CBSE Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 13 - MCQExams.com

The general solution of the equation $$\displaystyle sin\theta = \frac{1}{\sqrt2}$$ is
  • $$\displaystyle \theta = n\pi + \frac{\pi}{4}, n \in l$$
  • $$\displaystyle \theta = 2 n\pi + \frac{\pi}{4}, n \in l$$
  • $$\displaystyle \theta = n\pi + (-1)^n \frac{\pi}{4}, n \in l$$
  • none of these.
The general solution of the equation $$\displaystyle sin^2\theta = sin^2\alpha$$ is
  • $$\displaystyle \theta = n\pi + \alpha \in l$$
  • $$\displaystyle \theta = n\pi \pm \alpha, n \in l$$
  • $$\displaystyle \theta = 2n\pi + \alpha, n \in l$$
  • $$\displaystyle \theta = 2n\pi \pm \alpha, n \in l$$
The general solution of the equation $$\displaystyle tan^2\theta = tan^2\alpha$$ is
  • $$\displaystyle \theta = n\pi + \alpha \in l$$
  • $$\displaystyle \theta = 2n\pi + \alpha, n \in l$$
  • $$\displaystyle \theta = n\pi \pm \alpha, n \in l$$
  • $$\displaystyle \theta = 2n\pi \pm \alpha, n \in l$$
The general solution of the equation $$\displaystyle tan\theta = \frac{1}{\sqrt3}$$ is
  • $$\displaystyle \theta = n\pi + \frac{\pi}{6}, n \in I$$
  • $$\displaystyle \theta = 2 n\pi + \frac{\pi}{6}, n \in I$$
  • $$\displaystyle \theta = 2 n\pi \pm \frac{\pi}{6}, n \in I$$
  • none of these.
The general solution of the equation $$\displaystyle tan \theta = tan \alpha$$ is
  • $$\displaystyle \theta = n\pi + \alpha \in l$$
  • $$\displaystyle \theta = 2n\pi + \alpha, n \in l$$
  • $$\displaystyle \theta = 2n\pi \pm \alpha, n \in l$$
  • $$\displaystyle \theta = 2n\pi \pm \alpha, n \in l$$
The general solution of the equation $$\displaystyle cos^2\theta = cos^2\alpha$$ is
  • $$\displaystyle \theta = n\pi + \alpha \in l$$
  • $$\displaystyle \theta = 2n\pi + \alpha, n \in l$$
  • $$\displaystyle \theta = n\pi \pm \alpha, n \in l$$
  • $$\displaystyle \theta = 2n\pi \pm \alpha, n \in l$$
The general solution of the equation $$\displaystyle sin\theta = \frac{-\sqrt3}{2}$$ is
  • $$\displaystyle \theta = n\pi + \frac{4\pi}{3}, n \in I$$
  • $$\displaystyle \theta = 2 n\pi + \frac{4\pi}{3}, n \in I$$
  • $$\displaystyle \theta = n\pi + (-1)^n \frac{4\pi}{3}, n \in I$$
  • none of these.
The angles of a triangle are in $$\displaystyle AP$$ and the ratio of the number of degrees in the least to the number of radius in the greatest is $$\displaystyle 60 : \pi$$. The smallest angle is
  • $$\displaystyle 15^0$$
  • $$\displaystyle 30^0$$
  • $$\displaystyle 45^0$$
  • $$\displaystyle 60^0$$
The general solution of the equation $$\displaystyle cos\theta = \frac{1}{2}$$ is
  • $$\displaystyle \theta = n\pi + \frac{\pi}{3}, n \in I$$
  • $$\displaystyle \theta = 2 n\pi + \frac{\pi}{3}, n \in I$$
  • $$\displaystyle \theta = 2 n\pi \pm \frac{\pi}{3}, n \in I$$
  • none of these.
The general solution of the equation $$\displaystyle cos \theta = cos \alpha$$ is
  • $$\displaystyle \theta = \alpha$$
  • $$\displaystyle \theta = n\pi \pm \alpha, n \in l$$
  • $$\displaystyle \theta = 2n\pi \pm \alpha, n \in l$$
  • none of these
The general solution of the equation $$\displaystyle cosec \theta + \sqrt2 = 0$$ is
  • $$\displaystyle \theta = n\pi + \frac{5\pi}{4}, n \in I$$
  • $$\displaystyle \theta = n\pi - \frac{5\pi}{4}, n \in I$$
  • $$\displaystyle \theta = n\pi + (-1)^n \frac{5\pi}{4}, n \in I$$
  • none of these.
The general solution of the equation $$\displaystyle 4 sin^2\theta = 1$$ is
  • $$\displaystyle \theta = n\pi \pm \frac{\pi}{6}, n \in I$$
  • $$\displaystyle \theta = 2n\pi \pm \frac{\pi}{6}, n \in I$$
  • $$\displaystyle \theta = \frac{n\pi}{4} + \frac{\pi}{24}, n \in I$$
  • none of these.
The general solution of the equation $$\displaystyle cot \theta = -\sqrt3$$ is
  • $$\displaystyle \theta = n\pi +\frac{5\pi}{6}, n \in l$$
  • $$\displaystyle \theta = 2 n\pi + \frac{5\pi}{6}, n \in l$$
  • $$\displaystyle \theta = n\pi + \frac{2\pi}{3}, n \in l$$
  • none of these.
The general solution of the equation $$\displaystyle sin 2\theta = \frac{-1}{2}$$ is
  • $$\displaystyle \theta = \frac{n\pi}{4} + \frac{\pi}{24}, n \in I$$
  • $$\displaystyle \frac{n\pi}{2} + (-1)^n \frac{7\pi}{12}, n \in N$$
  • $$\displaystyle \theta = \frac{n\pi}{4} \pm \frac{\pi}{24}, n \in I$$
  • none of these.
The general solution of the equation $$\displaystyle 2 cos^2\theta = 1$$ is
  • $$\displaystyle \theta = 2n\pi \pm \frac{\pi}{4}, n \in I$$
  • $$\displaystyle \theta = \frac{n\pi}{2} + \frac{\pi}{8}, n \in I$$
  • $$\displaystyle \theta = n\pi \pm \frac{\pi}{4}, n \in I$$
  • none of these.
The general solution of the equation $$\displaystyle cot^2\theta = 3$$ is
  • $$\displaystyle \theta = n\pi + \frac{\pi}{6},n \in I$$
  • $$\displaystyle \theta = n\pi \pm \frac{\pi}{6},n \in I$$
  • $$\displaystyle \theta = 2n\pi + \frac{\pi}{6},n \in I$$
  • none of these.
The general solution of the equation $$\displaystyle cos\theta = \frac{-1}{2}$$ is
  • $$\displaystyle \theta = n\pi \pm \frac{2\pi}{3}, n \in I$$
  • $$\displaystyle \theta = 2 n\pi + \frac{\pi}{3}, n \in I$$
  • $$\displaystyle \theta = 2 n\pi \pm \frac{2\pi}{3}, n \in I$$
  • none of these.
If $$ x + 1 / x = 2 $$ , the principal value of $$ sin^{-1}x $$ is 
  • $$ \pi / 4 $$
  • $$ \pi / 2 $$
  • $$ \pi $$
  • $$ 3\pi / 2 $$
If $$ x_{1} $$ and $$ x_{2} $$ are two distinct roots of the equation $$ a \cos x+b \sin x=c, $$ then $$ \tan \dfrac{x_{1}+x_{2}}{2} $$ is equal to
  • $$ \dfrac{a}{b} $$
  • $$ \dfrac{b}{a} $$
  • $$ \dfrac{c}{a} $$
  • $$ \dfrac{a}{c} $$
If $$ \operatorname{cosec} \theta-\cot \theta=q $$, then the value of $$ \operatorname{cosec} \theta $$ is
  • $$ q+\dfrac{1}{q} $$
  • $$ q-\dfrac{1}{q} $$
  • $$ \dfrac{1}{2}\left(q+\dfrac{1}{q}\right) $$
  • none of these
The principal value of 
     $$ cos^{-1} \left (cos\dfrac{2\pi}{3} \right ) + sin^{-1} \left (sin\dfrac{2\pi}{3} \right ) $$ is
  • $$ \pi $$
  • $$ \pi/2 $$
  • $$ \pi/3 $$
  • $$ 4\pi/3 $$
Evaluate : $$ tan \left [ 2\, tan^{-1}\dfrac{1}{5} - \dfrac{\pi}{4} \right ] $$
  • $$ \dfrac{5}{4} $$
  • $$ \dfrac{5}{16} $$
  • $$- \dfrac{7}{17} $$
  • $$ \dfrac{7}{17} $$
The value of $$ \dfrac{5}{16} $$ right angles in sexagesimal system is equal to 
  • $$28^{\circ} 30' 7'' $$
  • $$ 27^{\circ} 5' 26'' $$
  • $$ 28^{\circ} 7' 30'' $$
  • $$ 29^{\circ} 3' 27'' $$
The value of $$ \dfrac{3 \pi}{4} $$ in sexagesimal system is:
  • $$ 75^{\circ} $$
  • $$ 135^{\circ} $$
  • $$ 120^{\circ} $$
  • $$ 220^{\circ} $$
1 radian is equal to:
  • $$180^{\circ} $$
  • $$200^{\circ}$$
  • $$100^{\circ}$$
  • None of these
Let $$f(X)=\sin (\pi\cos x) $$ and $$ g(x) =\cos (2\pi\sin x)$$ be two function defined for $$x>0$$. Define the following sets whose elements are written in increasing order
$$X=\{x:f(x)=0\},Y=\{x:f'(x)=0\}$$
$$Z=\{x:g(x)=0\},W=\{x:g'(x)=0$$
List I contains sets $$X,Y,Z$$ and $$W$$ List II contains some information regarding these set.
Which of the following is the only correct combination ?
 Sr.NoList I  Sr.No List II 
 (I)(P) $$\supseteq\left\{\dfrac{\pi}{2},\dfrac{3\pi}{2},4\pi,7\pi\right\}$$
 (II)
(Q)
 an arithmetic progression
  (III)(R)
 NOT an arithmetic progression
  (IV) W(S)
 $$\supseteq \left\{\dfrac{\pi}{6},\dfrac{7\pi}{6},\dfrac{13\pi}{6}\right\}$$
  (T)
 $$\supseteq \left\{\dfrac{\pi}{3},\dfrac{2\pi}{3},\pi\right\}$$
  (U)
 $$\supseteq \left\{\dfrac{\pi}{6},\dfrac{3\pi}{4}\right\}$$

  • (I) (P) (R)
  • (II) (Q) (T)
  • (I) (Q) (U)
  • (II) (R) (S)
How many right angles is equal to $$56^{\circ} 15' $$ ?
  • $$ \dfrac{8}{5} $$ right angles
  • $$ \dfrac{5}{8} $$ right angles
  • $$ \dfrac{3}{5} $$ right angles
  • $$ \dfrac{5}{4} $$ right angles
The number of solution of $$|\tan x |= \ tanx + \displaystyle \dfrac{1}{\cos x}$$ in $$[0,2\pi]$$ is 
  • $$4$$
  • $$1$$
  • $$2$$
  • $$6$$
A solution $$(\mathrm{x},\mathrm{y})$$ of $$\mathrm{x}^{2}+2\mathrm{x}$$ $$\sin(xy)+1=0$$ is
  • $$(1, 0)$$
  • $$(1, \dfrac{7\pi}2)$$
  • $$(-1,\dfrac{7\pi}2)$$
  • $$(-1,0)$$
The number of solution of the equation $$|\cot x|= cotx +\displaystyle \frac{1}{sin x}$$ in $$[0,2\pi]$$ is 
  • $$2$$
  • $$4$$
  • $$0$$
  • $$1$$
0:0:1


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