Question 4 :
In an isosceles triangle $ABC,AB=AC.$ If vertical angle $A$ is ${20}^{0},$ then ${a}^{3}+{b}^{3}$ is equal to
Question 5 :
<b>If</b> $A=\left\{ x\epsilon R/\frac { \pi }{ 4 } \le x\le \frac { \pi }{ 3 } \right\} \quad$<b>and </b>$f(x)=\sin { x } -x\quad$, <b>then </b>$f(A)=$
Question 6 :
$\tan \left( {45^\circ + \theta } \right) \cdot \tan \left( {45^\circ - \theta } \right)$
Question 7 :
If $\sin {\alpha}+\sin {\beta} = a, \cos {\alpha} + \cos {\beta} = b$, then $\cos {(\alpha+\beta)}$ is equal to<br/>
Question 8 :
$\tan \alpha + 2\tan 2\alpha + 4\tan 4\alpha + 8\cot 8\alpha $ is equal to :
Question 12 :
The general solution of the equation $\displaystyle \sum _{ r=1 }^{ n }{ \cos { { r }^{ 2 }\theta } \sin { r\theta } } =\frac { 1 }{ 2 } $ is
Question 16 :
The value of $\displaystyle \left( \text{cosec}\theta -\sin { \theta } \right) \left( \sec{ \theta }-\cos { \theta } \right) \left( \tan { \theta } +\cot { \theta } \right) $ is
Question 17 :
In $\triangle ABC$, if $a$ tends to $2c$ and $b$ tends to $3c$, then $\cos B$ tends to :
Question 18 : <div>In $\Delta$ $ABC$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively.<br/></div>If $\displaystyle \cos A+\sin A-\frac{2}{\cos B+\sin B}= 0,$ then the value of $\displaystyle \left ( \frac{a+b}{c} \right )^{4}$ is?
Question 19 :
Determine range $\displaystyle y= 3\sin x+4\cos \left ( x+\pi /3 \right )+7$
Question 20 :
If $\cos A = 3 / 4$ then the value of $16 \cos ^ { 2 } ( A / 2 ) - 32 \sin ( A / 2 ) \sin ( 5 A / 2 )$ is
Question 21 :
If $\displaystyle \frac{\cos(A+B)}{\cos(A-B)}+\frac{\cos(C-D)}{\cos(C+D)}=0$, then $\cot A\ cot B\cot C\, cot D$ is equal to
Question 22 :
lf $(a+b)^{2}=c^{2}+$ ab in $a\Delta ABC$ and if $\sqrt{2}(\sin A+\cos A)=\sqrt{3}$ then ascending order of angles $A,\ B,\ C$ is?<br/>
Question 23 :
If two adjacent sides of a parallelogram each of whose angles is 90$^{\circ}$ be of magnitudes $\sqrt{cos \theta}$ and $\sqrt{sin \theta}$, then the maximum value of the square of its diagonal for all values of $\theta$ is -<br>
Question 24 :
Let $S$ be the set of all $\alpha \epsilon R$ such that the equation, $\cos 2x + \alpha \sin x = 2\alpha - 7$ has a solution. Then $S$ is equal to:
Question 25 :
Assertion: Statement 1: $\displaystyle \tan 5^{\circ}$is an irrational number.
Reason: Statement 2: $\displaystyle \tan 15^{\circ}$ is an irrational number
Question 28 :
If $\alpha +\beta =\dfrac { 5\pi }{ 4 } $, then value of $\dfrac { \cot { \alpha } \cdot\cot { \beta } }{ \left( 1+\cot { \alpha } \right) \left( 1+\cot { \beta } \right) }$ is (wherever defined)-
Question 29 :
The value of $ \cos 2(\theta+\phi)+4 \cos (\theta+\phi) \sin \theta \sin \phi+2 \sin ^{2} \phi $ is
Question 33 : <div>In $\Delta$ $ABC$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively.<br/></div>If $\displaystyle a^{2},b^{2},c^{2}$ are in A.P., then which of the following is correct?<br/>
Question 34 :
$1)$ Principal value of $\cos\theta=-1$ is $\pi$<br/>$2)$ Principal value of $\sin\theta=0$ is $\pi$<br/>Which of the above statement is correct?<br/>
Question 35 : In $\Delta$ $ABC$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively.<div>If $ \left ( \sin A+\sin B+\sin C \right )\left ( \sin A+\sin C-\sin B \right )=\mu \sin A\:\sin C $, </div><div>where $ \sin A= ak,\:\sin B= bk,\:\sin C= ck $</div><br/><div>then the range of $ \mu $ is</div>
Question 36 :
If the angles of a triangle are in the ratio $4:1:1,$ then the ratio of the longest side to the perimeter is
Question 37 :
$ln$ a triangle $ABC,\ \displaystyle \angle B=\frac{\pi}{3},\angle C=\frac{\pi}{4}$ and $D$ divides $BC$ internally in the ratio 1:3. Then $\displaystyle \frac{\sin\angle BAD}{\sin\angle CAD}$ is equal to:<br/>
Question 39 :
<br>$A$ balloon is observed simultaneously from three points $A,\ B,\ C$ due west of it on a horizontal line passing directly underneath it. lf the angular elevations at $B$ and $C$ are respectively twice and thrice that at$A$and if $AB=220$ metres and $BC=100$ metres, then the height of the balloon from the ground is<br>
Question 40 :
If the angles of a triangle are in the ratio $4 : 1 : 1,$ then the ratio of the longest side to the perimeter is<br><br>
Question 42 :
If $\cos x+\cos y+\cos \alpha =0$ and $\sin x +\sin y +\sin \alpha =0$, then $\cot\left(\displaystyle\frac{x+y}{2}\right)=$.
Question 43 :
${\sec ^2}\theta = \dfrac{{4xy}}{{{{\left( {x - y} \right)}^2}}},\;Where\;x \in R,y \in R$ is true if and only if.
Question 44 :
If $ \theta$ is any angle, then $sec^4 \theta - sec^2 \theta$ is equal to<br>
Question 45 :
lf $p=\tan 8A, q=\tan 5A, r=\tan 3A$, then $ \displaystyle \frac{ p-q-r}{ pqr}=$<br>
Question 46 :
If ABC is a triangle in which $B = 45^o, C = 120^o$ and $a = 40$, the length of the perpendicular from A on BC produced is
Question 47 :
Find all values of $\theta$ in the interval $(-\pi/2, \pi/2)$ satisfying the equation $(1 - tan \theta) (1 + tan \theta) sec^2 \theta + 2 ^{tan^2 \theta} = 0$
Question 48 :
Find the value of <br/>$\quad \left(\displaystyle\frac{\cos^3\theta - \sin^3\theta}{\cos\theta - \sin\theta}\right)-\left(\displaystyle\frac{\cos^3\theta+\sin^3\theta}{\cos\theta+\sin\theta}\right) $
Question 49 :
The number of solutions of the equation $\dfrac{\sec x}{1-\cos x}=\dfrac{1}{1-\cos x}$ in $[0, 2\pi]$ is equal to?
Question 50 :
In $\triangle PQR$, $\dfrac { PQ }{ 1 } =\dfrac { PR }{ 2 } =\dfrac { QR }{ \sqrt { 3 } } $, then $m\angle R(in \ degrees)=....... .$
