# GATE (Graduate Aptitude Test in Engineering) Physics: Questions 633 - 637 of 659

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## Question 633

Appeared in Year: 2017

### Describe in Detail

Essay▾

Light is incident from a medium of refractive index onto vacuum. The smallest angle of incident of which light is not transmitted into vacuum is . (up to two decimal places) .

### Explanation

• The smallest angle of incident of which light is not transmitted into vacuum is critical angle .
• When we incident light at the angle of critical angle, the light is refracted along the intersection line of medium and vacuum. Therefore, refraction angle becomes .
• Applying Snell՚s law of refraction,

• Where, are the refractive index of medium and vacuum …

… (3 more words) …

## Question 634

Appeared in Year: 2017

### Describe in Detail

Essay▾

For the transistor amplifier circuit shown below with , and . Neglecting the emitter diode resistance, the input impedance of the amplifier looking into the base for small ac signal is . (up to two decimal places) .

### Explanation

The input impedance of common collector amplifier is,

## Question 635

Appeared in Year: 2017

### Question

MCQ▾

Let be a column vector of dimension with at least one non – zero entry. The number of non – zero eigenvalue of the matrix is:

### Choices

Choice (4)Response

a.

n

b.

0

c.

d.

1

## Question 636

Appeared in Year: 2017

### Describe in Detail

Essay▾

The integral is equal to ________. (up to two decimal places) .

### Explanation

Let,

As we know,

Now, from integration by part;

is a famous Gaussian integral, whose value is .

## Question 637

Appeared in Year: 2017

### Describe in Detail

Essay▾

A parallel plate capacitor with square plates of side separated by is filled with a medium of dielectric constant of . If the charges on the two plates are and , the voltage across the capacitor is . (up to two decimal places) .

### Explanation

According to question,

Area of the plate is,

Distance between two plates,

Dielectric constant is,

Charge on plates,

The capacitance of the capacitor is given as,

Now, capacitance of the capacitor is also given by,

Where, is the magnitude of charge on plate and is the voltage across the capacitor.

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