Matrices and Determinants (KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SBSX (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 P^{2} = P. Then (1 + P) ^{n} equals –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


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 –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d.  for some integer m 

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 –
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
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 –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 5
» Matrices and Determinants » Evaluation of Determinants
Appeared in Year: 2015
Question
The remainder when the determinant,
is divided by is –
Choices
Choice (4)  Response  

a.  1 

b.  3 

c.  4 

d.  2 
