of the tension it would be if the 5 kg block was glued down.
- A circular disc is rotating about its centre in the horizontal plane. A razor blade is balanced on edge in a grove along a radius of the wheel. If the blade is pulled along the radius toward the centre of the wheel, will it tend to fall : (A) In the direction of rotation (B) Opposite to the direction of rotation (C) On both sides with equal probability (D) In either in or opposite to the direction of rotation depending on the frictional force between the edge and the disc 28. Imagine the radius of the earth
shrinking by 1%, its mass remaining
the same. Then its kinetic energy of rotation :
(A) decreases by 2%
(B) increases by 2%
(C) increases by 1%
(D) decreases by 1%
- A uniform thin rod of mass M and
length L hangs from a frictionless
pivot and is connected at the bottom
by a spring to the wall as shown. The spring constant is K. Then the
period of motion, is a function of :
(A) M and K
(B) K and L
(C) M and L
(D) M, K and L
5 kg
10 kg
- What is the ratio of the mass of the
sun to the mass of the earth to one significant figure?
(A) 1 × 10^9
(B) 3 × 10^5
(C) 7 × 10^7
(D) 9 × 10^11
- Two persons of equal weights are
hanging by their hands from the ends of a rope hung over a frictionless pulley. They begin to climb. One person can climb twice the speed of the other (with respect to the rope). Who gets to the top first?
(A) faster climber
(B) slower climber
(C) get there together
(D) indeterminate
- The man in the figure weighs 150 kg. He sits in a sling and pulls himself slowly up by means of a rope one a pulley. With what force he must pull?
(A) 150 g (B) 100 g (C) 75 g (D) 50 g g : constant acceleration due to gravity on earth surface.
- A point charge q is placed at the origin. The flux of the electric field that passes through a square described by the vertices (0, 0, 1), (1, 0, 1), (1, 1, 1) and (0, 1, 1) is :
(A) 0
q ∈
(B) (^30)
q ∈
(C) (^60)
q ∈
(D) (^240)
q ∈
- A constant current is flowing through a cylindrical wire. Then the Poynting vector at the surface of the cylindrical wire : (A) is in the direction of the current (B) is in the radially outward direction (C) is in the radially inward direction (D) has zero magnitude
- A charged particle q is kept at center of a mettalic spherical shell. The magnitudes of the electric fields inside the shell and outside the shell are given by :
(A) 0, (^2) (^40)
q π ∈ r respectively
(B) 2
q π ∈ r , 0 respectively
(C) 2
q π ∈ r ,^402
q π ∈ r respectively
(D)
q π ∈ r ,^40
q π ∈ r respectively
( r denotes the distance from the center)
- Considering Hydrogen (H 2 ) and Helium (He) as classical ideal Maxwell-Boltzmann gas, the ratio of root mean square speeds of H 2 molecules to that of He atoms at the same temperature T is :
(A) 2
(B) (^2)
(C) 12
(D) 12
- The molar specific heat of conduction electrons at 300 K is :
(A) >> 32 R
(B) 32 R
(C) << 32 R
(D) R
Here R is the gas constant.
11 [P.T.O.
- Two identical particles are to be distributed over 3 energy levels. Treating the particles as distinguishable Maxwell-Boltzmann particles, the number of ways in which the particles can be distributed is : (A) 9 (B) 6 (C) 3 (D) 8
- A system of N identical independent
three dimensional harmonic oscillators vibrating with the same frequency ω. The system is contact with a heat reservoir at temperature T. Treating the oscillators as classical, the molar specific heat of the system is :
(A) 32 R
(B) 3NK
(C) 32 R
(D) 3R
- A system has a relaxation time of the order of a millisecond. A quasistatic process on this system can be carried out on the time scale of the order of :
(A) 0.001 s
(B) 0.1 s
(C) 0.0001 s
(D) 1 μs
- Let E be the mean kinetic energy and V be the volume of a classical ideal gas. The pressure of the gas is numerically equal to :
(A) 2 E3 V
(B) 1 E3 V
(C) 3 E2 V
(D) 1 E2 V
13 [P.T.O.
ROUGH WORK
ROUGH WORK
