Processing math: 4%

CBSE Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 6 - MCQExams.com

The least positive root of the equation cos3x+sin5x=0 is,
  • 3π16
  • π16
  • 7π16
  • 9π16
The value of cosπ15cos2π15cos4π15cos8π15 is
  • 116
  • 116
  • 1
  • 0
If f(x)=\cos ^{ 2 }{ x } +\cos ^{ 2 }{ 2x } +\cos ^{ 2 }{ 3x } , then the number of values of x\in \left[ 0,2\pi  \right] for which f(x) = 0 are
  • 4
  • 6
  • 8
  • 0
If \sin x = \dfrac {1}{2} and \cos x < 0, then x =
  • -\dfrac {\pi}{6}
  • \dfrac {\pi}{6}
  • \dfrac {\pi}{2}
  • \dfrac {2\pi}{3}
  • \dfrac {5\pi}{6}
Find the positive value of sin (tan^{-1} 3)
  • \dfrac{3}{10}
  • \dfrac{3}{5}
  • \dfrac{3}{\sqrt{10}}
  • \dfrac{1}{3}
  • \dfrac{1}{\sqrt{10}}
2 \cos^3 A \,\sin\, A + 2\, \sin^3 A\, \cos\, A equals which one of the following?
  • \cos 2A
  • 2 \sin A
  • 2 \cos A
  • \cos^2 A
  • \sin 2A
For acute angle \theta, find \text{cosec }^{2}\theta - \cot^{2}\theta
  • 2
  • 3
  • 0
  • 1
For acute angle \theta, find value of \sec^{2}\theta - \tan^{2} \theta
  • 1
  • 2
  • 3
  • 0
In any right angled triangle which of the following identity is true?
  • \sin^{2}\theta - \cos^{2}\theta = 1
  • \cos^{2}\theta = 1 + \sin^{2} \theta
  • 1 + \tan^{2}\theta = \sec^{2}\theta
  • \sec^{2}\theta + 1 = \tan^{2}\theta
(\cos^{2} \theta - 1)(\cot^{2}\theta + 1) + 1 =
  • 1
  • -1
  • 2
  • 0
The value of \left( 1+\tan ^{ 2 }{ \theta  }  \right) \sin ^{ 2 }{ \theta  } is
  • \sin ^{ 2 }{ \theta }
  • \cos ^{ 2 }{ \theta }
  • \tan ^{ 2 }{ \theta }
  • \cot ^{ 2 }{ \theta }
The value of 9\tan ^{ 2 }{ \theta  } -9\sec ^{ 2 }{ \theta  } is
  • 1
  • 0
  • 9
  • -9
(1 + tan^2 \theta) . sin^2 \theta =
  • sin^2 \theta
  • cos^2 \theta
  • tan^2 \theta
  • cot^2 \theta
If x = a \sec \theta, y = b\tan \theta, then the value of \dfrac {x^{2}}{a^{2}} - \dfrac {y^{2}}{b^{2}} =
  • 1
  • -1
  • \tan^{2}\theta
  • cosec^{2}\theta
If \sin( \pi \cos \theta) = \cos (\pi \sin \theta), then which of the following is correct.
  • \cos \theta =\dfrac {3}{2\sqrt {2}}
  • \cos \left (\theta - \dfrac {\pi}{2}\right ) = \dfrac {1}{2\sqrt {2}}
  • \cos \left (\theta - \dfrac {\pi}{4}\right ) = \dfrac {1}{2\sqrt {2}}
  • \cos \left (\theta + \dfrac {\pi}{4}\right ) = -\dfrac {1}{2\sqrt {2}}
\displaystyle \left ( 1+\cot^{2}\theta \right )\left ( 1-\cos\theta \right )\left ( 1+\cos\theta \right )=
  • \tan^{2}\theta-\sec^{2}\theta
  • \sin^{2}\theta-\cos^{2}\theta
  • \sec^{2}\theta-\tan^{2}\theta
  • \cos^{2}\theta-\sin^{2}\theta
Principal solutions of the equation \sin { 2x } +\cos { 2x } =0, where \pi< x< 2\pi are
  • \cfrac { 7\pi }{ 8 } ,\cfrac { 11\pi }{ 8 }
  • \cfrac {9 \pi }{ 8 } ,\cfrac { 13\pi }{ 8 }
  • \cfrac { 11\pi }{ 8 } ,\cfrac { 15\pi }{ 8 }
  • \cfrac { 15\pi }{ 8 } ,\cfrac { 19\pi }{ 8 }
The number of solutions \left[ \cos { x }  \right] +\left| \sin { x }  \right| =1 in \pi \le x < 3\pi where [x] is the greatest integer not exceeding x is
  • 3
  • 4
  • 2
  • 1
9\tan^{2}\theta - 9 \sec^{2}\theta =
  • 1
  • 0
  • 9
  • -9
The number of roots of the equation x + 2\tan x = \dfrac {\pi}{2} in the interval [0, 2\pi] is
  • 1
  • 2
  • 3
  • Infinite
The number of principal solutions of \tan 2\theta = 1 is
  • One
  • Two
  • Three
  • Four
The equation \sqrt {3} \sin x + \cos x = 4 has 
  • Infinitely many solutions
  • No solution
  • Two solutions
  • Only one solution
If \cos { \alpha  } +\cos { \beta  } +\cos { \gamma  } =\sin { \alpha  } +\sin { \beta  } +\sin { \gamma  } =0, then the value of \cos { 3\alpha  } +\cos { 3\beta  } +\cos { 3\gamma  } is
  • 0
  • \cos { \left( \alpha +\beta +\gamma \right) }
  • 3\cos { \left( \alpha +\beta +\gamma \right) }
  • 3\sin { \left( \alpha +\beta +\gamma \right) }
If 0\le x\le 2\pi , then the number of solutions of the equation \sin ^{ 6 }{ x } +\cos ^{ 6 }{ x } =1 is
  • 2
  • 3
  • 4
  • 5
  • 8
Principal solutions of the equation \sin 2x+\cos2x=0, where \pi < x < 2\pi are
  • 7\dfrac{\pi}{8}, 11\dfrac{\pi}{8}
  • 9\dfrac{\pi}{8}, 13\dfrac{\pi}{8}
  • 11\dfrac{\pi}{8}, 15\dfrac{\pi}{8}
  • 15\dfrac{\pi}{8}, 19\dfrac{\pi}{8}
If 2\sin^{2}\theta + \sqrt {3}\cos \theta + 1 = 0, then the value of \theta is
  • \dfrac {\pi}{6}
  • \dfrac {2\pi}{3}
  • \dfrac {5\pi}{6}
  • \pi
The set of values of a for which the equation \sin x(\sin x+\cos x)=a has real solutions is
  • [1-\sqrt{2}, 1+\sqrt{2}]
  • [2-\sqrt{3}, 2+\sqrt{3}]
  • [0, 2+\sqrt{3}]
  • \left[\displaystyle\frac{1-\sqrt{2}}{2}, \frac{1+\sqrt{2}}{2}\right]
Which one of the following equations has no solution?
  • \csc { \theta } -\sec { \theta } =\csc { \theta } \cdot \sec { \theta }
  • \csc { \theta } \cdot \sec { \theta } =1
  • \cos { \theta } +\sin { \theta } =\sqrt { 2 }
  • \sqrt { 3 } \sin { \theta } -\cos { \theta } =2
One of the principal solutions of \sqrt3 \sec x = - 2 is equal to :
  • \dfrac {2 \pi} {3}
  • \dfrac { \pi} {6}
  • \dfrac {5 \pi} {6}
  • \dfrac {\pi} {3}
  • \dfrac {\pi} {4}
The equation 4 sin^2 x - 2(\sqrt3 + 1) sinx + \sqrt3 = 0 has
  • 2 solutions in (0, \pi)
  • 4 solutions in (0, 2 \pi)
  • 2 solutions in (- \pi, \pi)
  • 4 solutions in (- \pi, \pi)
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Engineering Maths Quiz Questions and Answers