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Inverse Trigonometric Functions One Mark Questions with Answer

12th Standard EM

    Reg.No. :
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Maths

Time : 00:30:00 Hrs
Total Marks : 25
    25 x 1 = 25
  1. If \({ tan }^{ -1 }\left\{ \cfrac { \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1-{ x }^{ 2 } } } \right\} =\alpha \) then x2 =

    (a)

    \(sin2\alpha \)

    (b)

    \(sin\alpha \)

    (c)

    \(cos2\alpha \)

    (d)

    \(cos\alpha \)

  2. 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

  3. The number of solutions of the equation \({ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 } \) 

    (a)

    2

    (b)

    3

    (c)

    1

    (d)

    none

  4. If \(\alpha ={ tan }^{ -1 }\left( tan\cfrac { 5\pi }{ 4 } \right) \) and \(\beta ={ tan }^{ -1 }\left( -tan\cfrac { 2\pi }{ 3 } \right) \) then

    (a)

    \(4\alpha =3\beta \quad \)

    (b)

    \(3\alpha =4\beta \)

    (c)

    \(\alpha -\beta =\cfrac { 7\pi }{ 12 } \)

    (d)

    none

  5. The number of real solutions of the equation \(\sqrt { 1+cos2x } ={ 2sin }^{ -1 }\left( sinx \right) ,-\pi <x<\pi \) is

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    infinte

  6. ·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)

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

  7. \({ tan }^{ -1 }\left( \cfrac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \cfrac { 2 }{ 11 } \right) \) =

    (a)

    0

    (b)

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

    (c)

    -1

    (d)

    none

  8. If tan-1(3)+tan-1(x)=tan-1(8)then x= 

    (a)

    5

    (b)

    \(\cfrac { 1 }{ 5 } \)

    (c)

    \(\cfrac { 5 }{ 14 } \)

    (d)

    \(\cfrac { 14 }{ 5 } \)

  9. The value of \({ cos }^{ -1 }\left( \cfrac { cos5\pi }{ 3 } \right) +sin^{ -1 }\left( \cfrac { sin5\pi }{ 3 } \right) \) is 

    (a)

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

    (b)

    \(\cfrac { 5\pi }{ 3 } \)

    (c)

    \(\cfrac { 10\pi }{ 3 } \)

    (d)

    0

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

    (a)

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

    (b)

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

    (c)

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

    (d)

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

  11. If \(4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi \) then x is

    (a)

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

    (b)

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

    (c)

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

    (d)

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

  12. If \({ tan }^{ -1 }\left( \cfrac { x+1 }{ x-1 } \right) +{ tan }^{ -1 }\left( \cfrac { x-1 }{ x } \right) ={ tan }^{ -1 }\left( -7 \right) \) then x Is

    (a)

    0

    (b)

    -2

    (c)

    1

    (d)

    2

  13. If \({ cos }^{ -1 }x>x>{ sin }^{ -1 }x\) then

    (a)

    \(\cfrac { 1 }{ \sqrt { 2 } } <x\le 1\)

    (b)

    \(0\le x<\cfrac { 1 }{ \sqrt { 2 } } \)

    (c)

    \(-1\le x<\cfrac { 1 }{ \sqrt { 2 } } \)

    (d)

    x>0

  14. 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)

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

  15. \(cot\left( \cfrac { \pi }{ 4 } -{ cot }^{ -1 }3 \right) \)

    (a)

    7

    (b)

    6

    (c)

    5

    (d)

    none

  16. If tan-1(cot\(\theta\)) = 2\(\theta\), then\(\theta\) = _____________

    (a)

    \(\pm 3\)

    (b)

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

    (c)

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

    (d)

    none

  17. The domain of cos-1(x2 - 4) is______

    (a)

    [3, 5]

    (b)

    [-1, 1]

    (c)

    \(\left[ -\sqrt { 5 } ,-\sqrt { 3 } \right] \cup \left[ \sqrt { 3 } ,\sqrt { 5 } \right] \)

    (d)

    [0, 1]

  18. The value of tan \(\left( { cos }^{ -1 }\cfrac { 3 }{ 5 } +{ tan }^{ -1 }\cfrac { 1 }{ 4 } \right) \) is ______

    (a)

    \(\cfrac { 19 }{ 8 } \)

    (b)

    \(\cfrac { 8 }{ 19 } \)

    (c)

    \(\cfrac { 19 }{ 12 } \)

    (d)

    \(\cfrac { 3 }{ 4 } \)

  19. The value of sin(2(tan-1 0.75) is___________

    (a)

    0.75

    (b)

    1.5

    (c)

    0.96

    (d)

    sin-1(1.5)

  20. If x>1,then \(2{ tan }^{ -1 }x+{ sin }^{ -1 }\left( \cfrac { 2x }{ 1+{ x }^{ 2 } } \right) \) ________

    (a)

    4 tan-1x

    (b)

    0

    (c)

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

    (d)

    \(\pi \)

  21. If \(\theta ={ sin }^{ -1 }\left( sin(-{ 60 }^{ 0 }) \right) \) then one of the possible values of \(\theta\) is _________

    (a)

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

    (b)

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

    (c)

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

    (d)

    \(\cfrac { -2\pi }{ 3 } \)

  22. The value of \({ sin }^{ -1 }\left( cos\cfrac { 33\pi }{ 5 } \right) \) is________

    (a)

    \(\cfrac { 3\pi }{ 5 } \)

    (b)

    \(\cfrac { -\pi }{ 10 } \)

    (c)

    \(\cfrac { \pi }{ 10 } \)

    (d)

    \(\cfrac { 7\pi }{ 5 } \)

  23. If x < 0, y < 0 such that xy = 1, then tan--1(x) + tan-l(y) =_____

    (a)

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

    (b)

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

    (c)

    \(-\pi \)

    (d)

    none

  24. The pricipal value of \({ sin }^{ -1 }\left( \cfrac { -1 }{ 2 } \right) \) is _________

    (a)

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

    (b)

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

    (c)

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

    (d)

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

  25. \({ tan }^{ -1 }\left( tan\cfrac { 9\pi }{ 8 } \right) \)

    (a)

    \(\cfrac { 9\pi }{ 8 } \)

    (b)

    \(\cfrac { 9\pi }{ 8 } \)

    (c)

    \(\cfrac { \pi }{ 8 } \)

    (d)

    \(\cfrac { -\pi }{ 8 } \)

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