TS SET 2014: Paper II, Physical Sciences
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CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBJECT CODE SUBJECT PAPER
A-16-02 PHYSICAL SCIENCES II
HALL TICKET NUMBER
QUESTION BOOKLET NUMBER
OMR SHEET NUMBER
DURATION MAXIMUM MARKS NUMBER OF PAGES NUMBER OF QUESTIONS
1 HOUR 15 MINUTES 100 16 50
This is to certify that, the entries made in the above portion are correctly written and verified.
Candidates Signature Name and Signature of Invigilator
Instructions for the Candidates A¿æýÅÆæÿ$¦ËMæü$ çÜ*^èþ¯èþË$
1. Write your Hall Ticket Number in the space provided on the 1. D ç³#r ò³O ¿êVæü ÌZ CÐèþÓºyìþ¯èþ çÜ¦Ë ÌZ Ò$ çàÌý sìýMðüsý ¯èþ ºÆæÿ$ Æ>Äæý$ yìþ.
top of this page.
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2. This paper consists of fifty multiple-choice type of questions.
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correct booklet from the invigilator within the period {ç³Ôèý² ç³{é°² Ððþ r¯óþ Ððþ$$§æþsìý I§æþ$ °Ñ$ÚëÌZÏ ç³È> ç³ÆæÿÅÐóþæüMæü$°Mìü ÇW C_aÐóþíÜ
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correct response against each item. OMR ç³{èþÐèþ$$ÌZ {ç³ {ç³Ôé² çÜ QÅMæü$ CÐèþÓºyìþ¯èþ ¯éË$Væü$ Ðèþé¢ÌZÏ çÜÆðÿO¯èþ
Example : A B C D {ç³çܵ §æþ¯èþ¯èþ$ çÜ*_ ^óþ Ðèþ颰² »êÌý ´ëÆÿ$$ sý ò³¯þø Mìü §æþ ðþÍí³¯èþ Ñ«§æþ V>
where (C) is the correct response.
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the invigilators at the end of the examination compulsorily
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candidate is allowed to take away the carbon copy of OMR Ðésìý° ç³Èæü Væü¨ ºÄæý$rMæü$ ¡çÜ$Mæü$ÐðþâæýÏMæü*yæþ§æþ$. ç³Èæü ç³NÆæÿ¢Æÿ$$¯èþ èþÆæÿ$Ðéèþ A¿æýÅÆæÿ$¦Ë$
Sheet and used Question paper booklet at the end of the {ç³Ôèý² ç³{é°², OMR ç³{èþ Äñý$$MæüP M>Ææÿ¾¯þ M>ï³° ¡çÜ$Mæü$ÐðþâæýÏÐèþ^èþ$a.
examination. 10. ±Í/¯èþËÏ Ææÿ Væü$ »êÌý ´ëÆÿ$$ sý ò³¯þ Ðèþ*{èþÐóþ$ Eç³Äñý*W ^éÍ.
10. Use only Blue/Black Ball point pen. 11. ÌêVæüÇ£æþÐþ$ sôýº$ÌýÞ, M>ÅÍMæü$ÅÌôýrÆÿË$, GË[M>t°Mü ç³ÇMæüÆ>Ë$ Ððþ$$§æþËVæü$¯èþÑ ç³ÈæüVæü¨ÌZ
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12. There is no negative marks for incorrect answers. 12. èþç³ çÜÐèþ*«§é¯éËMæü$ Ðèþ*Ææÿ$PË èþWY ç³# Ìôý§æþ$.
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CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
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HE
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PHYSICAL SCIENCES
Paper – II
1. If f (x,y,z) = x2 + y2 + z2 than ∇2f is ⎡5 3 ⎤
4. The Eigen values of the matrix ⎢ ⎥
(A) 0 ⎣3 −3 ⎦
are
(B) 4
(C) 6 (A) 6, 4
(D) 8
(B) – 6, – 4
2. Which of the following pair of vectors are
(C) 6, – 4
orthogonal to each other ?
(A) [1, 2, 3], [3, 2, 1] (D) – 6, 4
(B) [1, 0, 0], [2, 0, 0]
(C) [1, 1, 1], [0, 2, 0]
5. Which of the following is true for a Bessel
(D) [3, 0, 2], [0, 4, 0]
differential equation ?
3. Of the following statements, which is true ∞
I. e ( 2 − 2 t ) = ∑ tn Jn (x)
xt x
for a skew symmetric matrix ? n = −∞
I. It is a square matrix II. J−n (x) = (−1)n Jn (x)
II. For all i, j, aij= –aji
III. The transpose of the matrix is the (A) I is true and II is false
matrix itself, i.e. AT = A
(B) I and II are true
(A) Only II is true
(B) I, II and III are true
(C) I and II are false
(C) II, III are true and I is false
(D) I and II are true, III is false (D) Only I is true
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6. Match the following : 8. Laplace transform of {sin at} is
I. ∫
f (z) dz = 0 s
1. Laurent series (A)
c s + a2
2
1 f (z) dz
II. f (a) = ∫
2 πi c z − a
2. Cauchy’s a2
(B)
theorem s2 + a2
∂u ∂v ∂v ∂u
III. = and =− 3. Cauchy’s a
∂x ∂y ∂x ∂y (C)
integral s + a2
2
formula
∞ s2
(D)
IV. f (z) = ∑ an (z − c)n 4. Cauchy- s2 + a2
n=−∞
Riemann
equations 9. When two coins are tossed simultaneously,
I II III IV the probability of getting two heads is
(A) 4 3 2 1
(A) 12
(B) 2 3 4 1
(B) 0
(C) 2 3 1 4
(D) 4 3 1 2 (C) 1
(D) 14
7. The Fourier transform of the function
1 10. The central limit theorem speaks of
f (x) = is
x
convergence to _______ distribution.
(A) π i
(A) Poisson
πi
(B)
2 (B) Normal
πi (C) Uniform
(C)
4
(D) 2πi (D) Chi-square
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11. If a rod is moving with a velocity (v) parallel 13. For a system characterized by the Lagrangian
to its length relative to the stationary 1 2 1
L= (x + y 2 ) − ω20 (x 2 + y 2 ) + α x y ,
observer, then it appears to be contracted 2 2
by a factor what restriction should be imposed on α
for the normal modes of vibrations
1
⎛ 2 ⎞2
(A) ⎜ 1 − v ⎟
⎜ c 2 ⎟⎠ (A) α > 0
⎝
1
− (B) α ≠ 1
⎛ v2 ⎞ 2
(B) ⎜⎜ 1 − ⎟
⎝ c 2 ⎟⎠
(C) α < 0
1
−
v
(C) ⎛⎜ 1 − ⎞⎟
2
⎝ c ⎠ (D) α > 1
2
⎛ v2 ⎞ 14. In a laboratory system for equal masses
(D) ⎜ 1 − ⎟
⎜ c 2 ⎟⎠
⎝
of a particle, the maximum angle of
scattering will be
12. The number of degrees of freedom
possessed by a single particle when it is π
(A)
2
moving in space will be
π
(A) 3N (B) 3
2
(B) One
(C) π
(C) 6N
π
(D)
(D) Three 4
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15. If a particle moves in a circular orbit under 17. The moment of inertia of a rigid body about
the action of a central force F(r) = – kr – 3
a given axis of rotation depends upon
and if the potential energy is zero at infinity,
the total energy of the particle becomes (A) Distribution of mass in the rigid body
(A) Infinity (B) Shape of a rigid body
(B) Zero (C) Position of axis of rotation of a rigid
(C) Constant body
(D) One (D) All the above
16. If a generalized coordinate qk does not 18. For the conservation of energy of a system,
appear explicitly in the Lagrangian
Lagrangian and Hamiltonian do not
function then
depend explicitly on
(A) the corresponding momentum (pk)
(A) momentum
becomes constant of motion
(B) position
(B) q is constant
k
(C) Mass
(C) Hamiltonian is constant
(D) p becomes cyclic coordinate (D) Time
k
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19. Simple pendulum with a variable length 21. If the Lagrangian of a system is
is an example for L = 1 m y 2 − V (y ) then y component of a
2
conjugate momentum is
(A) Rheonomic and Holonomic
∂V
constraints (A) −
∂y
(B) Non-holonomic constraints
(B) my
(C) Scleronomous constraints
(C) my
(D) Scleronomous and non-holonomic
constraints ∂V
(D) −
∂ y
20. A force which plays an important role in a 22. A usual expression for the conserved
Lagrangian via a velocity dependent angular momentum (l) in a central force
potential is problem is
(A) the force of nature (A) l = mr 2 θ
(B) the normal force (B) l = m / r 2 θ
(C) the kinetic friction force (C) l = l / k
(D) the Lorentz force (D) l = ( 12) mr 2 θ
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E
23. The ratio of electric field ( E ) and 25. An electromagnetic wave is given by
H
1 ⎡ ⎛ z ⎞⎤
magnetic field H has dimensions of E= cos ⎢ 4π × 107 ⎜ t − ⎟ ⎥ î then the
2 ⎣ ⎝ c ⎠⎦
wave is
(A) Resistance
(A) Plane polarized propagating along
(B) Inductance z-axis
(C) Capacitance (B) Plane polarized propagating along
y-axis
(D) Product of inductance and
capacitance
(C) Plane polarized propagating along
x-axis
24. Electromagnetic field equation in terms of
(D) Circularly polarized propagating
Scalar ( φ ) and vector potential (A) is
along z-axis
∂ 26. Magnetic vector potential due to a
(A) ∇2ϕ + (∇⋅ A) = − ρ /∈0
∂t
magnetic dipole is proportional to
∂
(B) ∇2 A + (∇φ) = − ρ /∈0 (A) r
∂t
(B) 1/r
2 ∂
(C) ∇ φ + (∇ ⋅ A) = + ρ /∈0
∂t
2
(C) 1/r
2
∂
(D) ∇ A + (∇ϕ) = + ρ /∈0 (D) 1/r3
∂t
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27. ∇2V = – 4πρ, where ‘V’ is potential and ρ is ⎛ 1⎞
⎜ ⎟
charge density, is 30. In the Dirac notation, if ex = ⎜ 0 ⎟ and
⎜⎜ ⎟⎟
⎝0⎠
(A) Maxwell equation
⎛0⎞
⎜ ⎟
ey = ⎜ 1 ⎟ , then ex ey is equal to
(B) Laplace equation ⎜⎜ ⎟⎟
⎝0⎠
(C) Poisson equation
(D) Gauss equation (A) 0
(B) 1
28. The Eigen functions of a Hermitian
⎛1 0 0⎞
operator belong to different Eigen values ⎜ ⎟
(C) ⎜ 0 1 0 ⎟
are ⎜⎜ ⎟⎟
⎝0 0 0⎠
(A) real
⎛ 1⎞
⎜ ⎟
(B) normal (D) ⎜⎜ 1 ⎟⎟
⎜0⎟
⎝ ⎠
(C) orthogonal
31. If two observables, in quantum mechanics,
(D) orthonormal
commute then they
29. A stationary state is a bound one if the
(A) can be measured simultaneously
corresponding wave function
(A) Vanishes at infinity (B) can not be measured simultaneously
(B) Vanishes at finite distance
(C) can have different eigen states
(C) Is finite at infinity
(D) have same eigen values
(D) None of these
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32. In the Stern-Gerlach experiment, beam of 35. If the perturbed Hamiltonian is H′ and the
silver atoms are used to know the
unperturbed Hamiltonian is H o for a
(A) orbital angular momentum
system, then the time-independent
(B) intrinsic spin angular momentum
perturbation theory can be used only when
(C) generalized angular momentum
(A) H ≈ H′
o
(D) orbital and spin angular momentum
(B) H < H′
o
33. One of the examples for a barrier penetration
(C) H > H′
in quantum mechanics problems o
(A) gamma emission (D) H ≥ H′
o
(B) beta emission
36. In quantum mechanics, using the
(C) beta and gamma emissions
variational method one can find the _____
(D) alpha emission
for the ground state energy of a system,
34. The solutions of the radial equation for a when other methods could not give results.
hydrogenic atom are
(A) Upper limit
(A) Hermite polynomials
(B) Lower limit
(B) Associated Legendre polynomials
(C) Intermediate value
(C) Associated Laguerre polynomials
(D) Bessel functions (D) Exact value
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37. If a matrix is a representative of a 39. Which of the following statements are valid
component of J which satisfies the relation for Canonical ensemble ?
J × J = i J, then the trace value is equal to
I. The independent assemblies have
(A) unity
same temperature, volume and
(B) zero number of identical particles
(C) a complex value II. The system can exchange energy
(D) a negative value III. The system can exchange particles
(A) Only I and III are true
38. Match the following :
List – I List – II (B) I, II, and III are true
I. Rayleigh – Jean’s law 1. E = σT 4 (C) I, II and III are false
II. Stefan’s law 2. λm T = constant
(D) I and II are true, III is false
8 πkT
III. Wien’s displacement 3. uλ dλ = dλ
λ4
40. The average energy associated to each
law
degree of freedom is
e
IV. Kirchoff’s law 4. λ = Eλ
αλ
(A) kT
I II III IV
(A) 4 1 2 3 1 kT
(B) 2
(B) 3 1 2 4
(C) 3 2 kT
(C) 2 1 3 4
(D) 3 4 kT
(D) 3 1 4 2
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41. Which of the following statements are valid 43. As per the laws of thermodynamics, the
for Bose-Einstein statistics
relation between pressure (P), volume (V),
I. It is applicable for the particles which
Temperature (T) and entroy (S) is given
are identical and indistinguishable
as
II. The particles have zero or integer
spins (A) TdS = – dU – PdV
III. The particles obey Pauli’s exclusion
(B) TdS = dU + PdV
principle
(A) I, II, III are true (C) SdT = – dU – PdV
(B) I is true, II and III are false (D) SdT = dU + PdV
(C) I and III are true, II is false
(D) I and II are true, III is false 44. In statistical physics, the absolute
temperature (T) of a system is related to
42. Triple point depends on
the number of accessible states (Ω) is
I. Temperature
∂Ω
(A) kT
II. Pressure ∂E
(A) Only I is true ∂
(B) kT (log Ω)
∂E
(B) Only II is true
1 ∂
(C) (log Ω)
(C) I and II are true kT ∂E
(D) I and II are false 1 ∂Ω
(D)
kT ∂E
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45. Which of the following is true for white 48. The following Boolean expression can be
dwarf stars ?
simplified to
I. The mass is nearly same as that of
Sun y =A B C D + ABCD+ A B CD +
—3
II. The luminosity is 3×10 times of A B CD + A B CD+ A B C D
that of Sun
(A) ABC + AD
(A) I is true, II is false
(B) I is false, II is true (B) ABC + AD
(C) I and II are true (C) ABC + A D
(D) I and II are false (D) ABC + A ⋅ D
46. At the junction of a semiconductor hetero 49. A 12-bit counter type A/D converter used
junction PN diode a 1 MHz clock. Its maximum conversion
time is
(A) Potential barrier spike is there
(A) 1 μs
(B) Capacitance discontinuity is there
(B) 12 μs
(C) Immobile charges are present
(C) 4096 μs
(D) All the above
(D) 4 μs
47. The output voltage of the ideal OP Amp
50. Einstein’s relation for holes in a
circuit shown below is
semiconductor material is
5K
1K Dp kT
+2V (A) =
μp q
+
+1V μp kT
1K (B) D = q
p
(A) –7V
Dpk
(B) 7V (C) μ = qT
p
(C) – 5V Dp
kq
(D) 5V (D) μ = T
p
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Source: Telangana State Eligibility Test. Question paper published by Telangana State Eligibility Test.