# KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SB-SX (Class 12 & 1st Year B.Sc.) Math: Questions 167 - 171 of 172

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## Question number: 167

» Basic Mathematics » Arithmetic » Simplifying Expressions

Appeared in Year: 2016

MCQ▾

### Question

The Polynomial equation has,

### Choices

Choice (4) Response

a.

three real roots for any , and exactly one real root for any

b.

exactly one real root for any real

c.

three real roots for any real

d.

three real roots for any , and exactly one real root for any

## Question number: 168

Appeared in Year: 2016

MCQ▾

### Question

Let be a polynomial with real coefficients such that , for all . Consider the following statements:

(i) is an even function

(ii) can be expressed as a polynomial in

(iii) is a polynomial of even degree.

Then,

### Choices

Choice (4) Response

a.

All are true

b.

Only and are true

c.

All are false

d.

Only and are true

## Question number: 169

» Basic Mathematics » Algebra » Solutions to Equations

Appeared in Year: 2016

MCQ▾

### Question

The number of integers for which the equation has at least two distinct integer roots is –

### Choices

Choice (4) Response

a.

2

b.

4

c.

1

d.

3

## Question number: 170

Appeared in Year: 2016

MCQ▾

### Question

The area of the region bounded by the curve and the axis, , is –

### Choices

Choice (4) Response

a.

b.

0

c.

d.

## Question number: 171

Appeared in Year: 2016

MCQ▾

### Question

Suppose the tangent to the parabola at has slop . Then equals –

### Choices

Choice (4) Response

a.

3

b.

1

c.

2

d.

0

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