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Revision Quiz on Definite Integration & Area

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Question 1

The value of the integral

Question 2

Question 3

The value of n for which

Question 4

Question 5

The value of the integral
, where [x] denotes the greatest integer less than or equal to x, is:

Question 6

If f(x) = f(π + e – x) and Description: Description: image415.png then Description: Description: image416.png is equal to

Question 7

If I1 = Description: E:\KCET-1-Feb\Karnataka_CET2013_files\image514.pngx.sinxdx and I2 = Description: E:\KCET-1-Feb\Karnataka_CET2013_files\image515.pngx.cosxdx then which one of the following is true?

Question 8

For a real number let [] denote the largest integer less than or equal to . The smallest positive integer for which the integral exceeds 60 is

Question 9

Define for all real x, where

Then

Question 10

Find where denotes the greatest integer function.

Question 11

Evaluate:

Question 12

The value of a > 1, where [x] denotes the greatest integer not exceeding x is

Question 13

equals

Question 14

Let be the infinite sum given by

where is a sequence defined by and for If is expressed in the form where are coprime positive integers, then equals

Question 15

Find
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Dec 23JEE & BITSAT