CBSE Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 15 - MCQExams.com

The solution set of the equation $$4 \sin \theta-2 \cos \theta-2\sqrt {3} \sin \theta+\sqrt {3}=0$$ in the interval $$(0,2\pi)$$ is-
  • $$\left\{ {\dfrac{{3\pi }}{4},\dfrac{{7\pi }}{4}} \right\}$$
  • $$\left\{ {\dfrac{\pi }{3},\dfrac{{5\pi }}{3}} \right\}$$
  • $$\left\{ {\dfrac{{3\pi }}{4},\dfrac{{7\pi }}{4},\dfrac{\pi }{3},\dfrac{{5\pi }}{3}} \right\}$$
  • $$\left\{ {\dfrac{\pi }{6},\dfrac{{5\pi }}{6},\dfrac{{11\pi }}{6}} \right\}$$
If $$\sin \theta +\cos \theta =1$$, then the value of $$\sin 2\theta$$ is equal to:
  • $$1$$
  • $$\dfrac{1}{2}$$
  • $$0$$
  • $$-1$$
The least value of a for which the expression $$f(x)=\cfrac{4}{\sin x}+\cfrac{1}{1-\sin x}=a^{2}$$ has at least one solution on the interval $$(0,\quad \pi /2)$$ is 
  • $$3$$
  • $$2$$
  • $$-3$$
  • $$1$$
If  x=$$\frac{{2\left( {\sin {1^o} + \sin {2^o} + \sin {3^o} + .... + \sin {{89}^o}} \right)}}{{2\left( {\cos {1^o} + \cos {2^o} + ..... + \cos {{44}^o}} \right) + 1}}$$, then the value of $${\log _x}2$$ is equal 
  • 1
  • 2
  • 1/2
  • 4
Total number of solutions of $$\sin^{2}x-\sin x-1=0$$ in $$[-2\pi, 2\pi]$$ is equal to:
  • $$2$$
  • $$4$$
  • $$6$$
  • $$8$$
The number of solution of $$\sin 3x=\cos 2x$$ in the interval $$\left(\dfrac{\pi}{2},\pi\right)$$ is :
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
If $$x\in \left[ 0,\dfrac { \pi  }{ 2 }  \right] $$, the number of solutions of the equation, $$\sin { 7x } +\sin { 4x } +\sin { x=0 }$$ is
  • $$3$$
  • $$5$$
  • $$6$$
  • $$None$$
If $$\sin B=\dfrac {1}{5}\sin (2A+B)$$, then $$\dfrac {\tan (A+B)}{\tan A}$$ is equal to
  • $$\dfrac53$$
  • $$\dfrac23$$
  • $$\dfrac32$$
  • $$\dfrac35$$
Find the general solution of $$x$$ $$\cos^2 2x+\cos^2 3x=1$$
  • $$(2k+1)\dfrac{\pi}{10},k \in I$$
  • $$(\pi+1)\dfrac{\pi}{10};k \in I$$
  • $$(2k-1)\dfrac{\pi}{10},k\in I $$
  • Both (A) and (C)
The solution set of equation
$$4\sin{\theta}\cos{\theta}-2\cos{\theta}-2\sqrt{3}\sin{\theta}+\sqrt{3}=0$$ in the interval $$(0, 2\pi)$$
  • $$\left\{ \dfrac { 3\pi }{ 4 } ,\dfrac { 7\pi }{ 4 } \right\}$$
  • $$\left\{ \dfrac { \pi }{ 3 } ,\dfrac { 5\pi }{ 3 } \right\}$$
  • $$\left\{ \dfrac { \pi }{ 6 } ,\dfrac { 5\pi }{ 6 } ,\dfrac{11\pi}{6}\right\}$$
  • None of these
Find the principal solution of the following equation:
$$\tan { x=\sqrt { 3 }  } $$
  • $$x=\dfrac{\pi}{3}$$ and $$x=\dfrac{4}{3}\pi$$ 
  • $$x=\dfrac{\pi}{2}$$ and $$x=\dfrac{1}{3}\pi$$ 
  • $$x=\dfrac{\pi}{4}$$ and $$x=\dfrac{2}{3}\pi$$ 
  • $$x={3}$$ and $$x=\dfrac{4}{3}\pi$$ 
If $$\dfrac{\sin^4x}{2}+\dfrac{\cos^4x}{3}=\dfrac{1}{5}$$, then
  • $$\tan^2x=\dfrac{2}{3}$$
  • $$\dfrac{\sin^8x}{8}+\dfrac{\cos^8x}{27}=\dfrac{1}{125}$$
  • $$\tan^2x=\dfrac{1}{3}$$
  • $$\dfrac{\sin^8x}{8}+\dfrac{\cos^8x}{27}=\dfrac{2}{125}$$
The value of $$\quad ({ tan }^{ 2 }\cfrac { \pi  }{ 7 } +{ tan }^{ 2 }\cfrac { 2\pi  }{ 7 } +{ tan }^{ 2 }\cfrac { 3\pi  }{ 7 } )$$ x $$({ cot }^{ 2 }\cfrac { \pi  }{ 7 } +cot^{ 2 }\cfrac { 2\pi  }{ 7 } +{ cot }^{ 2 }\cfrac { 3\pi  }{ 7 } )$$ is
  • $$105$$
  • $$35$$
  • $$210$$
  • None of these
The number of real solutions $$x$$ of the equation $$\cos ^ { 2 } ( x \sin ( 2 x ) ) + \frac { 1 } { 1 + x ^ { 2 } } - \cos ^ { 2 } x + \sec ^ { 2 } x$$ is
  • 0
  • 1
  • 2
  • infinite
 $$\dfrac{\cos A}{1- \sin A}$$=
  • $$\tan\left(\frac{\pi}{4}+\frac{A}{2}\right)$$
  • $$\tan\left(\frac{\pi}{2}+\frac{A}{2}\right)$$
  • $$\cot\left(\frac{\pi}{4}+\frac{A}{2}\right)$$
  • None of these
$$\dfrac{1}{\text{cosec}\ \theta+\cot\ \theta}-\dfrac{1}{\sin\ \theta}=\dfrac{1}{\sin\ \theta}-\dfrac{1}{\text{cosec}\ \theta-\cot\ \theta}$$
  • True
  • False
General solution of $${\sin ^3}x + {\cos ^3}x + \frac{3}{2}\sin 2x = 1$$
  • $$x = n\pi $$ when n is even integer
  • $$x = 2n\pi $$ when n is odd integer
  • $$x = n\pi + \frac{\pi }{2}$$ when n is odd integer
  • $$x = n\pi - \frac{\pi }{2}$$
The number of solution of $$\sec x \cos 5x+1=0$$ in the interval $$[0,2\pi]$$ is
  • $$5$$
  • $$8$$
  • $$10$$
  • $$12$$
If $$2 \tan ^ { 2 } \theta - 5 \sec \theta = 1$$ has exactly $$7$$ solutions in the interval $$\left[ 0 , \dfrac { n \pi } { 2 } \right] , n \in N$$ then the least and  greatest values of $$n$$ are 
  • $$6 , 8$$
  • $$12 , 14$$
  • $$13 , 15$$
  • $$15 , 17$$
The value of $$\sqrt { 3 } \cot 20 ^ { \circ } - 4 \cos 20 ^ { \circ }$$ = __________________________.
  • $$1$$
  • $$-1$$
  • $$0$$
  • none of these
If in a triangle $$ABC, \dfrac{b+c}{11}=\dfrac{c+a}{12}=\dfrac{a+b}{13}$$, then $$\cos A$$ is equal to:
  • $$\dfrac{19}{35}$$
  • $$\dfrac{5}{7}$$
  • $$\dfrac{1}{5}$$
  • $$\dfrac{35}{19}$$
The number of real solutions of the equation $$\sin \left( e ^ { x } \right) = 5 ^ { x } + 5 ^ { - x }$$ is ____________________.
  • $$0$$
  • $$1$$
  • $$2$$
  • infinite
The value of $$\sin \dfrac {2\pi}{7}+\sin \dfrac {4\pi}{7}+\sin \dfrac {8\pi}{7}$$ is
  • $$1$$
  • $$\dfrac {\sqrt {7}}{2}$$
  • $$\dfrac {3\sqrt {3}}{4}$$
  • $$\dfrac {\sqrt {15}}{4}$$
The value of $$\tan\theta+\sec\theta$$ is equal to
  • $$3t$$
  • $$t$$
  • $$t-t^{2}$$
  • $$t^{2}-2t$$
If $$\tan^{2}\alpha-\tan^{2}\beta-\dfrac{1}{2}\sin(\alpha-\beta)\sec^{2}\alpha\sec^{2}\beta$$ is zero then value of $$\sin(\alpha+\beta)$$ is $$(\alpha\neq\beta)$$
  • $$1$$
  • $$\dfrac{1}{3}$$
  • $$\dfrac{1}{4}$$
  • $$\dfrac{1}{2}$$
The value of $$\sin{\left(\alpha+\beta\right)}$$ is 
  • $$\dfrac{24}{25}$$
  • $$\dfrac{12}{13}$$
  • $$\dfrac{1}{25}$$
  • $$None\ of\ these$$
In a $$\triangle ABC, \sum a \cos A=4 \sin A \sin B \sin C$$, then value of $$\left(\dfrac{\sum \sin A}{\sum a}\right)^{2}$$ is-
  • $$\dfrac{1}{4}$$
  • $$\dfrac{1}{2}$$
  • $$1$$
  • $$\dfrac{1}{3}$$
$$sin\left( { 4tan }^{ -1 }{ \cfrac { 1 }{ 3 }  } \right) =$$
  • $$\frac { 12 }{ 25 } $$
  • $$\frac { 24 }{ 25 } $$
  • $$\frac { 1 }{ 5 } $$
  • none of these
If $$0 < \phi < \dfrac {\pi}{2}$$ and if $$\displaystyle x=\sum^{\alpha}_{n=0}\cos^{2}\phi:y=\sum^{\alpha}_{n=0}\sin^{2n}\phi$$ then 
  • $$x^{2}+y^{2}=1$$
  • $$x^{2}-y^{2}=1$$
  • $$x+y=xy$$
  • $$\dfrac {1}{x}+\dfrac {1}{y}=1$$
If $${ tan }^{ 2 }\theta +{ cot }^{ 2 }\theta =\frac { a }{ b-cos4\theta  } +c$$ (where defined) is satisfied for all $$\theta $$, then the value of (a + b + c) is equal to $$(a,b,c\in I)$$
  • 6
  • 7
  • 8
  • 9
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