KVPY Stream SBSX (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
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: 23
» Sequence and Series » Geometric Progressions
Appeared in Year: 2010
Question
The number of natural numbers n in the interval [500, 2010] for which the polynomial divides the polynomial 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
Question
Let be three vectors in the xyz space such that. If A, B, C are points with position vectors 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
Question
Let P be an arbitrary point on the ellipse. Suppose F_{1} and F_{2} are the foci of the ellipse. The locus of the centroid of the triangle PF_{1}F_{2} as P moves on the ellipse is –
Choices
Choice (4)  Response  

a.  A hyperbola 

b.  A circle 

c.  A parabola 

d.  An ellipse 
