In recombinant $DNA$ technique,the term vector refers to

Two wires $A$ and $B$ are of lengths $40 \ cm$ and $30 \ cm$. $A$ is bent into a circle of radius $r$ and $B$ into an arc of radius $r$. $A$ current $i_1$ is passed through $A$ and $i_2$ through $B$. To have the same magnetic inductions at the centre,the ratio of $i_1: i_2$ is

It takes $10$ minutes to cool a liquid from $61^oC$ to $59^oC$. If room temperature is $30^oC$,then the time taken in cooling from $51^oC$ to $49^oC$ is ....... $\min$.

$Fe$ is made passive by

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:

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