Question 1 :
<br/>Given that $\sec\theta+\tan\theta=1$ then one root of the equation $(a-2b+c)x^{2}+(b-2c+a)x+(c-2a+b)= 0$ is<br/>

Question 3 :
The value of the expression $\displaystyle 1\, - \,\frac{{{{\sin }^2}y}}{{1\, + \cos \,y}}\, + \frac{{1\, + \cos \,y}}{{\sin \,y}}\, - \,\frac{{\sin \,y}}{{1\, - \cos \,y}}$ is equal to&#160;

Question 4 :
If $cosec \theta -\sin \theta =m$ and $\sec \theta -\cos \theta =n$, eliminate $\theta $.<br><br>

Question 5 :
If $ \cos^{-1}\left ( 4x^{3}-3x \right )= 2\pi -3\cos^{-1}x $, then $ x $ lies in interval

Question 6 :
If $5\cos { A } =4\sin { A } $, then $\tan { A=\_ \_ \_ } $

Question 7 :
If $\displaystyle \frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1,\frac{x}{a}\sin \theta-\frac{y}{b}\cos \theta=1,$ then eliminate $\theta $<br>

Question 8 :
What is $\left(\dfrac{sec 18^{\circ}}{sec 144^{\circ}} + \dfrac{cosec 18^{\circ}}{cosec 144^{\circ}}\right)$ equals to?

Question 9 :
If the angles of a triangle are in arithmetic progression such that $\sin (2A+B)=\dfrac{1}{2}$, then

Question 10 :
If $\sin x + \sin^{2}x=1,$ then the value of $\cos^{12} x + 3 \cos^{10} x + 3 cos^{8} x + cos ^{6} x -1$ is equal to :

Question 11 :
The value of the expression $(\tan1^{0} \tan2^{0} \tan 3^{0}...\tan89^{0})$ is equal to<br/>

Question 12 :
If $\sin (\alpha+\beta)=1$ and $\sin(\alpha -\beta)=1/2$ where $\alpha, \beta \epsilon [0, \pi /2]$ then

Question 13 :
If $a=\cos\alpha \cos\beta+\sin \alpha \sin\beta \cos\gamma$<br/>$b=\cos\alpha \sin \beta-\sin\alpha \cos\beta \cos\gamma$<br/>and $c=\sin \alpha \sin\gamma$, then $a^2+b^2+c^2$ is equal to

Question 14 :
If $\sin (\alpha+\beta)=1$ and $\sin(\alpha -\beta)=1/2$ where $\alpha, \beta \epsilon [0, \pi /2]$ then

Question 15 :
The value of&#160;$\displaystyle \frac { \sin { { 70 }^{ o } } &#160;}{ \cos { { 20 }^{ o } } &#160;} +\frac { \text{cosec }{ 20 }^{ o } }{ \sec { { 70 }^{ o } } &#160;} -2\cos { { 70 }^{ o } } \text{cosec }{ 20 }^{ o }$ is :

Question 17 :
A person on the top of tower observes scooter moving with uniform velocity towards the base of the tower he finds that the angle of depression changes from$\displaystyle 30^{\circ}$ to$\displaystyle 60^{\circ}$ in 18 minutes The Scooter will reach the base of the tower in next

Question 18 :
In $\triangle ABC$, the measure of $\angle B$ is $90^{\circ}, BC = 16$, and $AC = 20$. $\triangle DEF$ is similar to $\triangle ABC$, where vertices $D, E,$ and $F$ correspond to vertices. $A, B$, and $C$, respectively, and each side of $\triangle DEF$ is $\dfrac {1}{3}$ the length of the corresponding side of $\triangle ABC$. What is the value of $\sin F$?

Question 19 :
The number of ordered pairs $(\alpha, \beta)$, where $\alpha, \beta $ $\in$ $(-\pi, \pi)$ satisfying $\cos(\alpha -\beta)=1$ and $\cos(\alpha+\beta)=\dfrac {1}{e}$ is

Question 20 :
If $x_{1}=1$ and $x_{n+1}=\frac{1}{x_{n}}\left ( \sqrt{1+x_{n}^{2}}-1 \right ),n\geq 1,n \in N$, then $x_{n}$ is equal to :<br>