Question 1 :
If $\displaystyle \sin B=\frac{1}{2}$ what is the value of $\displaystyle 3\cos B-4\cos ^{3}B?$
Question 2 :
If range of $f(x)=\cos x, x\in \left(\dfrac {-\pi}{3}, \dfrac {\pi}{6}\right)$ is $(a,b)$, then
Question 5 :
The value of $\cot 15^{\circ} \cot 20^{\circ} \cot 70^{\circ} \cot 75^{\circ}$ is equal to
Question 6 :
Consider the following statements :<br>1. $1^o$ in radian measure is less than 0.02 radians.<br>2. 1 radian in degree measure is greater <span>than $45^o$ <br>Which of the above statements is/are <span>correct ?</span></span>
Question 9 :
Given that A is positive acute angle and $ { sin }^{ }A=\dfrac { \sqrt { 3 } -1 }{ 2 } ,$ then A take the value (s)-
Question 12 :
If $\sin\alpha+\sin\beta+\sin\gamma=0$ and $\cos\alpha +\cos\beta +\cos\gamma=0$, then value of $\cos (\alpha-\beta)+\cos(\beta-\gamma)+\cos(\gamma+\alpha)$ is
Question 13 :
Whether the given equation : $\frac{{\sin 2x}}{{2 \cos x}} = \tan x$ is ?
Question 14 :
$\tan^{-1}\left [ \dfrac{a\cos x - b\sin x}{b \cos x+ a \sin x}\right]$= $\tan^{-1}\left (\dfrac {a}{b}\right)-x$
Question 15 :
If $\cot (\alpha + \beta) = 0$, then $\sin (\alpha + 2\beta)$ is equal to
Question 16 :
The value of $\tan 67\dfrac {1}{2}^{\circ} + \cot 67\dfrac {1}{2}^{\circ}$ is.
Question 17 :
The equation $\sin { 2x } +\cos { 2x } +\sin { x } +\cos { x } +1=0$ has no solution in:
Question 18 :
The values of $\theta$ in the interval $\left(\dfrac{-\pi}{2}, \dfrac{\pi}{2}\right)$ satifying the equation $\left(\sqrt{3}\right)^{sec^2\theta} = \tan^4\theta + 2\tan^{6}2\theta$ is
Question 19 :
If $\displaystyle \cos { 2B } =\frac { \cos { \left( A+C \right) } }{ \cos { \left( A-C \right) } } $, then $\tan { A } ,\tan { B } ,\tan { C } $ are in
Question 20 :
$If\,\,\sin 5\theta = a{\sin ^5}\theta + b{\sin ^3}\theta + c\sin \theta \,\,then$<br>(A) $a - 2c = 5$<br>(B) $a - 2c = 6$<br>(C) $b + 3c = 5$<br>(D) $b + 3c = - 5$<br>The general solution of $\tan 3\theta \,\tan \theta = 1\,\,is\,\,given\left( {n \in I} \right)$
Question 21 :
If $\tan { A } $ and $\tan { B } $ are the roots of ${ x }^{ 2 }-2x-1=0$, then $\sin ^{ 2 }{ \left( A+B \right) } $ is
Question 24 :
Assertion: $sin \displaystyle \left ( \frac{\pi x}{2 \sqrt{3}} \right ) = x^2 - 2 \sqrt{3} x + 4$ has only one solution
Reason: The smallest positive value of x in degrees, for which $tan (x + 100^o) = tan (x + 50^o) tan x tan (x - 50^o) $ is $30^o$.
Question 27 :
Let $f\left( x \right) = \sqrt {\cot \left( {5 + 3x} \right)\left( {\cot \left( 5 \right) + \cot \left( {3x} \right)} \right) - \sqrt {\cot 3x} + 1} $, the domain is
Question 28 :
If $\dfrac {x}{\tan (\theta +\alpha)}=\dfrac {y}{\tan (\theta +\beta)}=\dfrac {z}{\tan (\theta +\gamma)}$, then find the value of $\left (\dfrac {x+y}{x-y}\right )\sin^{2}(\alpha -\beta)+\left (\dfrac {y+z}{y-z}\right )\sin^{2}(\beta -\gamma)+\left (\dfrac {z+x}{z-x}\right )\sin^{2}(\gamma -\alpha)=$<br/>
Question 30 :
If $\cos ^{ 2 }{ x } +\cos ^{ 2 }{ 2x } +\cos ^{ 2 }{ 3x } =1$, then -
Question 31 : Statement I: If $m\cos(\theta+\alpha)=n\cos(\theta-\alpha)$ then $\tan\theta.\tan\alpha= \displaystyle \frac{m+n}{m-n}$<br/>Statement II: If $\displaystyle \frac{\sin(\alpha+\beta)}{\sin(\alpha-\beta)}=\frac{a+b}{a-b}$ then $\tan\alpha.\cot\beta=\dfrac{a}{b}$. <div>Which of the above statements is correct?<br/></div>
Question 33 :
The value of $ sin\theta .cos\left ( 90^{\circ}-\theta \right )+ cos\theta .sin\left ( 90^{\circ}-\theta \right )$ is<br/>
Question 34 :
If $q$ is a real number , then which of the following is incorrect?
Question 35 :
if $\displaystyle x,y\epsilon \left [ 0,2\pi \right ]$ and $\displaystyle \sin x+\sin y=2$ then the value of $ x+y$ is<br>
Question 37 :
If $n=\dfrac{cos \alpha}{cos \beta},m=\dfrac{sin \alpha}{sin \beta},$ then $(m^2- n^2) sin^2 \beta$ is <br>
Question 38 :
If $0< x\leq \cfrac {\pi}{2}$, then $(\sin x+ \text{cosec} x)$ is greater than or equal to
Question 39 :
$\displaystyle \frac{1}{4} \left [ \sqrt{3} \cos 23^{\circ} - \sin 23^{\circ} \right ]$ is equal to<br>
Question 40 :
$\dfrac{{\cot x}}{{\cot x - \cot 3x}} + \dfrac{{\tan x}}{{\tan x - \tan 3x}} = $
Question 41 :
$ \tan x + \tan2x + \tan3x = 0$ then x =<br/>
Question 42 :
If a is any real number, the number of roots of $\cot x - \tan x = a$ in the first quardrant is<br/><br/>
Question 43 :
Assertion: The minimum value of the expression $\sin\alpha+\sin\beta+\sin\gamma$ where $\alpha, \beta, \gamma$ are real number such that $\alpha+\beta+\gamma=\pi$, is negative because-
Reason: $\alpha, \beta, \gamma$ are angles of a triangle.
Question 44 :
If $\displaystyle \alpha ,\beta ,\gamma$ and $\delta$ be four angles of cyclic quadrilateral then the value of $\displaystyle \cos \alpha +\cos \beta +\cos \gamma +\cos \delta$ is
Question 45 :
The sum of all the solutions of the equation $ \displaystyle \cos \theta \cos \left (\frac{\pi }{3}+\theta \right )\cos \left (\frac{\pi }{3}-\theta \right )=\frac{1}{4}, \theta \epsilon \left [ 0,6\pi \right ]$<br>
Question 46 :
<br/> If $\alpha, \beta$ are different values of $\mathrm{x}$ satisfying<br/>$\mathrm{a}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{x}+ b\sin x =\mathrm{c}$, Then $t\displaystyle \mathrm{an}(\frac{\alpha+\beta}{2})=$<br/>
Question 48 :
For Problems 1 - 3<br/>Consider the cubic equation<br/>$x^{3} - \left ( 1 + \cos \theta + \sin \theta \right )x^{2} + \left (\cos \theta\sin\theta + \cos \theta + \sin \theta \right )x - \sin \theta \cos \theta = 0$<br/>whose roots are $x_1, x_2$ and $x_3$.<br/>1. The value of $x^{2}_1 + x^{2}_2 + x^{2}_3$ equals
Question 49 :
Solve for $x, (- \pi \leq x \leq \pi)$, the equation $2 (cos x + cos 2x) + sin 2x (1 + 2 cos x) = 2 sin x$
Question 51 :
In a $\triangle ABC$, if $\cot A \cot B \cot C > 0$. then the $\triangle$ is
Question 52 :
Solution of the equation $\displaystyle \frac{1+\tan x+\tan ^{2}x+....+tan^{n}x+...}{1-\tan x+tan^{2}x-...+\left ( -1\right )^{n}\tan ^{n}x+...}=1+\sin 2x$ is
Question 53 :
The arithmetic mean of the roots of the equation<br>$4\cos ^{ 2 }{ x } -4\cos ^{ 2 }{ x } -\cos { (315\pi +x) } =1$ in the interval $(0,315)$ is
Question 54 :
The solution of the equation $\displaystyle <br>1+(\sin x-\cos x) \sin \frac{\pi}{4}=2 \cos ^{2}\frac{5x}{2}$ is / are
Question 55 :
Total number of solution of $sinx. tan4x = cosx$ belonging to (0, $\pi$) are
Question 57 :
Match the following.<br/>List - I List - II<br/><br/>1.$\cos 6^{\circ}\sin 24^{\circ} \cos 72^{\circ}$ a.$\dfrac {3}{16}$<br/><span><br/>2. $\cos 10^{\circ}\cos 30^{\circ} \cos 50^{\circ} \cos 70^{\circ}$ b.$\dfrac {1}{16}$<br/><span><br/>3.$\sin 2^{\circ} \sin 24^{\circ} \sin 48^{\circ}\sin 84^{\circ} $ c.$\dfrac {3}{16}$<br/><span><br/>4. $\displaystyle \sin 20^{\circ}\sin 40^{\circ}\sin 60^{\circ}\sin 80^{\circ}$ d.$\dfrac {1}{8}$<br/></span></span></span>
Question 58 :
In a triangle $ABC$, angle $A$ is greater than angle $B$. If the measures of angles $A$ and $B$ satisfy the equation $3 \sin {x} - 4 \sin^{3} x - k = 0, 0 < k < 1$, then the measure of angle $C$ is
Question 59 :
If the angles of a triangle are in arithmetic progression such that $\sin (2A + B) =\dfrac 12$, then
Question 60 :
The range of the following function $f(x) = {\cos ^2}{x \over 4} + \sin {x \over 4},x \in R$ is <br><br>
