Exercise 9.10: Choose the correct answer

EXERCISE 9.10

Choose the correct or the most suitable answer from the given four alternatives :

1. The value of  is

(1) π/6

(2) π/2

(3) π/4

(4) π

2. The value of  is

(1) 1/2

(2) 3/2

(3) 5/2

(4) 7/2

3. For any value of n âˆˆ â„¤, Ï€âˆ«0 ecos2 x cos3 [ (2n +1)x] dx is

(1) π/2

(2) π

(3) 0

(4) 2

4. The value of sin2x cos x dx is

 (1) 3/2

(2) 1/2

(3) 0

(4) 2/3

5. The value of  is

 (1) Ï€

(2) 2Ï€

(3) 3Ï€

(4) 4Ï€

6. The value  is

(1) 4

(2) 3

(3) 2

(3) 0

7. If  

 f (x) = x∫0 t cos t dt , then df/ dx =

(1) cos x âˆ’ x sin x

(2) sin x + x cos x

(3) x cos x

(4) x sin x

8. The area between y2 = 4x and its latus rectum is

(1) 2/3

(2) 4/3

(3) 8/3

(4) 5/3

9. The value of  is

(1) 1/11000

(2) 1/10100

(3) 1/10010

(4) 1/10001

10. The value of  is

(1) π/2

(2) π

(3) 3Ï€ / 2

(4) 2Ï€

11. If  = 90 then n is

(1) 10

(2) 5

(3) 8

(4) 9

12. The value of Ï€/6∫0 cos33x dx is

(1) 2/3

(2) 2/9

(3) 1/9

(3) 1/3

13. The value of Ï€âˆ«0 sin4x dx is

(1) 3Ï€  / 10

(2) 3Ï€ / 8

(3) 3Ï€ / 4

(4) 3Ï€ / 2

14. The value of âˆžâˆ«0 e−3x x2dx is

(1) 7/27

(2) 5/27

(3) 4/27

(4) 2/27

15. If  then a is

(1) 4

(2) 1

(3) 3

(4) 2

16. The volume of solid of revolution of the region bounded by y2 = x(a − x) about x-axis is

(1) πa3

(2) Ï€a3 / 4

(3) Ï€a3  / 5

(4) Ï€a3 / 6

17. If f (x) = , x > 1 and , then one of the possible value of a is

(1) 3

(2) 6

(3) 9

(4) 5

18. The value of 1∫0 (sin−1 x )2 dx is

Answers: (4)

19. The value of  is

Answers: (2)

20. If x∫0 f (t) dt = x + 1∫x tf (t) dt , then the value of f (1) is

(1) 1/2

(2) 2

(3) 1

(4) 3/4