CBSE Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 16 - MCQExams.com

If $$sin \alpha + sin \beta = \dfrac{1}{2} $$ and $$cos \alpha + cos \beta = \dfrac{\sqrt{3}}{2}$$ then $$3 \beta + \alpha = $$
  • $$0^o$$
  • $$60^o$$
  • $$120^o$$
  • $$90^o$$
The value of $$\csc \dfrac{\pi}{13}-\sqrt{3} \sec \dfrac{\pi}{18}$$ is a 
  • Surd
  • Rational which is not integral
  • Negative integer
  • Natural number
The number of solution of the equation $${x^3} + 2{x^2} + 5x + 2\cos x = 0\,in\,[0,2\pi ]$$ is
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
 $$\displaystyle \frac { \tan ^{ 2 }{ \theta  }  }{ \tan ^{ 2 }{ \theta  } -1 } +\frac { \csc ^{ 2 }{ \theta  }  }{ \sec ^{ 2 }{ \theta  } -\csc ^{ 2 }{ \theta  }  } =\frac { 1 }{ \sin ^{ 2 }{ \theta  } -\cos ^{ 2 }{ \theta  }  } $$.
  • True
  • False
$$sec^{2}(Tan^{-1} 2) +Cosec^{2}(Cot^{-1}3)=$$
  • 5
  • 10
  • 15
  • 20
$$\dfrac { 1 }{ \text{cosec}\theta +\cot\theta  } -\dfrac { 1 }{ \sin\theta  } =\dfrac { 1 }{ \sin\theta  } -\dfrac { 1 }{ \text{cosec}\theta -\cot\theta  } $$
  • True
  • False
If y = acosx + bsinx then find the maximum value of y
  • $$\sqrt{a^2+b^2}$$
  • $${a^2}+{b^2}$$
  • $$\frac{a+b}{2}$$
  • $$\frac{\sqrt{a^2+b^2}}{2}$$
The value of $$\sum\limits_{r = 0}^9 {{{\sin }^2}\dfrac{{\pi r}}{{18}}} \;is\;equal\;to\;$$ 
  • $$\dfrac{9}{2}$$
  • $$\dfrac{7}{2}$$
  • 5
  • None of these
If $$\csc\theta=\dfrac{x^{2}-y^{2}}{x^{2}+y^{2}}$$ where $$x$$ and $$y$$ are two unequal non-zero real numbers, then the number of real values of $$\theta$$ is 
  • $$0$$
  • $$1$$
  • $$2$$
  • $$infinite$$
$$\displaystyle\sum_{r=1}^{n-1} \cos^2\left ( \dfrac{r\pi}{n} \right )=? $$
  • $$\dfrac{n}{2}$$
  • $$\dfrac{n-2}{2}$$
  • $$\dfrac{n-1}{2}$$
  • $$\dfrac{n-2}{4}$$
If $$sinx+{ sin }^{ 2 }x=1,$$ then value of $${ cos }^{ 2 }x+{ cos }^{ 4 }x$$ is
  • 1
  • 2
  • 1.5
  • none of these
If $$\frac { \cos { \theta  }  }{ p } =\frac { \sin { \theta  }  }{ q } $$, then $$\frac { p }{ \sec { 2\theta  }  } +\frac { q }{ cosec2\theta  } $$ is equal to 
  • p
  • q
  • qp
  • none of these
The value of $$\sum _{ r=1 }^{ 10 }{ \cos ^{ 3 }{ \frac { r\pi  }{ 3 }  }  } =$$?
  • $$-\frac { 1 }{ 8 } $$
  • $$-\frac { 7 }{ 8 } $$
  • $$-\frac { 9 }{ 8 } $$
  • None of the above
If $$x+y=\dfrac { 2\pi  }{ 3 } and\quad cosx+cosy=\dfrac { \sqrt { 3 }  }{ 2 } ,\quad then\quad x,y\quad is\quad equal\quad to$$ 
  • $$\dfrac { \pi }{ 3 } ,\dfrac { \pi }{ 6 } $$
  • $$\dfrac { \pi }{ 2 } ,\dfrac { \pi }{ 6 } $$
  • $$\dfrac { \pi }{ 4 } ,\dfrac { \pi }{ 3 } $$
  • no solution
$$\sqrt{\dfrac{1+ cosx }{1-cos x}}$$ 
  • $$\dfrac{1+ cosx }{1-cos x}$$
  • $$cosec x+ cot x$$
  • $$cosec x- cot x$$
  • $$cosec x$$
If $$f(x) = \frac{{{{\cos }^2}x + {{\sin }^4}x}}{{{{\sin }^2}x + {{\cos }^4}x}}$$ for $$x \in R$$ then $$f(2002)=$$
  • 1
  • 2
  • 3
  • 4
If $${T_n} = \left( {{{\sin }^n}\theta  + {{\cos }^n}\theta } \right),\;then\;for\;permissible\;values\;of\;\theta $$, $$\dfrac{{{T_5} - {T_3}}}{{{T_7} - {T_5}}}$$ is always equal to 
  • $$\dfrac{{{T_1}}}{{{T_3}}}$$
  • $$\dfrac{{{T_2}}}{{{T_4}}}$$
  • $$\dfrac{{{T_5}}}{{{T_7}}}$$
  • $$\dfrac{{{T_3}}}{{{T_7}}}$$
The smallest value of 0 satisfying the equation $$\sqrt { 3(cot0+\quad tan0)\quad =\quad 4 } $$ is 
  • $$2x/3$$
  • $$\pi /3$$
  • $$\pi /6$$
  • $$\pi /12$$
The number of real values of x such that  $$\left( {{2^{ - x}} + {2^x} - 2\cos x} \right)\;\left( {{3^{x + \pi }} + {3^{ - x - \pi }} + 2\cos x} \right)\left( {{5^{\pi  - x}} - 2\cos x + {5^{x - \pi }}} \right) = 0,is$$ 
  • 1
  • 2
  • 3
  • infinite
The number of solutions of the equation sin $$\left( \dfrac { \pi x }{ 2\sqrt { 3 }  }  \right) ={ x }^{ 2 }-2\sqrt { 3 } x+4$$ is
  • 0
  • 2
  • 1
  • none of these
Find the fix point through which the line $$(2cos\Theta +3sin\Theta )x+(3 cos\Theta-5sin\Theta  )y-(5cos\Theta -2sin\Theta )=0$$ passes for all values of $$\Theta $$-
  • (0,0)
  • (1,1)
  • (2,1)
  • None of these
The principal solutions of $$secx= \frac{2}{\sqrt{3}}$$   are _________
  • $$\frac{\pi }{3},\frac{||\pi }{6}$$
  • $$\frac{\pi }{6},\frac{11\pi }{6}$$
  • $$\frac{\pi }{4},\frac{||\pi }{4}$$
  • $$\frac{\pi }{6},\frac{||\pi }{4}$$
$$\dfrac { \tan\theta  }{ 1-\cot\theta  } +\dfrac { \cot\theta  }{ 1-\tan\theta  } $$ is equal to 
  • $$1+\tan\theta +\cot\theta $$
  • $$1-\tan\theta -\cot\theta $$
  • $$1+\tan\theta -\cot\theta $$
  • none of these
$$cos^{4}\Theta - sin^{4}\Theta $$ is equal 
  • $$\frac{1-tan^{2}\Theta }{1+ tan^{2}\Theta }$$
  • $$2 cos^{2}\Theta -1$$
  • $$1-2 sin^{2}\Theta $$
  • $$sin^{2}\Theta - cos^{2}\Theta $$
32 $$sin^{6}15^{0}-48sin^{4}15^{0}+18sin^{2}15^{0}=$$
  • 1
  • 2
  • 3
  • -1
Choose the correct answer.
$$(1+{ \tan }^{ 2 }\theta ){ \sin }^{ 2 }\theta =$$
  • $${ \tan }^{ 2 }\theta $$
  • $${ \cot }^{ 2 }\theta $$
  • $${ \sin }^{ 2 }\theta $$
  • $${ \cos }^{ 2 }\theta $$
The number of solutions of the equation $$\sin (9x) + \sin (3x) = 0$$ in the closed interval $$[0, 2\pi]$$ is 
  • $$7$$
  • $$13$$
  • $$19$$
  • $$25$$
If $$sec A=a+(\frac{1}{4a})$$ , then sec A + tan A is equal to 
  • $$2a \;or\; \frac{1}{2a}$$
  • $$a or \frac{1}{a}$$
  • $$2a or\frac{1}{a}$$
  • $$a or \frac{1}{2a}$$
If $$\displaystyle sin^{-1} x + sin ^{-1} y + sin^{-1} z = 3\pi / 2 $$ then the value of
$$ x^{100} + y ^{100} + z^{100} - \dfrac{3}{x^{101} + y^{101} + z^{101}} $$ is
  • $$ 0 $$
  • $$ 1 $$
  • $$ 2 $$
  • $$ 3 $$
Indicate the relation which is true 
  • $$ tan \left | tan^{-1} x \right | = \left | x \right | $$
  • $$ cot \left | cot^{-1}x \right | = x $$
  • $$ tan^{-1} \left | tan\,x \right | = \left | x \right | $$
  • $$ sin \left | sin^{-1} \right | = \left | x \right |$$
0:0:1


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