# KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math: Questions 26 - 29 of 172

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## Question number: 26

Appeared in Year: 2010

MCQ▾

### Question

Let be vectors in R3 and be a unit vector in the xy-plane. Then the maximum possible value of is –

### Choices

Choice (4) Response

a.

b.

c.

d.

## Question number: 27

Appeared in Year: 2010

MCQ▾

### Question

Let V1 be the volume of a given right circular cone with O as the centre of the base and A as its apex. Let V2 be the maximum volume of the right circular cone inscribed in the given cone whose apex is O and whose base is parallel to the base of the given cone. Then the ratio is –

### Choices

Choice (4) Response

a.

b.

c.

d.

## Question number: 28

» Basic Mathematics » Arithmetic » Simplifying Expressions

Appeared in Year: 2010

MCQ▾

### Question

Let I, ω and ω2 be the cube roots of unity. The lest possible degree of a polynomial, with real coefficients, having 2 ω2, 3 + 4 ω, 3 + 4 ω2 and 5 – ω – ω2 as roots is –

### Choices

Choice (4) Response

a.

8

b.

5

c.

6

d.

4

## Question number: 29

Appeared in Year: 2011

MCQ▾

### Question

Consider the cubic equation, where a, b, c are real numbers. Which of the following statements is correct?

### Choices

Choice (4) Response

a.

If then the equation has all real and distinct roots

b.

If then the equation has real and distinct roots

c.

If then the equation has one real and two imaginary roots

d.

If then the equation has all real roots

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