Integral Calculus-Integral as Limit of a Sum (KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math): Questions 1 - 4 of 4

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Question number: 1

» Integral Calculus » Integral as Limit of a Sum

Appeared in Year: 2012

MCQ▾

Question

Consider,

L=20123+20133++30113

R=20133+20143++30123

andI=20123012x3dxThen

Choices

Choice (4) Response

a.

L+R<2I

b.

L+R>2I

c.

L+R=2I

d.

LR=I

Question number: 2

» Integral Calculus » Integral as Limit of a Sum

Appeared in Year: 2014

MCQ▾

Question

For a real number x let [x] denote the largest integer less than or equal to x . The smallest positive integer n for which the integer 1n[x][x]dx exceed 60 is –

Choices

Choice (4) Response

a.

9

b.

10

c.

8

d.

[6023]

Question number: 3

» Integral Calculus » Integral as Limit of a Sum

Appeared in Year: 2014

MCQ▾

Question

For a real number x let [x] denote the largest integer less than or equal to x and {x}=x[x] . Let n be a positive integer. Then 0ncos(2π[x]{x})dx is equal to –

Choices

Choice (4) Response

a.

0

b.

2n1

c.

1

d.

n

Question number: 4

» Integral Calculus » Integral as Limit of a Sum

Appeared in Year: 2013

MCQ▾

Question

Let n be a positive integer. For a real number x , let [x] denoted the largest integer not exceeding x and {x}=x[x] . Then,

1n+1({x})[x][x]dx is equal to – (Model Paper)

Choices

Choice (4) Response

a.

loge(n)

b.

1n+1

c.

nn+1

d.

1+12++1n

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