# KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SB-SX (Class 12 & 1st Year B.Sc.) Math: Questions 23 - 27 of 172

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## Question number: 23

Appeared in Year: 2010

MCQ▾

### Question

The number of natural numbers n in the interval [500, 2010] for which the polynomial divides the polynomial is –

### Choices

Choice (4) Response

a.

1006

b.

503

c.

100

d.

0

## Question number: 24

Appeared in Year: 2011

MCQ▾

### Question

Let be three vectors in the xyz space such that. If A, B, C are points with position vectors respectively, then the number of possible of the centroid of triangle ABC is –

### Choices

Choice (4) Response

a.

1

b.

6

c.

3

d.

2

## Question number: 25

Appeared in Year: 2010

MCQ▾

### Question

Let P be an arbitrary point on the ellipse. Suppose F1 and F2 are the foci of the ellipse. The locus of the centroid of the triangle PF1F2 as P moves on the ellipse is –

### Choices

Choice (4) Response

a.

A hyperbola

b.

A circle

c.

A parabola

d.

An ellipse

## 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.

f Page