MCQ Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 11

If $$\cos\ \theta+\sin\ \theta=a$$, then $$\sin\ 2\theta=$$

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$$a^{2}+1$$
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$$a^{2}-1$$
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$$a^{2}$$
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$$1$$

If $$\sin^{2} x- \cos x=1/4$$, then the value of $$x$$ between $$0$$ and $$2\pi$$ are :

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$$\pi /3, 5\pi /3$$
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$$\pi /3, -\pi/3$$
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$$2 \pi/3, \pi/3$$
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$$None\ of\ these$$

$$\dfrac{1+cot\alpha+cosec\alpha}{1-cot\alpha+cosec \alpha}=$$

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$$\dfrac{sin\alpha}{1+cos\alpha}$$
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$$\dfrac{sin\alpha}{1-cos\alpha}$$
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$$\dfrac{1+cos\alpha}{sin\alpha}$$
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$$\dfrac{1-sin\alpha}{cos\alpha}$$

If $$\sin ^ { - 1 } x = y ,$$ then

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$$0 \leq y \leq \pi$$
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$$- \frac { \pi } { 2 } \leq y \leq \frac { \pi } { 2 }$$
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$$0 < y < \pi$$
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$$- \frac { \pi } { 2 } < y < \frac { \pi } { 2 }$$

The equation $$\sin x + \sin y + \sin z = -3$$ for $$0 \le x \le 2\pi, 0 \le y \le 2\pi, 0 \le z \le 2\pi$$, has

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One solution
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Two sets of solutions
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Four sets of solutions
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No solution

The general solution to the equation $$\sin 3\alpha = 4\sin \alpha \sin(x + \alpha) \sin(x - \alpha)$$ is.

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$$n\pi \pm \dfrac{\pi}{4}, \forall n \in I$$
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$$n\pi \pm \dfrac{\pi}{3}, \forall n \in I$$
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$$n\pi \pm \dfrac{\pi}{9}, \forall n \in I$$
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$$n\pi \pm \dfrac{\pi}{12}, \forall n \in I$$

Number of solutions of the equation $$4\sin^{2}x+\tan^{2}x+\cot^{2}x+\csc^{2}=6$$ in $$[0, \pi]$$ is

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$$2$$
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$$8$$
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$$0$$
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$$4$$

Solution of $$7 \sin ^ { 2 } x + 3 \cos ^ { 2 } x = 4$$ is

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$$n \pi \pm \frac { \pi } { 2 }$$
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$$n \pi \pm \frac { \pi } { 4 }$$
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$$n \pi \pm \frac { \pi } {3 }$$
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$$n \pi \pm \frac { \pi } { 6 }$$

Genral solution of the equation $$\theta -cosec\theta =\dfrac { 4 }{ 3 }$$ is :

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$$\frac { 1 }{ 2 } \left( \left[ n\pi +{ \left( -1 \right) }^{ n }{ sin }^{ -1 }\left( 3/4 \right) \right] \right) n\epsilon Z$$
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$$n\pi +{ \left( -1 \right) }^{ n }{ sin }^{ -1 }\left( 3/4 \right) n\epsilon Z$$
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$$\frac { n\pi }{ 2 } +{ \left( -1 \right) }^{ n }{ sin }^{ -1 }\left( 3/4 \right) n\epsilon Z$$
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none of these

If $$\sin \alpha = a \sin \beta$$ and $$\cos \alpha = b \cos \beta$$ then $$\tan \alpha =$$

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$$\pm \sqrt { \left( \frac { a ^ { 2 } b ^ { 2 } - a ^ { 2 } } { b ^ { 2 } - a ^ { 2 } b ^ { 2 } } \right) }$$
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$$\pm \sqrt { \left( \frac { a ^ { 2 } - a ^ { 2 } b ^ { 2 } } { b ^ { 2 } +a ^ { 2 } b ^ { 2 } } \right) }$$
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$$\pm \sqrt { \left( \frac { 1 - a ^ { 2 } } { 1 - b ^ { 2 } } \right) }$$
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$$\pm \sqrt { \left( \frac { 1 + a ^ { 2 } } { 1 + b ^ { 2 } } \right. ) } $$

If $$x = \tan \theta + \cot \theta, y = \cos \theta - \sin \theta$$, then

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$$x = y$$
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$$\dfrac {1-y^2}{2} = \dfrac{1}{x}$$
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$$\dfrac {y^2-1}{2} = \dfrac{1}{x}$$
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$$\dfrac {1+y^2}{2} = \dfrac{1}{x}$$

Explanation

$${\textbf{Step - 1: Deduce and simplify value of x.}}$$

$${\text{Given x}} = {\text{tan}}\theta + {\text{cot}}\theta .$$

$$ \Rightarrow {\text{x}} = \dfrac{{{\text{sin}}\theta }}{{{\text{cos}}\theta }} + \dfrac{{{\text{cos}}\theta }}{{{\text{sin}}\theta }}.$$

$$ \Rightarrow {\text{x}} = \dfrac{{{\text{si}}{{\text{n}}^2}\theta + {\text{co}}{{\text{s}}^2}\theta }}{{{\text{sin}}\theta {\text{cos}}\theta }}.$$

$$ \Rightarrow {\text{x}} = \dfrac{1}{{{\text{sin}}\theta {\text{cos}}\theta }}{\text{ - - - - - - - (i)}}$$

$${\textbf{Step - 2: Simplify value of y}}{\text{.}}$$

$${\text{Given y}} = {\text{cos}}\theta - {\text{sin}}\theta .$$

$${\text{so , }}\dfrac{{1 - {y^2}}}{2} = \dfrac{{1 - {{\left( {{\text{cos}}\theta - {\text{sin}}\theta } \right)}^2}}}{2}.$$

$$ \Rightarrow \dfrac{{1 - {y^2}}}{2} = \dfrac{{1 - {\text{co}}{{\text{s}}^2}\theta - {\text{si}}{{\text{n}}^2}\theta + 2{\text{sin}}\theta {\text{cos}}\theta }}{2}$$

$$ \Rightarrow \dfrac{{1 - {y^2}}}{2} = \dfrac{{1 - \left( {{\text{si}}{{\text{n}}^2}\theta + {\text{co}}{{\text{s}}^2}\theta } \right) + 2{\text{sin}}\theta {\text{cos}}\theta }}{2}$$

$$ \Rightarrow \dfrac{{1 - {y^2}}}{2} = \dfrac{{1 - 1 + 2{\text{sin}}\theta {\text{cos}}\theta }}{2}$$

$$ \Rightarrow \dfrac{{1 - {y^2}}}{2} = \dfrac{{{\text{2sin}}\theta {\text{cos}}\theta }}{2}$$

$$ \Rightarrow \dfrac{{1 - {y^2}}}{2} = {\text{sin}}\theta {\text{cos}}\theta $$

$$ \Rightarrow \dfrac{{1 - {y^2}}}{2} = \dfrac{1}{x}{\text{ }}\left[ {{\text{Put value of sin}}\theta c{\text{os}}\theta {\text{ from (i)}}} \right]$$

$${\textbf{So , as per given value of x and y they have a relation of }}\mathbf{\dfrac{{1 - {y^2}}}{2} = \dfrac{1}{x}(B)}.$$

If $$\cosh x=\sec \theta$$, then $$\coth^{2}(x/2)=$$

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$$\tan^{2}(\theta/2)$$
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$$\tan^{2}\theta$$
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$$\cot^{2}(\theta/2)$$
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$$\cot^{2}\theta$$

Choose the correct answer the following:
2) The principle solution of $$\sec{x}+2=0$$ is____

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$$\dfrac{4\pi}{3}$$
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$$-\dfrac{4\pi}{3}$$
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$$\dfrac{2\pi}{3}$$
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$$-\dfrac{2\pi}{3}$$

One of principal solution of $$\sqrt 3 \sec x = - 2$$ is equal to

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$$5\dfrac{\pi }{6}$$
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$$5\dfrac{\pi }{3}$$
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$$5\dfrac{\pi }{4}$$
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none

if $$\sqrt{2} cos \theta$$ = $$\sqrt { \dfrac { 2+\sqrt { 2+\sqrt { 2 } } }{ 2 } }$$ then the value of $$\theta$$ is

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$$\dfrac{\pi}{16}$$
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$$\dfrac{\pi}{32}$$
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$$\dfrac{\pi}{64}$$
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$$\dfrac{\pi}{128}$$

If $$sin A=\dfrac{3}{5},\tan B=\dfrac{1}{2}$$ and $$\dfrac{\pi}{2}<A<\pi<B<\dfrac{3\pi}{2}$$, then the value of $$8\tan A-\sqrt{5}sec B=$$

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$$5/2$$
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$$-5/2$$
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$$-7/2$$
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$$7/2$$

$$cos (4 \pi + \theta)$$ = ...

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$$sin \theta$$
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$$cos \theta$$
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$$- sin \theta$$
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$$-cos \theta$$

If $$4\cos{\theta}-3\sec{\theta}=2\tan{\theta}$$, then $${\theta}$$ is equal to

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$$n\pi+(-1)^{n}\dfrac{\pi}{10}$$
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$$n\pi+(-1)^{n}\dfrac{\pi}{6}$$
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$$n\pi+(-1)^{n}\dfrac{3\pi}{10}$$
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$$n\pi$$

The value(s) of $$\theta $$, which satisfy $$3-2cos\theta-4sin\theta -cos2\theta +sin2\theta =0$$ is/are

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$$\theta =2n\pi ;n\in 1$$
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$$2n\pi +\dfrac { \pi }{ 2 } ;n\in 1$$
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$$2n\pi -\dfrac { \pi }{ 2 } ;n\in 1$$
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$$n\pi ;n\in 1$$

Consider the operator a = X + $$\dfrac{d}{dx}$$ acting on smooth function of x. The commutator [a, cos x] is

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(A) - sin x
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(B) cos x
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(C) -cos x
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0

The value of the expression $$\dfrac { 1 - 4 \sin 10 ^ { \circ } \sin 70 ^ { \circ } } { 2 \sin 10 ^ { \circ } }$$ is

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$$\dfrac { 1 } { 2 }$$
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$$1$$
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$$2$$
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None if these

Number of solutions to the equation $$2 ^ { \sin ^ { 2 } x } + 5.2 ^ { \cos ^ { 2 } x } = 7 ,$$ in the interval $$[ - \pi , \pi ] ,$$ is

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$$2$$
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$$4$$
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$$6$$
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none of these

If $$5\left({\tan}^{2}x-{\cos}^{2}x\right)=2\cos2x+9$$, then the value of $$\cos4x$$ is:

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$$-\dfrac{3}{5}$$
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$$\dfrac{1}{3}$$
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$$\dfrac{2}{9}$$
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$$-\dfrac{7}{9}$$

$$\tan^4 \theta + \tan^2 \theta = \sec^4 \theta -\sec^2 \theta$$

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True
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False

$$\left(\dfrac {1+\tan^{2}A}{1+\cot^{2}A}\right)=\left(\dfrac {1-\tan^{2}A}{1-\cot^{2}A}\right)^{2}=\tan^{2}A$$

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True
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False

State whether the following statement is true or false
$$\sin^{2}\theta .\cos \theta +\tan \theta \sin \theta +\cos^{3}\theta =\sec \theta$$

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True
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False

$$(\sin \theta +\cos \theta)^{2}+(\sin \theta -\cos \theta)^{2}=2$$

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True
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False

$$\sin A(1+\tan A)+\cos A(1+\cot A)=\sec A+\csc A$$.

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True
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False

$$\dfrac {\sec A-\tan A}{\sec A+\tan A}=1-2\sec A\tan A+2\tan^{2}A$$.

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True
0%
False

State true or false.

$$\sec^{4}\theta-\tan^{4}\theta=1+2\tan^{2}\theta$$.

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True
0%
False

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

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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