The coefficient of $x$ in the equation $x^2 + px + q = 0$ was taken as $17$ in place of $13$. Its roots were found to be $-2$ and $-15$. The roots of the original equation are:

In a compound microscope,the focal lengths of two lenses are $1.5 \ cm$ and $6.25 \ cm$. An object is placed at $2 \ cm$ from the objective lens and the final image is formed at $25 \ cm$ from the eye lens. The distance between the two lenses is $.... \ cm$.

The atomic numbers of Vanadium $(V)$,Chromium $(Cr)$,Manganese $(Mn)$,and Iron $(Fe)$ are $23, 24, 25$,and $26$ respectively. Which of the following has the highest second ionization enthalpy?

In the following reaction,$A$ and $B$ respectively are:
$A$ $\xrightarrow{HBr} C_2H_5Br$ $\xrightarrow{B} A$

The values of $a$ and $b$,so that the function $f(x) = \begin{cases} x + a \sqrt{2} \sin x, & 0 \le x \le \frac{\pi}{4} \\ 2x \cot x + b, & \frac{\pi}{4} < x \le \frac{\pi}{2} \\ a \cos 2x - b \sin x, & \frac{\pi}{2} < x \le \pi \end{cases}$ is continuous for $0 \le x \le \pi$,are respectively:

The mean of a set of observations is $\bar{x}$. If each observation is divided by $\alpha$ $(\alpha \neq 0)$ and then increased by $10$,what is the mean of the new set?