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 in a triangle ABC, \(a{\cos ^2}\left( {{C \over 2}} \right) + c{\cos ^2}\left( {{A \over 2}} \right) = {{3b} \over 2},\) then its sides a, b, c are in
  • A
    A. P.
    Correct
  • B
    none of these
  • C
    H.P.
  • D
    G.P.
2
In a \(\Delta ABC\) , if a sin A = b sin B then the triangle is
  • A
    equilateral
  • B
    right angled
  • C
    right angled isosceles
  • D
    isosceles
    Correct
3
If in a \(\Delta ABC\) , a cos A = b cos B, then the triangle is
  • A
    equilateral
  • B
    isosceles
  • C
    right angled
  • D
    either isosceles or right angled
    Correct
4
In a\(\Delta ABC\) , \({{{{\cos }^2}\left( {{A \over 2}} \right)} \over a} + {{{{\cos }^2}\left( {{B \over 2}} \right)} \over b} + {{{{\cos }^2}\left( {{C \over 2}} \right)} \over c}\) Is equal to
  • A
    \({{{s^2}} \over {abc}}\)
    Correct
  • B
    \({s \over {abc}}\)
  • C
    none of these
  • D
    \({{2s} \over {abc}}\)
5
In a triangle ABC, a = 2b and \(\angle A = 3\angle B,\) then angle A is
  • A
    \({60^ \circ }\)
  • B
    \({30^o}\)
  • C
    none of these
  • D
    \({90^ \circ }\)
    Correct
6
In a triangle ABC, AD is the median A to BC, then its length is equal to
  • A
    \(\sqrt {{b^2} + {c^2} - {{{a^2}} \over 2}} \)
  • B
    \(\sqrt {{{{b^2} + {c^2} - {a^2}} \over 2}} \)
  • C
    \({{b + c} \over 2}\)
  • D
    \({1 \over 2}\sqrt {2({b^2} + {c^2}) - {a^2}} \)
    Correct
7
If cos A + cos B = 4\({\sin ^2}{C \over 2}\), then the sides of the triangle ABC are in
  • A
    A. P.
    Correct
  • B
    H. P.
  • C
    none of these
  • D
    G. P.
8
ABC is an equilateral triangle of each side a (\(>\) 0). The inradius of the triangle is
  • A
    \({a \over {2\sqrt 3 }}\)
    Correct
  • B
    \({a \over 3}\)
  • C
    \({{\sqrt 3 \;a} \over 3}\)
  • D
    \({{\;a} \over 2}\)
9
In any \(\Delta ABC,\) the expression (a + b + c) (a + b – c) (b + c – a) (c + a – b) is equal to
  • A
    \(16\Delta \)
  • B
    none of these
    Correct
  • C
    \(4\Delta \)
  • D
    \(4{\Delta ^2}\)
10
In any \(\Delta ABC\), if C =\({90^ \circ }\), then tan \({B \over 2}\) is equal to
  • A
    \(\sqrt {{{a - c} \over {a + c}}} \)
  • B
    \(\sqrt {{{c - a} \over {c + a}}} \)
    Correct
  • C
    none of these
  • D
    \(\sqrt {{{c - a} \over {c - a}}} \)
11
Angles of triangle are in A.P. If the number of degrees in the smallest to the number of radians in the largest is as \(60:\pi \), then the smallest angle is
  • A
    \({40^ \circ }\)
  • B
    \({30^ \circ }\)
    Correct
  • C
    \({20^ \circ }\)
  • D
    none of these.
12
If x, y, z are perpendiculars drawn from the vertices of a triangle having sides a, b and c, then \({{bx} \over c} + {{cy} \over a} + {{az} \over b} = \)
  • A
    \({{{a^2} + {b^2} + {c^2}} \over {4R}}\)
  • B
    \({{{a^2} + {b^2} + {c^2}} \over R}\)
  • C
    \({{{a^2} + {b^2} + {c^2}} \over {2R}}\)
    Correct
  • D
    \({{2({a^2} + {b^2} + {c^2})} \over R}\)
13
The largest value of sin \(\theta \cos \theta \) is
  • A
    \({{\sqrt 3 } \over 2}\)
  • B
    \({1 \over 2}\)
    Correct
  • C
    1
  • D
    \({1 \over {\sqrt 2 }}\)
14
If tan \(\theta + \sec \theta = \sqrt 3 ,0 < \theta \;\pi ,\) then \(\theta \) is equal to
  • A
    \({{2\pi } \over 3}\)
  • B
    \({\pi \over 6}\)
    Correct
  • C
    \({{5\pi } \over 6}\)
  • D
    \({\pi \over 3}\)
15
If sin \(({120^o} - \alpha ) = \sin ({120^o} - \beta )\) and 0 \( < \alpha ,\beta {\rm{ }} < {\rm{ }}\pi \) , then all values of \( \alpha {\rm{ and }}\beta \) are given by
  • A
    \(\alpha = \beta \;or\;\alpha + \beta = {\pi \over 3}\)
    Correct
  • B
    \(\alpha + \beta \; = 0\)
  • C
    \(\alpha = \beta \;\)
  • D
    \(\alpha + \beta \; = {\pi \over 3}\)