Inverse Trigonometric Functions Test

Inverse Trigonometric Functions

This is Inverse Trigonometric Functions Test-01 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The value of is
Question 1 figure 1
  • A
    0
  • B
    1/2
    Correct
  • C
    2
  • D
    1/4
2
The maximum value of \({\text{sin x }} + {\text{ cos x}}\) is
  • A
    \(\frac{1}{{\sqrt 2 }}\).
  • B
    \(\sqrt 2 \)
    Correct
  • C
    2
  • D
    1
3
The minimum value of \({\text{sin x }}--{\text{ cos x}}\) is
  • A
    \( - \sqrt 2 \)
    Correct
  • B
    1
  • C
    0
  • D
    -1
4
If \(5\sin \theta = 3,then\frac{{\sec \theta + \tan \theta }}{{\sec \theta - \tan \theta }}\) is equal to
  • A
    \(\frac{1}{4}\)
  • B
    4
    Correct
  • C
    2
  • D
    none of these.
5
If \(\sec \theta = x + \frac{1}{{4x}},x \in R,x \ne 0,\)then the value of \(\sec \theta + \tan \theta \)is
  • A
    none of these.
  • B
    2x
  • C
    \(2x\,\,or\,\,\frac{1}{{2x}}\)
    Correct
  • D
    \(\frac{1}{{2x}}\)
6
\(\cos 2\theta \) is not equal to
  • A
    \(\frac{{1 - {{\tan }^2}\theta }}{{1 + {{\tan }^2}\theta }}\)
  • B
    \(2{\cos ^2}\theta - 1\)
  • C
    \(1 - 2{\sin ^2}\theta \)
  • D
    \(\frac{{1 + {{\tan }^2}\theta }}{{1 - {{\tan }^2}\theta }}\)
    Correct
7
When \(x = \frac{\pi }{2},\)then tan x, is
  • A
    \(\infty \,\,or\,\, - \,\infty \)
  • B
    \(\infty \)
  • C
    not defined.
    Correct
  • D
    \( - \,\infty \)
8
tan x is periodic with period
  • A
    \(\pi \)
    Correct
  • B
    \(2\pi \)\(\frac{\pi }{3}.\)
  • C
    \(\frac{{3\pi }}{2}.\)
  • D
    \(\frac{\pi }{2}\)
9
The period of the function \({\text{f}}\left( {\text{x}} \right) = {\text{tan 3x}}\) is
  • A
    \(\frac{\pi }{3}\)
    Correct
  • B
    \(\pi \)
  • C
    \(\frac{\pi }{2}\)
  • D
    2\(\pi \)
10
\({\sin ^2}{25^0} + {\sin ^2}{65^0}\) is equal to
  • A
    1
    Correct
  • B
    none of these.
  • C
    \(\frac{1}{2}\)
  • D
    0
11
\(If\;x + y = \frac{\pi }{4}.then(1 + \tan x)(1 + \tan y)\) is equal to
  • A
    1
  • B
    2
    Correct
  • C
    -1
  • D
    none of these.
12
The period of the function \({\text{f}}\left( {\text{x}} \right) = {\text{cos 4x }} + {\text{ tan 3x}}\) is
  • A
    \(\frac{\pi }{2}\)
  • B
    \(\frac{\pi }{3}\)
  • C
    \(\pi \)
    Correct
  • D
    none of these
13
\(\frac{{\cos {8^0} - \sin {8^0}}}{{\cos {8^0} + \sin {8^0}}}\)is equal to
  • A
    none of these.
  • B
    \(\tan {53^0}\)
  • C
    \(\tan {82^0}\)
  • D
    \(\tan {37^0}\)
    Correct
14
The general solution of the equation \(\cot \theta - \tan \theta = \sec \theta \;is\;(n \in I)\)
  • A
    \(n\pi + \frac{\pi }{6}\)
  • B
    \(n\;\pi + {( - 1)^n}\frac{\pi }{6}\)
    Correct
  • C
    \(2n\pi + \frac{\pi }{6}\)
  • D
    \(2n\;\pi \pm \frac{\pi }{6}\)
15
\(\sin {265^0} - \cos {265^0}\)is
  • A
    Positive
  • B
    non-negative.
  • C
    negative
    Correct
  • D
    Zero