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

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Q. 1. 

                         (1987 - 2 Marks)

Ans. 

Solution. Given that,

Expanding along R₁, we get

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

Q. 2.                (1988 - 2 Marks)

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

Ans. 2 - √2

Solution. 

Q. 3.                 (1989 - 2 Marks)

Ans. 4

Solution.

Q. 4.                 (1993 -  2 Marks)

Ans. 

Solution. 

Q. 5.                    (1994 -  2 Marks)

Ans. 1/2

Solution.

Adding (1) and (2), we get

Q. 6. If for nonzero   then               (1996 - 2 Marks)

Ans. 

Solution.               …(1)

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

Replacing 

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

Eliminate   between (2) and (3) by multiplying (2) by a and (3) by b and subtracting

Q. 7.               (1996 - 1 Mark)

Ans. π²

Solution.

     …(2)

Adding (1) and (2) we get

  … (3)

[ Using above property again]

    ....(4)

Adding (3) and (4) we get

Q. 8. The value of                    (1997 - 2 Marks)

Ans. 2

Solution.

Q. 9. then one of the possible values of k is .......                 (1997 - 2 Marks)

Ans. 16

Solution.

True / False

Q. 1. The value of the integral equal to a.             (1997 - 2 Marks)

Ans. T

Solution.

                … (1)

             … (2)
Adding (1) and (2), we get

∴ The given statement is true.