Matrices and Determinants (KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SB-SX (Class 12 & 1st Year B.Sc.) Math): Questions 1 - 5 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
Question
Let P be an m × m matrix such that P2 = P. Then (1 + P) n equals –
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Question number: 2
» Matrices and Determinants » Evaluation of Determinants
Appeared in Year: 2011
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 (the identity matrix) and (the zero matrix). Then –
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| d. | for some integer m |
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Question number: 3
» Matrices and Determinants » Solution of Simultaneous Linear Equations in Two or Three Variables
Appeared in Year: 2010
Question
Let A denote the matrix , where , and let I denote the identity matrix . Then is –
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| Choice (4) | Response | |
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| a. | f has local minima at x = c, a and a local maximum at x = b |
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| b. | f has local minima at x = a, b and a local maximum at x = c |
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| c. | f has local minima at x = b, c and a local maximum at x = a |
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| d. | All of the above |
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Question number: 4
» Matrices and Determinants » Area of Triangles Using Determinants
Appeared in Year: 2011
Question
Let be two points in the plane. The locus of a point C such that the area of triangle ABC is 18 sq. units is –
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Question number: 5
» Matrices and Determinants » Evaluation of Determinants
Appeared in Year: 2015
Question
The remainder when the determinant,
is divided by is –
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| Choice (4) | Response | |
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| a. | 1 |
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| b. | 3 |
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| c. | 4 |
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| d. | 2 |
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