KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SBSX (Class 12 & 1st Year B.Sc.) Math: Questions 43  47 of 172
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Question number: 43
» Trigonometry » Trigonometric Identities and Equations
Appeared in Year: 2012
Question
Let then –
Choices
Choice (4)  Response  

a.  f is strictly increasing function 

b.  f is strictly decreasing function 

c.  but for any 

d.  f is a constant function: 

Question number: 44
» Basic Mathematics » Algebra » Solutions to Equations
Appeared in Year: 2012
Question
In the real number system, the equation has –
Choices
Choice (4)  Response  

a.  No solution 

b.  Exactly two distinct solutions 

c.  Infinitely many solutions 

d.  Exactly four distinct solutions 

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 
