Matrices and Determinants (KVPY (Kishore Vaigyanik Protsahan Yojana) 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.

Equation

b.

Equation

c.

Equation

d.

Equation

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 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: 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 Equation , where Equation , and let I denote the identity matrix Equation . Then Equation 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 Equation 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.

Equation

b.

Equation

c.

Equation

d.

Equation

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