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

Find out the value of $K_C$ for the following reaction from the value of $K_P$
$2NOCl_{(g)} \rightleftharpoons 2NO_{(g)} + Cl_{2(g)}$
[Given : $K_P = 8 \times 10^{12} \ atm$ at $500 \ K$ use $R = 0.08 \ L \ atm \ mol^{-1} \ K^{-1}$ ]

The lines represented by the equation $3x^2 + 8xy - 3y^2 + 2x - 4y - 1 = 0$ and the line $4x - 3y - 2 = 0$:

$A$ rifle of $20 ~kg$ mass can fire $4$ bullets per second. The mass of each bullet is $35 \times 10^{-3} ~kg$ and its final velocity is $400 ~ms^{-1}$. What force must be applied on the rifle so that it does not move backwards while firing the bullets (in $~N$)?

An inductor $(L = 0.03 \ H)$ and a resistor $(R = 0.15 \ k\Omega)$ are connected in series to a battery of $15 \ V$ $EMF$ in a circuit as shown below. The key $K_1$ has been kept closed for a long time. Then at $t = 0$,$K_1$ is opened and key $K_2$ is closed simultaneously. At $t = 1 \ ms$,the current in the circuit will be ....... $mA$ $(e^5 \cong 150)$.

The solution of $\frac{dy}{dx} + y = e^x$ is