#### 12th Standard Maths Applications of Integration English Medium Free Online Test One Mark Questions 2020 - 2021

12th Standard

Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

10 x 1 = 10
1. The value of $\int _{ -4 }^{ 4 }{ \left[ { tan }^{ -1 }\left( \frac { { x }^{ 2 } }{ { x }^{ 4 }+1 } \right) +{ tan }^{ -1 }\left( \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } \right) \right] dx }$ is

(a)

$\pi$

(b)

$2\pi$

(c)

$3\pi$

(d)

$4\pi$

2. The value of $\int _{ 0 }^{ 1 }{ x{ (1-x) }^{ 99 }dx }$ is

(a)

$\frac{1}{11000}$

(b)

$\frac{1}{10100}$

(c)

$\frac{1}{10010}$

(d)

$\frac{1}{10001}$

3. The value of  $\int _{ 0 }^{ \pi }{ { sin }^{ 4 }xdx }$ is

(a)

$\frac{3\pi}{10}$

(b)

$\frac{3\pi}{8}$

(c)

$\frac{3\pi}{4}$

(d)

$\frac{3\pi}{2}$

4. If $\int _{ a }^{ a }{ \frac { 1 }{ 4+{ x }^{ 2 } } dx=\frac { \pi }{ 8 } }$then a is

(a)

4

(b)

1

(c)

3

(d)

2

5. The value of $\int _{ 0 }^{ \frac { 2 }{ 3 } }{ \frac { dx }{ \sqrt { 4-9{ x }^{ 2 } } } }$ is

(a)

$\frac{\pi}{6}$

(b)

$\frac{\pi}{2}$

(c)

$\frac{\pi}{4}$

(d)

${\pi}$

6. $\int _{ 1 }^{ \sqrt { 3 } }{ \frac { dx }{ 1+{ x }^{ 2 } } }$ is

(a)

$\frac { \pi }{ 3 }$

(b)

$\frac { \pi }{ 6 }$

(c)

$\frac { \pi }{ 12 }$

(d)

$-\frac { \pi }{ 6 }$

7. The area bounded by the parabola y = x2 and the line y = 2x is

(a)

$\frac43$

(b)

$\frac23$

(c)

$\frac{51}{3}$

(d)

$\frac{30}{3}$

8. The area enclosed by the curve y2 = 4x, the x-axis and its latus rectum is ............ sq.units.

(a)

$\frac23$

(b)

$\frac43$

(c)

$\frac83$

(d)

$\frac{16}{3}$

9. The volume generated by the curve y2 = 16x from x = 2 to x = 3 rotating about x - axis ......... cu. units

(a)

72π

(b)

$\frac { 256\times 19 }{ 3 }$

(c)

40ㅠ

(d)

80ㅠ

10. $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { sin \ x-cos \ x }{ 1+sin \ x cos \ x } dx= }$ ............

(a)

$\frac { \pi }{ 2 }$

(b)

0

(c)

$\frac { \pi }{ 4 }$

(d)

$\pi$