JEE Exam  >  JEE Notes  >  Chapter-wise Tests for JEE Main & Advanced  >  JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced PDF Download

Q. 1. JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced                         (1987 - 2 Marks)

Ans. JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

Solution. Given that,

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

Expanding along R1, we get

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

Multiply the above by π/2 when n is even. We get

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced


Q. 2. JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced               (1988 - 2 Marks)

Where [ ] denotes the greatest integer function, equals .......

Ans. 2 - √2

Solution. 

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced


Q. 3. JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced                (1989 - 2 Marks)

Ans. 4

Solution.

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced


Q. 4. JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced                (1993 -  2 Marks)

Ans. JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

Solution. 

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced


Q. 5. JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced                   (1994 -  2 Marks)

Ans. 1/2

Solution.

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
Adding (1) and (2), we get

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

Q. 6. If for nonzero  JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced then  JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced             (1996 - 2 Marks)

Ans.  JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

Solution.   JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced            …(1)

Integrating both sides within the limits 1 to 2, we get 

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

Replacing  JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

Integrating both sides within the limits 1 to 2, we get 

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

Eliminate  JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced between (2) and (3) by multiplying (2) by a and (3) by b and subtracting

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced


Q. 7. JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced              (1996 - 1 Mark)

Ans. π2

Solution.

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced     …(2)

Adding (1) and (2) we get

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced  … (3)

[ Using above property again]

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced    ....(4)

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

Adding (3) and (4) we get

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

Q. 8. The value of JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced                   (1997 - 2 Marks)

Ans. 2

Solution.

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced


Q. 9. JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advancedthen one of the possible values of k is .......                 (1997 - 2 Marks)

Ans. 16

Solution.

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced


True / False

Q. 1. The value of the integral JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advancedequal to a.             (1997 - 2 Marks)

Ans. T

Solution.

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced                … (1)
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced             … (2)
Adding (1) and (2), we get

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

∴ The given statement is true.

The document JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced is a part of the JEE Course Chapter-wise Tests for JEE Main & Advanced.
All you need of JEE at this link: JEE
447 docs|930 tests

Up next

447 docs|930 tests
Download as PDF

Up next

Explore Courses for JEE exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Previous Year Questions with Solutions

,

Free

,

video lectures

,

study material

,

Extra Questions

,

ppt

,

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

,

practice quizzes

,

Viva Questions

,

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

,

Objective type Questions

,

past year papers

,

mock tests for examination

,

JEE Advanced (Fill in the Blanks): Definite Integrals & Applications of Integrals | Chapter-wise Tests for JEE Main & Advanced

,

Summary

,

pdf

,

Semester Notes

,

Exam

,

Sample Paper

,

Important questions

,

MCQs

,

shortcuts and tricks

;