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
In a triangle ABC, tan \({A \over 2} = {5 \over 6},\tan {B \over 2} = {{20} \over {37}},\) then tan \({C \over 2}\) is equal to
  • A
    \({{34} \over {37}}\)
  • B
    \({{100} \over {222}}\)
  • C
    \({5 \over 2}\)
  • D
    \({2 \over 5}\)
    Correct
2
In a triangle ABC, if A = \({75^o}\) and B = \({45^o}\) then b + \(\sqrt 2 \) c is equal to
  • A
    a + b + c
  • B
    2 a
    Correct
  • C
    \({1 \over 2}(a + b + c)\)
  • D
    a
3
The angles of a triangle are as 1 : 2 : 7, then ratio of greatest side to least side is
  • A
    \((\sqrt 5 + 1):(\sqrt 5 - 1)\)
    Correct
  • B
    \((\sqrt 2 + 3):(2 - \sqrt 3 )\)
  • C
    \((\sqrt 3 + 1):(\sqrt 3 - 1)\)
  • D
    \((\sqrt 2 + 1):(\sqrt 2 - 1)\)
4
If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is
  • A
    \({\pi \over 3}\)
  • B
    \({{2\pi } \over 3}\)
    Correct
  • C
    \({\pi \over 2}\)
  • D
    \({{3\pi } \over 2}\)
5
There exists a triangle ABC satisfying the conditions
  • A
    b sin A \(<\) a.
  • B
    b sin A \(<\) a, a = b, \(A = {\pi \over 2}\)
  • C
    b sin A = a, a \(>\) b
  • D
    b sin A \(<\)a.
    Correct
6
In a \(\Delta ABC,\) (b +c) cos A + (c + a) cos B + (a + b) cos C is equal to
  • A
    none of these
  • B
    a + b + c
    Correct
  • C
    0
  • D
    R r
7
If the angles of a triangle ABC are in A.P., then
  • A
    \({c^2} = {a^2} + {b^2}\)
  • B
    one of these
  • C
    \({a^2} + {c^2} - ac = {b^2}\)
    Correct
  • D
    \({c^2} = {a^2} + {b^2} + ab\)
8
The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is
  • A
    \({60^ \circ }\)
  • B
    \({120^ \circ }\)
  • C
    \({90^ \circ }\)
    Correct
  • D
    \({30^ \circ }\)
9
In a triangle ABC, \(\tan {{A + B} \over 2}\cot {{A - B} \over 2}\) is equal to
  • A
    \({{a - b} \over c}\)
  • B
    none of these
  • C
    \({{a + b} \over {a - b}}\)
    Correct
  • D
    \({{a - b} \over {a + b}}\)
10
The area of a triangle is \(80c{m^2}\) and its perimeter is 8 cm. The radius of its inscribed circle is
  • A
    none of these
  • B
    10 cm
  • C
    5 cm
  • D
    20 cm
    Correct
11
If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is
  • A
    none of these
  • B
    \(1:\left( {\sqrt 5 - 1} \right)\)
  • C
    \({\text{5 }}:{\text{ 1}}\)
  • D
    \((\sqrt 5 + 1):1\)
    Correct
12
If a = 4, b = 3 and A =\({60^ \circ }\), then c is a root of the equation
  • A
    \({x^2} - 3x + 7 = 0\)
  • B
    \({x^2} - 3x + 7 = 0\)
  • C
    \({x^2} - 3x - 7 = 0\)
    Correct
  • D
    \({x^2} - 3x + 7 = 0\)
13
If \({b^2} + {c^2} = 3{a^2},\) then cot B + cot C - cot A =
  • A
    1
  • B
    \({{ab} \over {4\Delta }}\)
  • C
    \({{ac} \over {4\Delta }}\)
  • D
    0
    Correct
14
bc \({\cos ^2}{A \over 2} + ca{\cos ^2}{B \over 2} + ab{\cos ^2}{C \over 2}is\) equal to
  • A
    \({(s - b)^2}\)
  • B
    \({s^2}\)
    Correct
  • C
    \({(s - a)^2}\)
  • D
    \({(s - c)^2}\)
15
If the sides of a triangle be 2x + 1, \({x^2}\)- 1 and \({x^2}\) +x +1, then the greatest angle is
  • A
    \({150^o}\)
  • B
    \({90^o}\)
  • C
    \({120^o}\)
    Correct
  • D
    \({135^o}\)