Inverse Trigonometric Functions Test

Inverse Trigonometric Functions

This is Inverse Trigonometric Functions Test-04 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
\({\tan ^{ - 1}}( - 2) + {\tan ^{ - 1}}( - 3)\)is equal to
  • A
    \(\frac{{3\pi }}{4}\)
  • B
    \(\frac{\pi }{4}\)
    Correct
  • C
    \(\frac{{5\pi }}{4}\).
  • D
    \( - \frac{\pi }{4}\)
2
The number of solutions of the equation \({\sin ^{ - 1}}x - {\cos ^{ - 1}}x = {\sin ^{ - 1}}\left( {\frac{1}{2}} \right)\)is
  • A
    1
    Correct
  • B
    2
  • C
    3
  • D
    infinite.
3
Domain of f(x) = \({\sin ^{ - 1}}x - se{c^{ - 1}}x\;is\;\)
  • A
    0 or 1
  • B
    { -1 ,1}
    Correct
  • C
    { 0, 1}
  • D
    none of these
4
The number of solutions of the equation \({\cos ^{ - 1}}(1 - x) - 2{\cos ^{ - 1}}x = \frac{\pi }{2}is\)
  • A
    none of these.
  • B
    One
    Correct
  • C
    two
  • D
    more than one
5
\({\tan ^{ - 1}}\frac{1}{4} + {\tan ^{ - 1}}\frac{2}{9} = \)
  • A
    \(\frac{1}{2}{\cos ^{ - 1}}\frac{3}{5}\)
    Correct
  • B
    \(\frac{1}{2}{\tan ^{ - 1}}\frac{3}{5}\)
  • C
    \(\frac{1}{2}{\tan ^{ - 1}}\frac{1}{2}.\)
  • D
    \(\frac{1}{2}{\sin ^{ - 1}}\frac{3}{5}\)
6
\(\cos \left( {{{\cos }^{ - 1}}\left( {\frac{7}{{25}}} \right)} \right) = \)
  • A
    \(\frac{{25}}{7}\)
  • B
    none of these
    Correct
  • C
    \(\frac{{24}}{{25}}\)
  • D
    \(\frac{{25}}{{24}}\)
7
\(4{\tan ^{ - 1}}\left( {\frac{1}{5}} \right) - {\tan ^{ - 1}}\left( {\frac{1}{{239}}} \right) = \)
  • A
    \(\frac{\pi }{4}.\)
    Correct
  • B
    \(\frac{\pi }{2}\)
  • C
    \(\pi \)
  • D
    \(\frac{\pi }{3}\)
8
\({\sin ^{ - 1}}\left( {\frac{1}{{\sqrt 5 }}} \right) + {\cot ^{ - 1}}(3) = \)
  • A
    \(\frac{\pi }{6}\)
  • B
    \(\frac{\pi }{3}\)
  • C
    \(\frac{\pi }{4}.\)
    Correct
  • D
    \(\frac{\pi }{2}\)
9
The solution of the equation \({\cos ^{ - 1}}(\sqrt 3 x) + {\cos ^{ - 1}}x = \frac{\pi }{2}\)is given by
  • A
    \( \pm \frac{1}{2}\)
  • B
    \( - \frac{1}{2}\)
  • C
    none of these.
  • D
    \(\frac{1}{2}\)
    Correct
10
If \({\cos ^{ - 1}}x + {\sin ^{ - 1}}\left( {\frac{x}{2}} \right) = \frac{\pi }{6},\) then x =
  • A
    \(\frac{1}{{\sqrt 2 }}\)
  • B
    0
  • C
    1
    Correct
  • D
    \( \pm \sqrt {3.} \)
11
If \({\tan ^{ - 1}}x + {\tan ^{ - 1}}\frac{1}{7} = \frac{\pi }{4}\), then x =
  • A
    \(\frac{3}{4}\)
    Correct
  • B
    \(\frac{7}{6}\)
  • C
    \(\frac{4}{3}\)
  • D
    \(\frac{6}{7}\)
12
\({\tan ^{ - 1}}3 - {\tan ^{ - 1}}2 = \)
  • A
    \({\tan ^{ - 1}}\left( {\frac{2}{3}} \right)\)
  • B
    \({\tan ^{ - 1}}\left( {\frac{1}{7}} \right)\)
    Correct
  • C
    \({\tan ^{ - 1}}\left( {\frac{3}{2}} \right)\)
  • D
    \({\tan ^{ - 1}}\left( {\frac{1}{5}} \right).\)
13
The value of \({\cos ^{ - 1}}( - 1) - {\sin ^{ - 1}}(1)\) is
  • A
    \(\pi \)
  • B
    \(\frac{\pi }{2}.\)
    Correct
  • C
    \(\frac{{3\pi }}{2}\)
  • D
    \( - \frac{{3\pi }}{2}\)
14
Question 14 figure 1
  • A
    \(\frac{1}{{\sqrt 3 }}\)
    Correct
  • B
    2
  • C
    \(\frac{1}{{\sqrt 2 }}\)
  • D
    \(1`\)
15
\({\cot ^{ - 1}}\left( {\frac{5}{3}} \right) + {\cos ^{ - 1}}\left( {\frac{4}{5}} \right) = \)
  • A
    \({\cot ^{ - 1}}\left( {\frac{{27}}{{11}}} \right)\)
  • B
    0
  • C
    \({\cos ^{ - 1}}\left( {\frac{{27}}{{2\sqrt {38} }}} \right)\)
  • D
    \({\tan ^{ - 1}}\left( {\frac{{27}}{{11}}} \right)\)
    Correct