Trigonometric Functions CBSE Questions & Answers

Trigonometric Functions

This is Mathematics Class 11 Trigonometric Functions CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
sin \(\left( {180 + \phi } \right)\) sin\(\left( {180 - \phi } \right)\) \(cose{c^2}\) \(\phi \)
  • A
    1
  • B
    - 1
    Correct
  • C
    0
  • D
    none of these
2
The general solution of the equation sin x + cos x = 2 is
  • A
    \(\;n\;\pi ,n \in I\)
  • B
    \(2\;n\;\pi + {\pi \over 2}or\;2n\;\pi ,n \in I\)
  • C
    \(2\;n\;\pi + {\pi \over 2}or\;2n\;\pi ,n \in I\)
  • D
    none of these
    Correct
3
Which of the following is not possible ?
  • A
    \(\sin \theta = {5 \over 7}\)
  • B
    \(\cos \theta = {{1 + {t^2}} \over {1 - {t^2}}},t \ne 0\)
    Correct
  • C
    \(\sec \theta = {5 \over 2}\)
  • D
    \(\tan \theta = 100\)
4
If ( 1 + tan \(\theta \)) ( 1 + tan \(\phi \) ) = 2, then \(\theta \) + \(\phi \) =
  • A
    \({45^ \circ }\)
    Correct
  • B
    \({75^ \circ }\)
  • C
    \({60^ \circ }\)
  • D
    \({30^ \circ }\)
5
The set of values of x for which \({{\tan 3x - \tan 2x} \over {1 + \tan 3x\tan 2x}} = 1\) is
  • A
    \(\phi \)
    Correct
  • B
    \(\left\{ {{\pi \over 4}} \right\}\)
  • C
    \(\left\{ {n\pi + {\pi \over 4}:n = 1,2,3...} \right\}\)
  • D
    \(\left\{ {2n\pi + {\pi \over 4}:n = 1,2,3...} \right\}\)
6
The general value of \(\theta \) satisfying the equation \(2{\sin ^2}\theta - 3\sin \theta - 2 = 0\) is
  • A
    \(n\pi + {( - 1)^n}{\pi \over 2}\)
  • B
    \(n\pi + {( - 1)^{n + 1}}{\pi \over 6}\)
    Correct
  • C
    \(n\pi + {( - 1)^n}{{5\pi } \over 6}\)
  • D
    \(n\pi + {( - 1)^n}{\pi \over 6}\)
7
Number of solutions of the equation tan x + sec x = 2 cos x. lying in the interval \(\left[ {0,2\pi } \right]\) is
  • A
    0
  • B
    2
    Correct
  • C
    1
  • D
    3
8
In a triangle ABC, if a, b, c are in A. P., then tan \({A \over 2},\tan {B \over 2},\tan {C \over 2}\) are in
  • A
    H.P.
    Correct
  • B
    none of these
  • C
    H.P.
  • D
    G.P.
9
In a \(\Delta ABC,\) \({{\cos A} \over a} = {{\cos B} \over b} = {{\cos C} \over c}\) and the side a = 2, then area of the triangle is
  • A
    2
  • B
    \(\sqrt 3 \)
    Correct
  • C
    1
  • D
    \({{\sqrt 3 } \over 2}\)
10
In a \(\Delta ABC\) , a = 4, b = 3 and A = \({60^ \circ }\) ; then c is a root of the equation
  • A
    \({c^2} - 3c + 7 = 0\)
  • B
    \({c^2} - 3c - 7 = 0\)
    Correct
  • C
    \({c^2} + 3c + 7 = 0\)
  • D
    \({c^2} - 3c - 7 = 0\)
11
Which of the following statements is incorrect ?
  • A
    \(\sin \theta = - {1 \over 5}\)
  • B
    \(\sec \theta = {1 \over 2}\)
    Correct
  • C
    \(\cos \theta = 1\)
  • D
    tan \(\theta \) = 1
12
If x = y cos \({{2\pi } \over 3} = z\cos {{4\pi } \over 3},\) then xy + yz + zx =
  • A
    2
  • B
    1
  • C
    -1
  • D
    0
    Correct
13
The values of \(\theta \) (0 < \(\theta \) < \({360^o}\)) satisfying \({\text{cosec}}\theta + {\text{ 2 }} = {\text{ }}0\) are
  • A
    \({210^o},{300^o}\)
  • B
    \({210^o},{240^o}\)
  • C
    \({240^o},{300^o}\)
  • D
    \({210^o},{330^o}\)
    Correct
14
If \({z_{1}}and{z_2}\) are non real complex numbers such that \({z_1} + {z_{2}}and{z_1}{z_2}\) are real numbers , then
  • A
    none of these
  • B
    \({z_1} = - \overline {{z_2}} \)
  • C
    \({z_1} = \overline {{z_2}} \)
    Correct
  • D
    \({z_1} = \overline {{z_1}} \) and \({z_2} = \overline {{z_2}} \)
15
If sin \(\alpha = {\rm{ sin}}\beta \) and \({\rm{cos}}\alpha = {\rm{ cos}}\beta \) , then
  • A
    \(\cos {{\alpha - \beta } \over 2} = 0\)
  • B
    \(\sin {{\alpha - \beta } \over 2} = 0\)
    Correct
  • C
    \(\cos {{\alpha + \beta } \over 2} = 0\)
  • D
    \(\sin {{\alpha + \beta } \over 2} = 0\)