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CBSE Questions for Class 12 Commerce Maths Inverse Trigonometric Functions Quiz 5 - MCQExams.com

If f(x)=sec1(2|x|4), then the domain of f(x) is ______________.
  • [2,2]
  • [6,6]
  • (,6][6,)
  • None Of These
If 3tan1(12+3)tan11x=tan113 then x=
  • 1
  • 2
  • 3
  • 3
nr=1tan1(2r11+22r1) is equal to :
  • tan1(2n)
  • tan1(2n)π4
  • tan1(2n+1)
  • tan1(2n+1)π4
For 0<x<1 the value of cos1x+cos1(x)=?
  • 0
  • π
  • π
  • none of these
The value of sin h(cos h1x) is 
  • x2+1
  • 1/x2+1
  • x21
  • noneofthese
The value of r=0tan1(11+r+r2)  is equal to
  • π4
  • π2
  • π
  • π2
The value of sin1(sin12)+cos1(cos12) is equal to :
  • Zero
  • 242π
  • 4π24
  • None of these
The simplified form of { cos }^{ -1 }\left( \frac { 3 }{ 5 } { cos }x+\frac { 4 }{ 5 } { sin }x \right)  is :
  • { tan }^{ -1 }\frac { 4 }{ 3 } -x
  • { tan }^{ -1 }\frac { 1 }{ 3 } -x
  • { tan }^{ -1 }\frac { 4 }{ 3 } +x
  • None of these
\displaystyle \sum^{\infty}_{r=1}\tan^{-1}\left(\dfrac {3}{r^{2}-r+9}\right) is -
  • \dfrac {\pi}{3}
  • \dfrac {\pi}{6}
  • \dfrac {\pi}{2}
  • \dfrac {\pi}{12}
If\,\cos \left( {2{{\sin }^{ - 1}}x} \right) = \frac{1}{9},\,then\,\,x\,\,is\,\,equal\,\,to
  • Only\,\frac{2}{3}\,
  • Only - \frac{2}{{3\,}}
  • \,\frac{2}{3}, - \frac{2}{3}
  • \frac{1}{3}
If { cos }^{ -1 }\dfrac { 3 }{ 5 } -{ sin }^{ -1 }\dfrac { 4 }{ 5 } ={ cos }^{ -1 }x, then x is equal to -
  • 0
  • 1
  • -1
  • None of these
Number of solution of the equation \tan^{-1}\left(\dfrac {1}{x-1}+\dfrac {1}{x-2}+\dfrac {1}{x-3}+\dfrac {1}{x-4} \right)+\cos^{-1}(x)=\dfrac {3\pi}{4}-\sin^{-1}(x) are
  • 0
  • 1
  • 2
  • 3
The range of the function f(x)=\ell n\ (\sin^{-1}(x^{2}+x)) is
  • \left[-\ell n \left(\sin^{-1}\dfrac {1}{4}\right),\ell n \dfrac {\pi}{4}\right]
  • \left[-\ell n \dfrac {\pi}{4},\ell n \dfrac {\pi}{2}\right]
  • \left(0,\ell n \dfrac {\pi}{2}\right]
  • \left(-\infty ,\ell n \dfrac {\pi}{2}\right]
The trigonometric equation \sin^{-1}x=2\sin^{-1}a, has a solution for-
  • \left|a\right|\le\dfrac{1}{\sqrt{2}}
  • \dfrac{1}{2}<\left|a\right|<\dfrac{1}{\sqrt{2}}
  • all\ real\ values\ of\ a
  • \left|a\right|<\dfrac{1}{2}
If f(x)=\cos^{-1}\left(\dfrac {\sqrt {2x^{2}+1}}{x^{2}+1}\right), then range of f(x) is
  • [0,\pi]
  • \left(0,\dfrac {\pi}{4}\right]
  • \left(0,\dfrac {\pi}{3}\right]
  • \left[0,\dfrac {\pi}{2}\right)
Number of solution(s) to the equation {\cos ^{ - 1}}x + {\sin ^{ - 1}}\left( {\dfrac{x}{2}} \right) = \dfrac{\pi }{6}\, is/are 
  • 0
  • 1
  • 2
  • 3
cos^{-1}\left(\dfrac{\pi}{3}+sec^{-1}(-2)\right)=
  • -1
  • 1
  • 0
  • None of these
The value of \cot\left(cosec^{-1}\dfrac{5}{3}+\tan^{-1}\dfrac{2}{3}\right) is equal to-
  • \dfrac{6}{17}
  • \dfrac{3}{17}
  • \dfrac{4}{17}
  • \dfrac{5}{17}
\int _{ 0 }^{ \pi  }{ \left[ cotx \right] dx,where\left[ \cdot  \right]  } denotes the greatest integer function, is equal to:
  • 1
  • -1
  • -\dfrac { \pi }{ 2 }
  • \dfrac { \pi }{ 2 }
{ sec\quad h }^{ -1 }\left( sin\quad \theta  \right) =
  • log\left( tan\frac { \theta }{ 2 } \right)
  • log\left( sin\frac { \theta }{ 2 } \right)
  • log\left( cos\frac { \theta }{ 2 } \right)
  • log\left( cot\frac { \theta }{ 2 } \right)
\cos^{ -1 }\left[\cos\left( -\frac { 17 }{ 15 } \pi  \right)  \right] is equal to 
  • -\frac { 17\pi }{ 15 }
  • \frac { 17\pi }{ 15 }
  • \frac { 13\pi }{ 15 }
  • \frac { -2\pi }{ 15 }
Find \displaystyle \int x.\sin xdx
  • \sin x+x\cos x=C
  • \sin x-x\cos x+C
  • \sin x+x\sin x+C
  • \sin x-x\sin x+C
If A=\tan^{1-}\left(\dfrac {x\sqrt {3}}{2k-x}\right) and B=\tan^{-1}\left(\dfrac {2x-k}{k\sqrt {3}}\right) then A.B=
  • 0^{o}
  • \pi /6
  • \pi /4
  • \pi /3
if x>0\quad then\quad { tanh }^{ -1 }\left( \frac { { x }^{ 2 }-1 }{ { x }^{ 2 }+1 }  \right)
  • { log }_{ e }\left( 2x \right)
  • { log }_{ e }x
  • { log }_{ e }\left( 3x \right)
  • { log }_{ e }\left( 5x \right)
if\quad x>0\quad then\quad { tanh }^{ -1 }\left( \frac { { x }^{ 2 }-1 }{ { x }^{ 2 }+1 }  \right) 
  • { log }_{ e }\left( 2x \right)
  • { log }_{ e }x
  • { log }_{ e }\left( 3x \right)
  • { log }_{ e }\left( 5x \right)
If \cos^{-1}x-\cos^{-1}(\dfrac {y}{2})=\alpha ax^{2}-4xy\cos \alpha +y^{2}=
  • -4\sin^{2}\alpha
  • 4\sin^{2}\alpha
  • 4
  • 2\sin 2\alpha
If \cot^{-1}{x}+\tan^{-1}\left (\dfrac{1}{3}\right)=\dfrac{\pi}{2}, then x will be
  • 1
  • 3
  • \dfrac {1}{3}
  • None of these
If x={ \sin }^{ -1 }(\sin10) and y={ \cos }^{ -1 }(\cos10), then find y - x.
  • \pi
  • 7\pi
  • 0
  • 10
State true or false.
\sin^{-1}x+\cos^{-1}x=\dfrac {\pi}{2}
  • True
  • False
{ \sin }^{ -1 }\left (\dfrac { 3 }{ 5 }\right )+{ \cos }^{ -1 }\left (\dfrac { 12 }{ 13 }\right )={ \sin }^{ -1 }\left (\dfrac { 56 }{ 65 } \right)
  • True
  • False
\cos ^{ -1 }{ \left\{ \dfrac { 1 }{ 2 } { x }^{ 2 }+\sqrt { 1-{ x }^{ 2 } } \sqrt { 1-\dfrac { { x }^{ 2 } }{ 4 }  }  \right\} =\cos ^{ -1 }{ \dfrac { x }{ 2 } -\cos ^{ -1 }{ x }  }  } holds for:
  • |x|\le 1
  • x\in R
  • 0\le x\le 1
  • -1\le x\le 0
\frac{\cos ^{-1}(41 / 49)}{\sin ^{-1}(2 / 7)}=
  • 4
  • 3
  • 2
  • 1
The value of tan(\frac { 1 }{ 2 } { cos }^{ -1 }(\frac { \sqrt { 5 }  }{ 3 } )) is
  • \frac { 3+\sqrt { 5 } }{ 2 }
  • 3-\sqrt { 5 }
  • \frac { 1 }{ 2 } (3-\sqrt { 5 } )
  • none of these
\sin^{-1}\left(\dfrac{4}{5}\right)+\sin^{-1}\left(\dfrac{7}{25}\right)=\sin^{-1}\left(\dfrac{117}{125}\right)
  • True
  • False
If tan (x + y) = 33 and x = { tan }^{ -1 }3, then y will be
  • 0.3
  • { tan }^{ -1 }(1.3)
  • { tan }^{ -1 }(0.3)
  • { tan }^{ -1 }(\frac { 1 }{ 18 } )
If sin^{-1}(\dfrac{1}{3}) + sin^{-1}(\dfrac{2}{3}) = sin^{-1} x, then x is equal to
  • 0
  • \dfrac{\sqrt{5}+4\sqrt{2}}{9}
  • \dfrac{5\sqrt{2}-4\sqrt{5}}{9}
  • \dfrac{\pi}{2}
The value of \sin ^{-1}(\sin 5\frac {\pi}{3})=
  • -\frac {\pi}3
  • \frac {\pi}3
  • \frac {4\pi}3
  • \frac {3\pi}3
The value of \displaystyle sec\left [ sin^{-1}\left (sin \dfrac{50\pi }{9} \right ) + cos^{-1}cos\left ( \dfrac{31\pi }{9} \right ) \right ] is equal to
  • sec\dfrac{10\pi}{9}
  • sec \ 9{\pi}
  • -1
  • 1
\tan { ^{ -1 }\left( 3/5 \right)  } +\tan { ^{ -1 }\left( 1/4 \right)  } =
  • 0
  • \pi /4
  • 3n/4
  • None of these
\tan { ^{ -1 }\left( \tan { 3\pi /4 }  \right) = }
  • 5\pi /4
  • \pi /4
  • -\pi /4
  • None of these
The value of \sin^{-1}(\cos (\log_{2}(4\alpha -44))) is
  • \dfrac {\pi}{3}
  • \dfrac {\pi}{2}
  • 0
  • 1
\tan (2\cos ^{-1}\frac 35)=_____
  • \frac 83
  • \frac {24}{25}
  • \frac 7{25}
  • \frac {-24}7
{ \tan }^{ -1 }\left( \dfrac { 1 }{ 7 }  \right) +{ \tan }^{ -1 }\left( \dfrac { 1 }{ 13 }  \right) =\cos ^{ -1 }{ \left( \dfrac { 9 }{ 2 }  \right)  }
  • True
  • False
The solution set of the equation2 cos^{ -1 } x = cot^{ -1 } \left(\dfrac { 2x^{ 2 } - 1 }{ 2x \sqrt { 1 x^{ 2 } } }\right) is
  • \left(0, 1\right)
  • \left(-1, 1\right)-{ 0 }
  • \left(-1, 0\right)
  • \left[-1, 1\right]
{ \cos   }^{ -1 }\left[ \cos  \left( 2{ \cot   }^{ -1 }\left( \sqrt { 2 } -1 \right)  \right)  \right] is equal to
  • \sqrt{2}-1
  • 1-\sqrt{2}
  • \pi/4
  • 3\pi/4
The number of solutions of the equation 3\cos^{-1}x-\pi x-\dfrac {\pi}{2}=0
  • 0
  • 1
  • 2
  • infinite
If \alpha =\cos^{-1}\left(\dfrac{3}{5}\right),\beta=\tan^{-1}\left(\dfrac{1}{3}\right) where 0<\alpha,beta <\dfrac{\pi}{2},then \alpha -\beta is equal to :
  • \sin^{-1}\left(\dfrac{9}{5\sqrt{10}}\right)
  • \tan^{-1}\left(\dfrac{9}{14}\right)
  • \cos^{-1}\left(\dfrac{9}{5\sqrt{10}}\right)
  • \tan^{-1}\left(\dfrac{9}{5\sqrt{10}}\right)
If \;\sin {\;^{ - 1}}\dfrac{1}{x} = 2\;{\tan ^{ - 1}}\dfrac{1}{7} + {\cos ^{ - 1}}\dfrac{3}{5}, then x = ___
  • \dfrac {24}{117}
  • \dfrac {7}{3}
  • \dfrac {125}{117}
  • None of these
If \cos ^{ -1 }{ x } -\cos ^{ -1 }{ \cfrac { y }{ 2 }  } =\alpha where -1-1\le x\le 1,-2\le y\le 2,x\le \cfrac { y }{ 2 } then for all 4{ x }^{ 2 }-4xy\cos { \alpha  } +{ y }^{ 2 } is equal to
  • 4\sin ^{ 2 }{ \alpha } -2{ x }^{ 2 }{ y }^{ 2 }
  • 4\cos ^{ 2 }{ \alpha } +2{ x }^{ 2 }{ y }^{ 2 }
  • 4\sin ^{ 2 }{ \alpha }
  • 2\sin ^{ 2 }{ \alpha }
The value of tan \left (\cos^{-1} \dfrac {3}{5} + \tan^{-1} \dfrac {1}{4}\right ) is
  • \dfrac {19}{8}
  • \dfrac {8}{19}
  • \dfrac {19}{12}
  • \dfrac {3}{4}
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