$A$ motor-car tyre has a pressure of $2\, atm$ at $27\,^{\circ}C$. It suddenly bursts. If $\gamma = \frac{C_p}{C_v} = 1.4$ for air,find the resulting temperature. (Given $4^{1/7} = 1.219$)

Match the organism with its use in biotechnology.

$(a)$ Bacillus thuringiensis	$(i)$ Cloning vector
$(b)$ Thermus aquaticus	$(ii)$ Construction of first $rDNA$ molecule
$(c)$ Agrobacterium tumefaciens	$(iii)$ $DNA$ polymerase
$(d)$ Salmonella typhimurium	$(iv)$ Cry proteins

Select the correct option from the following:

Which one of the following is correct about the stability of the given ions?

If the half-life of a reaction is halved when the initial concentration of the reactant is doubled,what is the order of the reaction?

The ratio of minimum wavelengths of Lyman and Balmer series will be

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10 \, cm^2$ and length $\ell = 20 \, cm$. If one of the solenoids has $N_1 = 300$ turns and the other has $N_2 = 400$ turns,their mutual inductance is (given $\mu_0 = 4\pi \times 10^{-7} \, T \cdot m \cdot A^{-1}$):