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
The equation (cos p – 1) \({x^2}\) + cos p) x + sin p = 0, where x is a variable, has real roots. Then the interval of p may be any one of the following:
  • A
    \(\left( { - {\pi \over 2},{\pi \over 2}} \right)\)
  • B
    \(\left( { - \pi ,0} \right)\)
  • C
    \(\left( {0,\pi } \right)\)
    Correct
  • D
    \(\left( {0,\pi } \right)\)
2
In a triangle ABC, a = 13, b = 14, c = 15; r =
  • A
    2
  • B
    4
    Correct
  • C
    6
  • D
    8
3
If sin \(\theta + {\rm{ cosec }}\theta \) = 2, then \({\sin ^2}\theta + \cos e{c^2}\theta = \)
  • A
    1
  • B
    2
    Correct
  • C
    4
  • D
    none of these
4
The value of tan \({75^ \circ }\) - cot \({75^ \circ }\) is equal to
  • A
    \(2 + \sqrt 3 \)
  • B
    \(2 - \sqrt 3 \)
  • C
    \(1 + 2\sqrt 3 \)
  • D
    \(2\sqrt 3 \)
    Correct
5
In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals
  • A
    1
    Correct
  • B
    \({a \over c}\)
  • C
    none of these
  • D
    \({c \over a}\)
6
If the angles of at triangle are in the ratio 1 : 2 : 3, then the sides are in the ratio
  • A
    \(\sqrt 3 :\sqrt 2 :1\)
  • B
    \(\sqrt 3 :1:2\)
  • C
    \(1:\sqrt 3 :\sqrt {2.} \)
  • D
    \(1:\sqrt 3 :2\)
    Correct
7
In a triangle ABC right angled at C, tan A and tan B satisfy the equation
  • A
    \(ab{x^2} - ({a^2} + {b^2})x - ab = 0\)
  • B
    \({c^2}{x^2} - abx + {c^2} = 0\)
  • C
    \(ab{x^2} - {c^2}x + ab = 0\)
    Correct
  • D
    \(a{x^2} - bx + a = 0\)
8
Let the angles A, B, C of \(\Delta ABC\) be in A.P. and let b: c:: \(\sqrt 3 :\sqrt 2 ,\) then the angle A is
  • A
    \({75^ \circ }\)
    Correct
  • B
    \({60^ \circ }\)
  • C
    \({45^ \circ }\)
  • D
    none of these
9
cot \(\theta \) = sin 2 \(\theta (\theta \) \( \ne \)n \(\pi \) , n integer) if \(\theta \) equals
  • A
    \({45^ \circ }and\;{90^ \circ }\)
    Correct
  • B
    \({45^ \circ }and\;{60^ \circ }\)
  • C
    \({45^ \circ }\) only
  • D
    \({90^ \circ }\) only
10
If A = \({\sin ^2}\theta + {\cos ^4}\theta \) then for all real values of \(\theta \)
  • A
    \({{13} \over {16}} \le A \le 1\)
  • B
    \({3 \over 4} \le A \le {{13} \over {16}}\)
  • C
    \(1 \le A \le 2\)
  • D
    \({3 \over 4} \le A \le 1\)
    Correct
11
The general solution of tan 3x = 1 is (n \( \in \) I)
  • A
    \(n\pi \pm {\pi \over 4}\)
  • B
    \({\rm{n}}\pi \)
  • C
    \(n\pi + {\pi \over 4}\)
  • D
    \({{n\pi } \over 3} + {\pi \over {12}}\)
    Correct
12
The value of sin \({\pi \over {14}}\sin {{3\pi } \over {14}}\sin {{5\pi } \over {14}}\sin {{7\pi } \over {14}}\sin {{9\pi } \over {14}}\sin {{11\pi } \over {14}}\sin {{13\pi } \over {14}}\) is
  • A
    none of these
  • B
    \({1 \over {16}}\)
  • C
    \({1 \over {64}}\)
    Correct
  • D
    \({1 \over {128}}\)
13
If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ ( = PR), then the angle P is
  • A
    \({\pi \over 2}\)
  • B
    \({\pi \over 6}\)
  • C
    \({{2\pi } \over 3}\)
    Correct
  • D
    \({\pi \over 3}\)
14
The maximum value of sin \(\left( {x + {\pi \over 6}} \right) + \cos \left( {x + {\pi \over 6}} \right)\) in the interval \(\left( {0,{\pi \over 2}} \right)\) is attained at
  • A
    \({\pi \over 2}\)
  • B
    \({\pi \over {12}}\)
    Correct
  • C
    \({\pi \over 6}\)
  • D
    \({\pi \over 3}\)
15
The solution of tan 2 \(\theta \) tan \(\theta \) = 1 is
  • A
    \({\pi \over 3}\)
  • B
    \((2n + 1){\pi \over 6}\)
  • C
    \((4n \pm 1){\pi \over 6}\)
  • D
    \((6n \pm 1){\pi \over 6}\)
    Correct