KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SBSX (Class 12 & 1st Year B.Sc.) Math: Questions 16  22 of 172
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Question number: 16
» Permutations and Combinations » Simple Applications
Appeared in Year: 2010
Question
Three vertices are chosen randomly from the seven vertices of a regular 7sided polygon. The probability that they form the vertices of an isosceles triangle is –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 17
» Coordinate Geometry » Intercepts of a Line on Coordinate Axes
Appeared in Year: 2010
Question
A circle touches the parabola y^{2} = 4x at (1, 2) and also touches its directrix. The ycoordinates of the point of contact of the circle and the directrix is –
Choices
Choice (4)  Response  

a.  4 

b.  3 

c. 


d. 


Question number: 18
» Sequence and Series » Geometric Progressions
Appeared in Year: 2011
Question
Suppose n is a natural number such that where is the square root of – 1. Then n is –
Choices
Choice (4)  Response  

a.  18 

b.  9 

c.  36 

d.  72 

Question number: 19
» Sequence and Series » Arithmetico  Geometric Progression
Appeared in Year: 2011
Question
The minimum value of n for which
Choices
Choice (4)  Response  

a.  Is 101 

b.  Is 121 

c.  Is 151 

d.  All of the above 

Question number: 20
» Basic Mathematics » Arithmetic » Number Games
Appeared in Year: 2010
Question
Suppose m, n are positive integers such that. The value of the expression is –
Choices
Choice (4)  Response  

a.  19 

b.  21 

c.  7 

d.  13 

Question number: 21
» 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: 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 
