# Mathematical Physics-Linear Differential Equations [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 1 - 5 of 12

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## Question 1

Appeared in Year: 2014

### Question MCQ▾

The solution of the differential equation

Subject to the boundary condition and , is –

### Choices

Choice (4)Response

a.

b.

c.

d.

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## Question 2

Appeared in Year: 2015

### Question MCQ▾

A function satisfies the ordinary differential equation , where Consider the four statements P, Q, R, S as given below.

P: and are linearly independent solution for all values of

Q: and are linearly independent solution for all values of

R: and 1 are linearly independent solution for

S: and are linearly independent solution for all values of

The correct option for the combination of valid statements is –

### Choices

Choice (4)Response

a.

Q and R

b.

P and R

c.

R and S

d.

P, R and S

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## Question 3

Appeared in Year: 2015

If and , then –

### Choices

Choice (4)Response

a.

is discontinuous at

b.

and are differentiable everywhere

c.

is differentiable everywhere but is not

d.

is differentiable everywhere but is not

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## Question 4

Appeared in Year: 2016

### Question MCQ▾

Consider the linear differential equation . If at then the value of at is given by,

### Choices

Choice (4)Response

a.

b.

c.

d.

Edit

## Question 5

Appeared in Year: 2013

### Question MCQ▾

For a scalar function satisfying the Laplace equation, has –

### Choices

Choice (4)Response

a.

Zero curl and zero divergence

b.

Zero curl and non – zero divergence

c.

Non – zero curl and non – zero divergence

d.

Non – zero curl and zero divergence

Edit