KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math: Questions 23 - 26 of 155

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Question number: 23

» Sequence and Series » Geometric Progressions

Appeared in Year: 2010

MCQ▾

Question

The number of natural numbers n in the interval [500, 2010] for which the polynomial 1+x+x2+x3++xn1 divides the polynomial 1+x2+x4++x2010 is –

Choices

Choice (4) Response

a.

1006

b.

503

c.

100

d.

0

Question number: 24

» Vector Algebra » Scalar and Vector Products

Appeared in Year: 2011

MCQ▾

Question

Let a,b,c be three vectors in the xyz space such that a×b=b×c=c×a0 . If A, B, C are points with position vectors a,b,c 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

» Coordinate Geometry » Ellipse

Appeared in Year: 2010

MCQ▾

Question

Let P be an arbitrary point on the ellipse x2a2+y2b21,a>b>0 . 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

» Vector Algebra » Scalar and Vector Triple Product

Appeared in Year: 2010

MCQ▾

Question

Let u=2i^j^+k^,v=3j^+2k^ be vectors in R3 and w be a unit vector in the xy-plane. Then the maximum possible value of (u×v)w is –

Choices

Choice (4) Response

a.

13

b.

5

c.

12

d.

17

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