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 ∈ ℤ, π∫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) π
(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 − 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 π/6∫0 cos33x dx is
(1) 2/3
(2) 2/9
(3) 1/9
(3) 1/3
13. The value of π∫0 sin4x dx is
(1) 3Ï€ / 10
(2) 3Ï€ / 8
(3) 3Ï€ / 4
(4) 3Ï€ / 2
14. The value of ∞∫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) πa3 / 4
(3) πa3 / 5
(4) πa3 / 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
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