CBSE Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 14 - MCQExams.com


The set of values of $${x}$$ for which $$\sin x\cos^{3}x>\cos x\sin^{3} x,    0\leq x\leq\pi$$ is
  • $$(0,\pi)$$
  • $$(0,\displaystyle \frac{\pi}{4})$$
  • $$(\displaystyle \frac{\pi}{4},\pi)$$
  • $$(0,\displaystyle \frac{\pi}{2})$$
If  $$\displaystyle {\frac{\sin^{3}\theta-\cos^{3}\theta}{\sin\theta-\cos\theta}-\frac{\cos\theta}{\sqrt{1+\cot^{2}\theta}}}-2\tan\theta\cot\theta=-1, \theta\in [0,2\pi]$$, then
  • $$\displaystyle \theta\in(0,\frac{\pi}{2})-\{\frac{\pi}{4}\}$$
  • $$\displaystyle \theta\in(\frac{\pi}{2}, \pi)-\{\frac{3\pi}{4}\}$$
  • $$\displaystyle \theta\in(\pi,\frac{3\pi}{2})-\{\frac{5\pi}{4}\}$$
  • $$\displaystyle \theta\in(0, \pi)-\{\frac{\pi}{4},\frac{\pi}{2}\}$$

The number of the solutions of thc equation $$\cos(\pi\sqrt{\mathrm{x}-4})\cos(\pi\sqrt{\mathrm{x}})=1$$ is
  • $$> 2$$
  • $$2$$
  • $$1$$
  • $$0$$
$$ 0<\mathrm{x}<2\pi;0<\mathrm{y}<2\pi$$ and $$3^{\sin \mathrm{x}+\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{y}}=1$$ and $$25^{\mathrm{s}\mathrm{i}{\mathrm{n}\mathrm{x}^{2}}+\cos^{2}\mathrm{y}}= 5$$ then (x,y) is
  • $$(\displaystyle \frac{7\pi}{6},\frac{\pi}{3})$$
  • $$(\displaystyle \frac{7\pi}{6},\frac{5\pi}{3})$$
  • $$(\displaystyle \frac{11\pi}{6},\frac{\pi}{3})$$
  • $$(\displaystyle \frac{11\pi}{6},\frac{5\pi}{3})$$

The number of values of $$\mathrm{x}$$ in $$[0,2\pi]$$ satisfying the equation $$|\cos x-\sin \mathrm{x}|\geq\sqrt{2}$$, is
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
If $$\mathrm{n}$$ be the number of solutions of the equation $$|\cot \mathrm{x}|= \cot x +\displaystyle \frac{1}{\sin \mathrm{x}}(0<\mathrm{x}<2\pi)$$ , then n $$=$$
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
If $$\mathrm{s}in(\pi \mathrm{c}\mathrm{o}s\theta)= \mathrm{c}os$$$$(\pi\sin\theta)$$ , then which of the following is correct
  • $$\cos \displaystyle \theta=\frac{3}{2\sqrt{2}}$$
  • $$\cos (\theta-\dfrac{\pi}{2})=\dfrac{1}{2\sqrt{2}}$$
  • $$\cos (\theta-\dfrac{\pi}{4})=\dfrac{1}{2\sqrt{2}}$$
  • $$\cos \left(\dfrac{\pi\theta}{4}\right )=\dfrac{1}{2\sqrt{2}}$$
The total number of solutions of $$\cos x=\sqrt{1-\sin 2x}$$ in $$\left [ 0,2\pi  \right ]$$ is equal to
  • $$2$$
  • $$3$$
  • $$5$$
  • None of these

$$|\tan x + \sec x| = |\tan x| - |\sec x|, x \epsilon [0,2\pi]$$if and only if x belongs to the interval
  • $$[0,\pi]$$
  • $$[0,\dfrac{\pi}{2})\cup (\dfrac{\pi}{2},\pi]$$
  • $$[\pi,\dfrac{3\pi}{2})\cup (\dfrac{3\pi}{2},2\pi]$$
  • none of these
The difference between greatest and least solution of $$x$$ is-
  • $$\dfrac {3\pi}{2}$$
  • $$\dfrac {\pi}{2}$$
  • $$\pi$$
  • $$10\pi$$
Find the value of $$\cot^{-1}\left(\dfrac{\sqrt {1-\sin x}+\sqrt {1+\sin x}}{\sqrt {1-\sin x}-\sqrt {1+\sin x}}\right)$$
  • $$\pi -\dfrac{x}{2}$$
  • $$\pi$$
  • $$\dfrac{x}{2}$$
  • $$\dfrac{\pi}{2}$$
The value of $$\dfrac{\tan \alpha}{1-\cot \alpha}+\dfrac{\cot \alpha}{1-\tan \alpha}$$ is identically equal to
  • $$\sec \alpha.\csc \alpha$$
  • $$\sin \alpha. \cos \alpha$$
  • $$\sec \alpha. \csc \alpha +1$$
  • $$\sin \alpha . \cos \alpha +1$$
If $$ \cos \theta - \sin \theta =\sqrt{2} \sin \theta$$, then $$ \cos \theta + \sin \theta$$ is
  • $$\sqrt{2}\cos \theta$$
  • $$\sqrt{2} \sin \theta$$
  • $$0$$
  • $$1$$
The trigonometric equation is-
$$\sin x+3 \sin 2x+\sin 3x=\cos x+3 \cos 2x+\cos 3x$$
when $$x$$ lies in first four quadrants. It means $$x\epsilon [0, 2\pi]$$, then-

How many solutions are there-
  • $$2$$
  • $$3$$
  • $$4$$
  • $$5$$
If $$\sec$$ $$\beta=\alpha+\dfrac{1}{4a}$$,then the value of $$\sec\beta+\tan\beta$$ is
  • $$a$$ or $$\dfrac{1}{a}$$
  • $$2a$$ or$$\dfrac{1}{2a}$$
  • $$4a$$ or $$\dfrac{1}{4a}$$
  • $$1$$
$$|\tan\theta+\sec\theta|=|\tan\theta|+|\sec\theta|, 0\leq \theta \leq 2\pi$$  is possible only if-
  • $$\theta \epsilon [0, \pi]-\left \{\dfrac {\pi}{2}\right \}$$
  • $$\theta \epsilon [0, \pi]$$
  • $$\theta \epsilon [0, \dfrac {\pi}{2})$$
  • $$(0, \dfrac {\pi}{2}]$$
The sum of the solution of $$x$$ is-
  • $$\frac {14\pi}{23}$$
  • $$\frac {3\pi}{4}$$
  • $$\frac {9\pi}{8}$$
  • $$6\pi$$
Consider the system of equations $$\displaystyle \sin x \cos 2y= (a^{2}-1)^{2}+1,\ \cos x\sin 2y= a+1$$, then the number of values of $$\displaystyle y\in [0,2\pi]$$ when the system has solution for permissible values of $$a$$ are,
  • $$2$$
  • $$3$$
  • $$4$$
  • $$5$$
The value of $$\displaystyle \sin ^{2}1^{\circ}+\sin ^{2}2^{\circ}+\sin ^{2}2^{\circ}+...+\sin ^{2}89^{\circ}+\sin ^{2}90^{\circ}$$
  • 1
  • 0
  • 45.5
  • 44
If $$\displaystyle \sin x+\mathrm{cosec}\: x=2, $$ then $$\displaystyle \sin ^{n} x + \mathrm{cosec} ^{n} \: x$$ is equal to 
  • $$2$$
  • $$\displaystyle 2^{n}$$
  • $$\displaystyle 2^{n-1}$$
  • $$\displaystyle 2^{n-2}$$
Consider the system of equations $$\displaystyle \sin x. \cos 2y= (a^{2}-1)^{2}+1,\ \cos x.\sin 2y= a+1$$, then the number of values of $$\displaystyle x\epsilon [0,2\pi]$$ when the system has a solution for permissible values of a is/are,
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
The total number of solutions of $$\displaystyle \sin \left \{ x \right \}=\cos \left \{ x \right \}$$ (where $$\displaystyle  \left \{ . \right \}$$ denotes the fractional part) in $$\displaystyle  \left [ 0,2\pi  \right ]$$ is equal to
  • $$5$$
  • $$6$$
  • $$8$$
  • None of these
In the given figure, $$\displaystyle \angle B =90^{\circ}$$ and $$\displaystyle \angle ADB=x^{\circ}$$, then find $$\displaystyle \cos^{2} C^{\circ}+\sin^{2} C^{\circ} $$.

188072_94cbda8c36124f36adc86ac88bdcfee3.png
  • 1
  • 2
  • 0
  • -1
The number of solutions of $$\displaystyle \sum_{r=1}^{5} \cos r x=5 $$ in the interval of $$\displaystyle \left [ 0,2\pi  \right ]$$ is
  • $$0$$
  • $$2$$
  • $$5$$
  • $$10$$
If $$3x = \text{cosec } \theta$$ and $$\dfrac {3}{x} = \cot \theta$$, then $$\left (x^{2} - \dfrac {1}{x^{2}}\right ) =$$
  • $$\dfrac {1}{27}$$
  • $$\dfrac {1}{81}$$
  • $$\dfrac {1}{3}$$
  • $$\dfrac {1}{9}$$
The value of $$\displaystyle \frac { \sin { \theta  } \cos { \theta  } .\sin { \left( { 90 }^{ o }-\theta  \right)  }  }{ \cos { \left( { 90 }^{ o }-\theta  \right)  }  } +\frac { \cos { \theta  } .\sin { \theta  } .\cos { \left( { 90 }^{ o }-\theta  \right)  }  }{ \sin { \left( { 90 }^{ o }-\theta  \right)  }  } +\frac { { \sin }^{ 2 }{ 27 }^{ o }+{ \sin }^{ 2 }{ 63 }^{ o } }{ { \cos }^{ 2 }{ 40 }^{ o }+{ \cos }^{ 2 }{ 50 }^{ o } } $$ is :
  • $$1$$
  • $$2$$
  • $$3$$
  • $$0$$
If $$\displaystyle p=\sqrt{\frac{1-\sin x}{1+\sin x}},q=\frac{1-\sin x}{\cos x},r=\frac{\cos x}{1+\sin x}$$ 
Which one of the following statement is correct ?
  • $$\displaystyle p=q\neq r$$
  • $$\displaystyle q=r\neq p$$
  • $$\displaystyle r=p\neq q$$
  • $$\displaystyle p=q=r$$
The value of $$\alpha \varepsilon (- \pi, 0)$$ satisfying $$sin \alpha + \int_{\alpha}^{2 \alpha} . cos 2x dx = 0$$ is
  • $$0$$
  • $$- \dfrac{\pi}{3}$$
  • $$-\pi$$
  • All of these
$$\cos (2001) \pi + \cot (2001)\dfrac {\pi}{2} + \sec (2001) \dfrac {\pi}{3} + \tan (2001) \dfrac {\pi}{4} + cosec (2001) \dfrac {\pi}{6}$$ equal to
  • $$0$$
  • $$1$$
  • $$-2$$
  • Not defined
$$\dfrac12\sin{(2x)}(1+\cot ^{ 2 }{ (x) } )$$ is equal to
  • $$\tan(x)$$
  • $$\sin (x)$$
  • $$\cos(x)$$
  • $$\cot(x)$$
  • $$\sec(x)$$
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