Higher Math 2nd Paper MCQ-Sylhet Board-2023

1. $x^{2}+a x+(a+2)=0$ is a quadratic equation whose roots are $\frac{1}{\alpha}, \frac{1}{\beta}$.

What is the value of $\alpha+\beta$ ?

2. Which one is the value of $\operatorname{cosec}^{2}\left(\tan ^{-1} \frac{1}{2}\right)-\sec ^{2}\left(\cot ^{-1} \sqrt{3}\right) ?$

3. Which one is the parametric equation of the hyperbola $\frac{y^{2}}{25}-\frac{x^{2}}{16}=1$ ?

4. $x^{2}+5 y=0$ is a conic.

Which one is the coordinates of focus of the conic?

5. If $\sin ^{-1} \frac{2 a}{1+a^{2}}+\cot ^{-1} \frac{1-b^{2}}{2 b}=2 \tan ^{-1} x$, then what is the value of $x$?