*Mudra* Physical Sciences For NET & SET Exams. Of UGC-CSIR

_____________________________________________________________________________ (MCQs) Part B & C Vol-01

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MUDRA PHYSICAL SCIENCES

VOLUME-01

PART B & C

MODEL QUESTION BANK FOR THE TOPICS:

1. Mathematical Methods of Physics

UNIT-I 1

UNIT-II 15

UNIT-II 47

2. Classical Mechanics 63

UNIT-I 63

UNIT-II 79

*Mudra* Physical Sciences For NET & SET Exams. Of UGC-CSIR

_____________________________________________________________________________ (MCQs) Part B & C Vol-01

1

1. Mathematical Methods of Physics

UNIT-I

1. A point at which a function zf ceases to be analytic is called –a) Zero b) Singularityc) Pole d) Limit point

2. The limit point of the poles of a function zf is –a) A pole b) An isolated singularityc) A non-isolated singularity d) A non-isolated essential singularity

3. The sequence

ne

nis –

a) Divergent b) Convergent c) Monotonic increasing d) Oscillating

4. Regular falsi is better than bisection method because of its –a) Simplicity b) Accuracyc) Faster convergence d) None of these

5. Which of the following statements applies to the bisection method used for finding roots of functions?

a) Converges within a few iterationsb) Guaranteed to work for all continuous functionsc) Is faster than the Newton-Raphson methodd) Requires that there be no error in determining the sign of the function

6. The convergence of which of the following method is sensitive to starting values? a) Gauss seidal method b) False positionc) Newton-Raphson method d) All of these

7. The constant p for which CBA

where kiA 2

; kjpiB

; kjiC 32

is –a) 1 b) – 2 c) 2 d) – 1

8. The integral dzzzn 12 2

around 3z vanishes if the integer n is such that –

a) n < – 2 b) n < – 2c) n = – 2 d) None of these

9. There are two functions z and z . Find out correct answer –a) Both are analytic b) z is analytic and z is not analytic c) Both are not analytic d) z is analytic and z is not analytic

*Mudra* Physical Sciences For NET & SET Exams. Of UGC-CSIR

_____________________________________________________________________________ (MCQs) Part B & C Vol-01

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10. In the Fourier series expansion of a periodic function –a) Even functions have only a constant and cosine terms in their FS expansionb) Function with half-wave symmetry contain only odd harmonicsc) Odd functions have only sine terms in their FS expansiond) All the above

11. Newton-Raphson method is applicable to the solution of –a) Both algebric and transcendental equationsb) Both algebric and transcendental and also used when the roots are complexc) Algebric equations onlyd) Transcendental equations only

12. The value of the complex integral C

dzztanh ; 1: zc is –

a) πi b) 2πic) 0 d) 4πi

13. Order of the differential equation 3

2

2

dx

dy

dx

ydxy is –

a) 1 b) 2c) 3 d) 0

14. 04522 yxDDx is a homogenous linear differential equation of order 2 –a) True b) Falsec) Partially true d) None of these

15. A vector A

is solenoidal if its –a) Divergence is zero b) Gradient is zeroc) Divergence is non-zero d) Gradient is non-zero

16. If the line integral of a vector field depends only upon the co-ordinates of the two points in the field and independent of actual path taken between them, then the field is said to be –

a) Curled b) Non conservativec) Conservative d) Non-lamellar

17. We have m equations in n unknowns and then the coefficient matrix A will be of the type nm . Let r be the rank of the matrix. If nr , then equation AX = 0 will have –

a) rn linearly independent solutions b) Infinite number of solutions c) rm linearly independent solutions d) No linearly independent solutions

18. We have m equations in n unknowns and then the coefficient matrix A will be of the type nm . Let r be the rank of the matrix. If nr , then equation AX = 0 will have –

a) rn linearly independent solutions b) Infinite number of solutionsc) rm linearly independent solutions d) No linearly independent solutions

*Mudra* Physical Sciences For NET & SET Exams. Of UGC-CSIR

_____________________________________________________________________________ (MCQs) Part B & C Vol-01

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19. Which of the following equation is linear?

a) 1dx

dyyx b) CBx

dx

dyA

c) 0 dxdyxa d) 0tantan dx

dyyx

20. Solution of the differential equation 022 xydydxyx is –

a) Aye xy /2

b) Axe xy /2

c) Aye yx 2/ d) Axe yx

2/

21. Which one of the following is tensor of order zero? a) BA b) BA c) BA d) BA

22. Evaluate

0sin xdx by taking equal interval using Trapezoidal rule–

a) 1.902 b) 1.941c) 1.888 d) 1.984

23. The vectors jibkia 2,3 are adjacent sides of a parallelogram. Its area is:

a) 172

1b) 14

c) 41 c) 72

1

24. Sort out the covariant vector component –

a) t

xi

b) jx

u

c) ii d) None of these

25. Inverse of Laplace transform of 45

102 ss

is –

a) tt ee 410 b) tt ee 410

c) tt ee 4

3

10 d) tt ee 4

3

10

26. Fourier transform of tf is tdtt cos20

if and only if –

a) t is real and tf is real b) The function is tjetf

c) tf is real and tf is even d) tf is real and tf is odd

*Mudra* Physical Sciences For NET & SET Exams. Of UGC-CSIR

_____________________________________________________________________________ (MCQs) Part B & C Vol-01

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27. The polynomial 32 2 xx

a) 012 11343

1PPP b) 012 1134

3

1PPP

c) 012 11343

1PPP d) 012 1134

3

1PPP

28. If 21

1

dxxPn , then n is –

a) 1 b) 0c) – 1 d) None of these

29. How many four digit EVEN numbers have all 4 digits distinct?a) 2240 b) 2296c) 2620 d) 4536

30. If kjibkjia 2,322 and jic 3 then bta is perpendicular to c if t is equal to:

a) 8 b) 4c) 6 d) 2

31. Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is –

a) 8

1b)

8

7

c) 16

1d)

16

15

32. The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is –

a) 3 b) 8c) 9 d) 12

33. The amount of flux diverging from a point per unit area per second is called –a) Divergence of a scalar field b) Divergence of a vector fieldc) Gradient of a scalar field d) Gradient of a vector field

34. The direction of grad is –a) Tangential to level surface b) Normal to level surfacec) Inclined at 450 to level surface d) Arbitrary

35. The function 211

1/z

:

a) Is analytic in the region 2z b) Has a pole at 1z

c) Has a branch point at 1z d) Has an essential singularity at 1z

*Mudra* Physical Sciences For NET & SET Exams. Of UGC-CSIR

_____________________________________________________________________________ (MCQs) Part B & C Vol-01

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36. The condition that the vector A

should be the gradient of a scalar function is –

a) 0. A

b) 0 A

c) 0 A

d) 02 A.A

37. The curl of a vector field can be represented as –

a) curl A b) A

c) A.

d) A

38. The Gauss divergence theorem is –

a) dVAsd.Avs

div b) dVAsd.A

vs

grad

c) C

srd.Asd.A

d) sd.Ard.As

curl

39. The Stoke’s theorem is –

a) Cs

rd.Asd.A

b) sC

sd.Ard.A

curl answer

c) dVAsd.Ass

div d) dVAsd.A

ss

grad

40. If DCBA ,,, be any four vectors then which of the products is meaningful?

a) CBA . b) CBA. c) CBA d) DCBA

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