CSIR Physical Sciences: Questions 213 - 216 of 389

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Question number: 213

» Mathematical Methods of Physics » Poles, Residues & Evaluation of Integrals

Appeared in Year: 2012

MCQ▾

Question

The value of the integral c(z3dzz25z+6) , where C is a closed contour defined by the equation 2 z 5=0 , traversed in the anti – clockwise direction, is –

(December)

Choices

Choice (4) Response
a.

16πi

b.

2πi

c.

8πi

d.

16πi

Question number: 214

» Classical Mechanics » Phase Space Dynamics

MCQ▾

Question

Which of the following set of phase – space trajectories is not possible for a particle obeying Hamilton’s equations of motion? (December)

Choices

Choice (4) Response
a.
A phase – space trajectories – Choice A

A Phase – Space Trajectories – Choice a

In figure a phase – space trajectories is shown.

b.
A phase – space trajectories – Choice B

A Phase – Space Trajectories – Choice B

In figure a phase – space trajectories is shown.

c.
A phase – space trajectories – Choice C

A Phase – Space Trajectories – Choice C

In figure a phase – space trajectories is shown.

d.
A phase – space trajectories – Choice D

A Phase – Space Trajectories – Choice D

In figure a phase – space trajectories is shown.

Question number: 215

» Mathematical Methods of Physics » Taylor & Laurent Series

Appeared in Year: 2012

MCQ▾

Question

The Taylor expansion of the function ln(coshx) , where x is real, about the point x=0 starts with the following terms – (December)

Choices

Choice (4) Response
a.

12x2112x4+

b.

12x2+112x4+

c.

12x2+16x4+

d.

12x2+16x4+

Question number: 216

» Mathematical Methods of Physics » Partial Differential Equations

Appeared in Year: 2013

MCQ▾

Question

If A=i^yz+j^xz+k^xy , then the integral CAdI

(Where C is along the perimeter of a rectangle area bounded by x=0,x=a and y=0,y=b ) is – (Dec -2013)

Choices

Choice (4) Response
a.

π(a3+b3)

b.

12(a3+b3)

c.

π(ab2+a2b)

d.

0

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