Matrices and Determinants (KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math): Questions 1 - 4 of 5

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Question number: 1

» Matrices and Determinants » Solution of Simultaneous Linear Equations in Two or Three Variables

Appeared in Year: 2011

MCQ▾

Question

Let P be an m × m matrix such that P2 = P. Then (1 + P) n equals –

Choices

Choice (4) Response

a.

I+(2n−1)P

b.

I+nP

c.

I+P

d.

I+2nP

Question number: 2

» 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 Ak=I (the identity matrix) and Bl=0 (the zero matrix). Then –

Choices

Choice (4) Response

a.

Det(A+B)≠0

b.

Det(AB)=0

c.

A+B=I

d.

(A+B)m=0 for some integer m

Question number: 3

» Matrices and Determinants » Solution of Simultaneous Linear Equations in Two or Three Variables

Appeared in Year: 2010

MCQ▾

Question

Let A denote the matrix (0ii0) , where i2=−1 , and let I denote the identity matrix (1001) . Then I+A+A2+…+A2010 is –

Choices

Choice (4) Response

a.

f has local minima at x = c, a and a local maximum at x = b

b.

f has local minima at x = a, b and a local maximum at x = c

c.

f has local minima at x = b, c and a local maximum at x = a

d.

All of the above

Question number: 4

» Matrices and Determinants » Area of Triangles Using Determinants

Appeared in Year: 2011

MCQ▾

Question

Let A=(4, 0),B=(0, 12) be two points in the plane. The locus of a point C such that the area of triangle ABC is 18 sq. units is –

Choices

Choice (4) Response

a.

(y+3x−12)2=81

b.

(y+3x−81)2=14

c.

(y+3x+12)2=81

d.

(y+3x+81)2=12

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