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12th Standard Maths Inverse Trigonometric Functions English Medium Free Online Test One Mark Questions with Answer Key 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. If sin-1 x+sin-1 y=\(\frac{2\pi}{3};\)then cos-1x+cos-1 y is equal to

    (a)

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

    (b)

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

    (c)

    \(\frac{\pi}{6}\)

    (d)

    \(\pi\)

  2. If sin-1 x+sin-1 y+sin-1 z=\(\frac{3\pi}{2}\), the value of x2017+y2018+z2019\(-\frac { 9 }{ { x }^{ 101 }+{ y }^{ 101 }+{ z }^{ 101 } } \)is

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    3

  3. The domain of the function defined by f(x)=sin−1\(\sqrt{x-1} \) is

    (a)

    [1,2]

    (b)

    [-1,1]

    (c)

    [0,1]

    (d)

    [-1,0]

  4. \({ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 3 } \right) \)is equal to

    (a)

    \(\frac { 1 }{ 2 } { cos }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)

    (b)

    \(\frac { 1 }{ 2 } { sin }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)

    (c)

    \(\frac { 1 }{ 2 } {tan }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)

    (d)

    \({ tan}^{ -1 }\left( \frac { 1}{ 2 } \right) \)

  5. sin-1(2cos2x-1)+cos-1(1-2sin2x)=

    (a)

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

    (b)

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

    (c)

    \(\frac{\pi}{4}\)

    (d)

    \(\frac{\pi}{6}\)

  6. sin(tan-1x), |x|<1 ia equal to

    (a)

    \(\frac{x}{\sqrt{1-x^2}}\)

    (b)

    \(\frac{1}{\sqrt{1-x^2}}\)

    (c)

    \(\frac{1}{\sqrt{1+x^2}}\)

    (d)

    \(\frac{x}{\sqrt{1+x^2}}\)

  7. If \({ sin }^{ -1 }x-cos^{ -1 }x=\cfrac { \pi }{ 6 } \) then

    (a)

    \(\cfrac { 1 }{ 2 } \)

    (b)

    \(\cfrac { \sqrt { 3 } }{ 2 } \)

    (c)

    \(\cfrac { -1 }{ 2 } \)

    (d)

    none of these

  8. ·If \(\alpha ={ tan }^{ -1 }\left( \cfrac { \sqrt { 3 } }{ 2y-x } \right) ,\beta ={ tan }^{ -1 }\left( \cfrac { 2x-y }{ \sqrt { 3y } } \right) \) then \(\alpha -\beta \)

    (a)

    \(\cfrac { \pi }{ 6 } \)

    (b)

    \(\cfrac { \pi }{ 3 } \)

    (c)

    \(\cfrac { \pi }{ 2 } \)

    (d)

    \(\cfrac { -\pi }{ 3 } \)

  9. \(sin\left\{ 2{ cos }^{ -1 }\left( \cfrac { -3 }{ 5 } \right) \right\} =\)

    (a)

    \(\cfrac { 6 }{ 15 } \)

    (b)

    \(\cfrac { 24 }{ 25 } \)

    (c)

    \(\cfrac { 4 }{ 5 } \)

    (d)

    \(\cfrac { -24 }{ 25 } \)

  10. In a \(\Delta ABC\)  if C is a right angle, then  \({ tan }^{ -1 }\left( \cfrac { a }{ b+c } \right) +{ tan }^{ -1 }\left( \cfrac { b }{ c+a } \right) =\) 

    (a)

    \(\cfrac { \pi }{ 3 } \)

    (b)

    \(\cfrac { \pi }{ 4 } \)

    (c)

    \(\cfrac { 5\pi }{ 2 } \)

    (d)

    \(\cfrac { \pi }{ 6 } \)

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