KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math: Questions 22 - 25 of 172

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Question number: 22

» Matrices and Determinants » Evaluation of Determinants

Appeared in Year: 2011

MCQ▾

Question

Let A and B be any two n × n matrices such that the following conditions hold: AB = BA and there exist positive integers k and l such that Equation (the identity matrix) and Equation (the zero matrix). Then –

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation for some integer m

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 Equation divides the polynomial Equation 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 Equation be three vectors in the xyz space such that Equation . If A, B, C are points with position vectors Equation 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 Equation . 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

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