KVPY Stream SBSX (Class 12 & 1st Year B.Sc.) Math: Questions 69  72 of 172
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Question number: 69
» Sets, Relations and Functions » Types of Relations
Appeared in Year: 2012
Question
Let and . A subset B of A is said to be a good subset if for every . Then the number of good subsets of A is –
Choices
Choice (4)  Response  

a. 


b. 


c.  1 

d. 


Question number: 70
» Integral Calculus » Evaluation of Simple Integrals
Appeared in Year: 2012
Question
The value is
Choices
Choice (4)  Response  

a.  4024 

b.  0 

c.  2012 

d.  2013 

Question number: 71
» Permutations and Combinations » Fundamental Principle of Counting
Appeared in Year: 2012
Question
Three children, each accompanied by a guardian, seek admission in a school. The principal wants to interview all 6 persons one after the other subject to the condition that no child is interviewed before its guardian. In how many ways can this be done?
Choices
Choice (4)  Response  

a.  180 

b.  90 

c.  60 

d.  120 

Question number: 72
» Integral Calculus » Integration Using Trigonometric Identities
Appeared in Year: 2013
Question
For x, t ∈ R let,
be a family of quadratic polynomials in x with variable coefficients. Let
Which of the following statements are true?
(i) for all t.
(ii) has infinitely many critical points.
(iii) for infinitely many t
(iv) for all t.
Choices
Choice (4)  Response  

a.  (i) and (ii) only 

b.  (iii) and (iv) only 

c.  (ii) and (iii) only 

d.  (iv) and (i) only 
