An ideal transformer has $500$ and $5000$ turns in primary and secondary windings respectively. If the primary voltage is connected to a $6\,V$ battery, then the secondary voltage is.......$V$.

Modern cereal $Triticale$ is developed by crossing between

If $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$ and $|\overrightarrow{a}|=3, |\overrightarrow{b}|=4$ and $|\overrightarrow{c}|=\sqrt{37}$,then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is:

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 $T.V.$ transmission tower in Delhi has a height of $245 \ m$. The distance up to which the broadcast can be received (taking the radius of earth to be $6.4 \times 10^6 \ m$) is........$km$ :

What is $X$ in the following reaction?
$2 CH_3COCH_3 \stackrel{Ba(OH)_2}{\longrightarrow} X$