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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

    Answer all the questions

    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)

    \( \pi\)

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