Integral Calculus (KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math): Questions 14 - 17 of 17

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Question number: 14

» Integral Calculus » Fundamental Theorem of Calculus

Appeared in Year: 2013

MCQ▾

Question

For a real number x let [x] denote the largest integer less than or equal to x and {x}=x[x] . The smallest possible integer value of n for which 1n[x]{x}dx 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

MCQ▾

Question

Define a function f:RR by f(x)=max{ x , x1 ,, x2n } , where n is fixed natural number. Then

02nf(x)dx is –

Choices

Choice (4) Response
a.

n2

b.

3n2

c.

n

d.

3n

Question number: 16

» Integral Calculus » Fundamental Integrals Involving Functions

Appeared in Year: 2015

MCQ▾

Question

Let f:RR be a continuous function satisfying,

f(x)+0xtf(t)dt+x2=0,

For all xR . Then –

Choices

Choice (4) Response
a.

limxf(x)=2

b.

f(x) is an odd function

c.

limxf(x)=2

d.

f(x) has more than 1 point in common with the x axis

Question number: 17

» Integral Calculus » Properties of Definite Integrals

Appeared in Year: 2015

MCQ▾

Question

If p(x) is a cubic polynomial with p(1)=3 , p(0)=2 and p(1)=4 , then

11p(x)dxis

Choices

Choice (4) Response
a.

3

b.

2

c.

5

d.

4

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