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
If sin \(\alpha + {\rm{ sin}}\beta \) = 0 = \({\rm{cos}}\alpha + {\rm{ cos}}\beta \), then \({\rm{cos 2}}\alpha + {\rm{ cos 2}}\beta \) =
  • A
    - 2 \({\rm{cos }}(\alpha + \beta )\)
    Correct
  • B
    2 \({\rm{cos }}(\alpha + \beta )\)
  • C
    - 2 \({\rm{sin }}(\alpha + \beta )\)
  • D
    2 \({\rm{sin }}(\alpha + \beta )\)
2
If cot \({A \over 2} = {{b + c} \over a},\) then \(\Delta ABC\) is
  • A
    none of these
  • B
    right angled
    Correct
  • C
    isosceles
  • D
    equilateral
3
In a \(\Delta ABC\) , tan \({A \over 2} = {5 \over 6}\) and \({C \over 2} = {2 \over 5},\) then
  • A
    a, c, b are in A.P.
  • B
    b , a, c are in A.P.
  • C
    a, b, c are in A.P.
    Correct
  • D
    a, b, c are in G.P.
4
In a triangle ABC, the line joining the circumcentre and the incentre is parallel to BC, then cos B + cos C =
  • A
    \({3 \over 2}\)
  • B
    1
    Correct
  • C
    \({1 \over 2}\)
  • D
    \({3 \over 4}\)
5
The value of the expression tan \({1^o}\) tan \({2^o}\) tan \({3^o}\) … tan \({89^o}\) is equal to
  • A
    \(\infty \)
  • B
    1
    Correct
  • C
    not defined
  • D
    0
6
If sin 2 \(\theta \) = cos 3 \(\theta \), then \(\theta \) is equal to \(\left( {0 \le \theta \le {{90}^ \circ }} \right)\)
  • A
    none of these
  • B
    \({36^o}\)
  • C
    \(18\;or\;{90^ \circ }\)
    Correct
  • D
    \({18^o}\)
7
When the length of the shadow of a pole is equal to the height of the pole, then the elevation of source of light is
  • A
    \({30^o}\)
  • B
    \({75^o}\)
  • C
    \({60^o}\)
  • D
    \({45^o}\)
    Correct
8
In a \(\Delta ABC,B = {\pi \over 3}\) and C\( = {\pi \over 4}\). Let D divide BC internally in the ratio 1 : 3, then \({{\sin (\angle BAD)} \over {\sin (\angle CAD)}} = \)
  • A
    \({1 \over {\sqrt 6 }}\)
    Correct
  • B
    \({1 \over {\sqrt 3 }}\)
  • C
    \(\sqrt {{2 \over 3}} \)
  • D
    \({1 \over 3}\)
9
The maximum value of \({\rm{sin}}\alpha + {\rm{ sin}}\beta + {\rm{ sin}}\gamma \) , where \(\alpha ,{\rm{ }}\beta ,{\rm{ }}\gamma \) are positive real numbers satisfying \(\alpha {\rm{ }} + \beta {\rm{ }} + \gamma {\rm{ }} = {\rm{ }}\pi \) is
  • A
    (-) 3
  • B
    positive
    Correct
  • C
    negative
  • D
    zero
10
If the sides a, b c of a triangle ABC are in A.P., then
  • A
    \(\sin {A \over 2}\sin {B \over 2} = 2\sin {C \over 2}\)
  • B
    \(\sin {B \over 2}\sin {C \over 2} = \sin {A \over 2}\)
  • C
    \(2\sin {A \over 2}\sin {C \over 2} = \sin {B \over 2}\)
    Correct
  • D
    \(2\sin {A \over 2}\sin {B \over 2} = \sin {C \over 2}\)
11
If the sides of a triangle ABC are given as 4, 5, 7 respectively then cot \({B \over 2}\cot {C \over 2}\) equals
  • A
    \({{16} \over 9}\)
  • B
    2
    Correct
  • C
    1
  • D
    3
12
If sin x - cos x =\(\sqrt 2 \), then x = ( n is any integer)
  • A
    n \(\pi \)
  • B
    ( 2 n + 1) \(\pi \)
  • C
    \(2n\pi + {{3\pi } \over 4}\)
    Correct
  • D
    2 n \(\pi \)
13
The general value of \(\theta \) satisfying sin = - \({1 \over 2}\) and tan \(\theta \) = \({1 \over {\sqrt 3 }}\) is
  • A
    \(2n\pi + {{11\pi } \over 6},n \in I\)
  • B
    \(n\pi + {( - 1)^n}{{7\pi } \over 6},n \in I\)
  • C
    \(2n\pi + {{7\pi } \over 6},n \in I\)
    Correct
  • D
    \(n\pi + {\pi \over 6},n \in I\)
14
The equation sin \(x - {\pi \over 2} + 1\) = 0 has no root in the interval
  • A
    \(\left( {0,{\pi \over 2}} \right)\)
  • B
    \(\left( {{\pi \over 2},\pi } \right)\)
  • C
    \(\left( {{\pi \over 2},{{3\pi } \over 2}} \right)\)’
  • D
    none of these
    Correct
15
The number of values of x satisfying the condition sin x + sin 5 x = sin 3x in the interval [ 0 , \(\pi \)] is
  • A
    10
  • B
    0
  • C
    6
    Correct
  • D
    2