KVPY Stream SBSX (Class 12 & 1st Year B.Sc.) Math: Questions 45  49 of 172
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Question number: 45
» Statistics and Probability » Probability of an Event
Appeared in Year: 2012
Question
Let denote the sum of the first n positive integers. The numbers S_{1}, S_{2}, S_{3}, …, S_{99} are written on 99 cards. The probability of drawing a card with an even number written on it is –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 46
» Integral Calculus » Integration Using Trigonometric Identities
Appeared in Year: 2012
Question
The value of the integral , where is –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 47
» Sets, Relations and Functions » Equivalence Relations
Appeared in Year: 2012
Question
Let n be a natural number and let ‘a’ be a real number. The number of zeros of in the interval [1, 1] is
Choices
Choice (4)  Response  

a.  2 if a < 0 

b.  At least three for every value of a 

c.  2 if a > 0 

d.  At most one for every value of a 

Question number: 48
» Sets, Relations and Functions » Functions and Composition
Appeared in Year: 2012
Question
Let a, b, c, d be numbers in the set {1, 2, 3, 4, 5, 6} such that the curves and have no point in common. The maximum possible value of is
Choices
Choice (4)  Response  

a.  36 

b.  5 

c.  30 

d.  0 

Question number: 49
» Integral Calculus » Evaluation of Simple Integrals
Appeared in Year: 2012
Question
Let [x] and {x} are be the integer part and fractional part of a real number x respectively. The value of the integral, is –
Choices
Choice (4)  Response  

a.  5 

b. 


c.  35.5 

d.  34.5 
