Integral Calculus (KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SBSX (Class 12 & 1st Year B.Sc.) Math): Questions 12  16 of 20
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Question number: 12
» Integral Calculus » Evaluation of Definite Integrals
Appeared in Year: 2014
Question
Let, Where, is a nonnegative integer. Then,
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 13
» Integral Calculus » Integral as Limit of a Sum
Appeared in Year: 2013
Question
Let be a positive integer. For a real number , let denoted the largest integer not exceeding and . Then,
is equal to – (Model Paper)
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 14
» Integral Calculus » Fundamental Theorem of Calculus
Appeared in Year: 2013
Question
For a real number let denote the largest integer less than or equal to and . The smallest possible integer value of for which exceeds 2013 is – (Model Paper)
Choices
Choice (4)  Response  

a.  90 

b.  64 

c.  63 

d.  91 

Question number: 15
» Integral Calculus » Evaluation of Definite Integrals
Appeared in Year: 2015
Question
Define a function by , where is fixed natural number. Then
is –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 16
» Integral Calculus » Fundamental Integrals Involving Functions
Appeared in Year: 2015
Question
Let be a continuous function satisfying,
For all . Then –
Choices
Choice (4)  Response  

a. 


b.  is an odd function 

c. 


d.  has more than 1 point in common with the axis 
