Integral Calculus (KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SBSX (Class 12 & 1st Year B.Sc.) Math): Questions 1  7 of 20
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Question number: 1
» Integral Calculus » Evaluation of Definite Integrals
Appeared in Year: 2010
Question
Let, where n is nonnegative integer. Then is equal to –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 2
» 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: 3
» 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 

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

a. 


b. 


c. 


d. 


Question number: 5
» Integral Calculus » Integral as Limit of a Sum
Appeared in Year: 2012
Question
Consider,
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 6
» 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: 7
» 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 
