# GATE (Graduate Aptitude Test in Engineering) Physics: Questions 287 - 292 of 659

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## Question 287

Appeared in Year: 2010

### Question

MCQ▾

If , then the Laplace transform of is –

### Choices

Choice (4)Response

a.

b.

c.

d.

### Passage

In a one – dimensional harmonic oscillator, and are respectively the ground, first and the second excited states. These three states are normalized and are orthogonal to one another.

, where is a constant.

## Question 288 (1 of 2 Based on Passage)

Appeared in Year: 2011

### Question

MCQ▾

For the value of determined in above question, the expectation value of energy of the oscillator in the state is –

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 289 (2 of 2 Based on Passage)

Appeared in Year: 2011

### Question

MCQ▾

The value of for which is orthogonal to is –

### Choices

Choice (4)Response

a.

1

b.

c.

d.

2

## Question 290

Appeared in Year: 2010

### Question

MCQ▾

A system of non – interacting classical point particle is constrained to move on the two – dimensional surface of a sphere. The internal energy of the system is –

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 291

Appeared in Year: 2010

### Question

MCQ▾

For any set of inputs, A and B, the following circuits give the same output, except one. Which one is it?

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 292

Appeared in Year: 2010

### Question

MCQ▾

The first three energy levels of are shown below

The expected spin – parity and energy of the next level are given by –

### Choices

Choice (4)Response

a.

b.

c.

d.

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