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

12th Standard

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Maths

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

    Answer all the questions

    10 x 1 = 10
  1. The area between y2 = 4x and its latus rectum is

    (a)

    \(\frac{2}{3}\)

    (b)

    \(\frac{4}{3}\)

    (c)

    \(\frac{8}{3}\)

    (d)

    \(\frac{5}{3}\)

  2. The value of \(\int _{ 0 }^{ \pi }{ \frac { dx }{ 1+{ 5 }^{ cos\ x } } } \) is

    (a)

    \(\frac{\pi}{2}\)

    (b)

    \(\pi\)

    (c)

    \(\frac{3\pi}{2}\)

    (d)

    \(2\pi\)

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

    (a)

    \(\pi a^2\)

    (b)

    \(\frac { \pi { a }^{ 2 } }{ 4 } \)

    (c)

    \(\frac { \pi { a }^{ 2 } }{ 5 } \)

    (d)

    \(\frac { \pi { a }^{ 2 } }{ 6 } \)

  4. The value of \(\int _{ -1 }^{ 2 }{ |x|dx } \)

    (a)

    \(\frac{1}{2}\)

    (b)

    \(\frac{3}{2}\)

    (c)

    \(\frac{5}{2}\)

    (d)

    \(\frac{7}{2}\)

  5. The value of \(\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }xcosxdx } \) is

    (a)

    \(\frac{3}{2}\)

    (b)

    \(\frac{1}{2}\)

    (c)

    0

    (d)

    \(\frac{2}{3}\)

  6. The value of \(\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \sqrt { \frac { 1-cos2x }{ 2x } } } \) dx is

    (a)

    \(\frac { 1 }{ 2 } \)

    (b)

    2

    (c)

    0

    (d)

    1

  7. If \(\int _{ 0 }^{ 2a }{ f(x) } dx=2\int _{ 0 }^{ a }{ f(x) } \) then

    (a)

    f(2a -x) = - f(x)

    (b)

    f(2a - x) = f(x)

    (c)

    f(x) is odd

    (d)

    f(x) is even

  8. The area enclosed by the curve y = \(\frac { { x }^{ 2 } }{ 2 } \) , the x - axis and the lines x = 1, x = 3 is

    (a)

    4

    (b)

    8\(\frac23\)

    (c)

    13

    (d)

    4\(\frac{1}{3}\)

  9. \(\int _{ 0 }^{ \frac { \pi }{ 4 } }{ { cos }^{ 3 }2x \ dx= } \)

    (a)

    \(\frac { 2 }{ 3 } \)

    (b)

    \(\frac { 1 }{ 3 } \)

    (c)

    0

    (d)

    \(\frac { 2\pi }{ 3 } \)

  10. The volume when  \(y=\sqrt { 3+{ x }^{ 2 } } \) from x = 0 to x = 4 is rotated about x-axis is .................

    (a)

    \(100\pi \)

    (b)

    \(\frac { 100\pi }{ 9 } \)

    (c)

    \(\frac { 100\pi }{ 3 } \)

    (d)

    \(\frac { 100 }{ 3 } \)

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