Mathematical Physics (GATE Physics): Questions 10 - 15 of 39

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Question number: 10

» Mathematical Physics » Elements of Complex Analysis » Cauchy-Riemann Conditions

Appeared in Year: 2014

MCQ▾

Question

The length element ds of an arc is given by, (ds)2=2(dx1)2+(dx2)2+3dx1dx2 . The metric tensor gij is –

Choices

Choice (4) Response
a.

(232321)

b.

(213232)

c.

(132322)

d.

(2331)

Question number: 11

» Mathematical Physics » Linear Differential Equations

Appeared in Year: 2015

MCQ▾

Question

If f(x)=ex2 and g(x)= x ex2 , then –

Choices

Choice (4) Response
a.

g is differentiable everywhere but f is not

b.

f and g are differentiable everywhere

c.

f is differentiable everywhere but g is not

d.

g is discontinuous at x=0

Question number: 12

» Mathematical Physics » Elements of Complex Analysis » Cauchy-Riemann Conditions

Appeared in Year: 2016

MCQ▾

Question

Which of the following is an analytic function of z everywhere in the complex plane?

Choices

Choice (4) Response
a.

z

b.

z2

c.

z 2

d.

(z*)2

Question number: 13

» Mathematical Physics » Linear Differential Equations

Appeared in Year: 2016

MCQ▾

Question

Consider the linear differential equation dydx=xy . If y=2 at x=0, then the value of y at x=2 is given by,

Choices

Choice (4) Response
a.

e2

b.

2e2

c.

e2

d.

2e2

Question number: 14

» Mathematical Physics » Matrices

Appeared in Year: 2012

MCQ▾

Question

The eigen values of the matrix (010101010) are –

Choices

Choice (4) Response
a.

0,2,2

b.

12,12,0

c.

0,1,1

d.

2,2,0

Question number: 15

» Mathematical Physics » Linear Vector Space » Orthogonality and Completeness

Appeared in Year: 2012

MCQ▾

Question

Identify the correct statement for the vectors a=3i^+2j^ and b=i^+2j^

Choices

Choice (4) Response
a.

The vectors a and b linearly dependent

b.

The vectors a and b are orthogonal

c.

The vectors a and b are normalized

d.

The vectors a and b are linearly independent

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