KVPY Stream SBSX (Class 12 & 1st Year B.Sc.) Math: Questions 71  74 of 172
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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 

Question number: 73
» Sets, Relations and Functions » Equivalence Relations
Appeared in Year: 2012
Question
Let f: R ⟶ R be the function with. Then if and only if –
Choices
Choice (4)  Response  

a.  are all positive and distinct 

b.  are all distinct 

c.  At least two of are equal 

d. 


Question number: 74
» Basic Mathematics » Arithmetic » Number Games
Appeared in Year: 2012
Question
Suppose a_{1}, a_{2}, a_{3}, …, a_{2012} are integers arranged on a circle. Each number is equal to the average of its two adjacent numbers. If the sum of all even indexed numbers is 3018, what is the sum of all numbers?
Choices
Choice (4)  Response  

a.  1509 

b.  3018 

c.  6036 

d.  0 
