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

The condition for the coaxial system $x^2+y^2+2\lambda x+c=0$,where $\lambda$ is a parameter and $c$ is a constant,to have distinct limiting points,is

$\sum_{k=1}^{\infty} \frac{1}{k!}\left(\sum_{n=1}^k 2^{n-1}\right)$ is equal to

The rate constant of a first order reaction at $27^{\circ} C$ is $10^{-3} \ min^{-1}$. The temperature coefficient of this reaction is $2$. What is the rate constant (in $min^{-1}$) at $17^{\circ} C$ for this reaction?

$A$ neutron moving with velocity $u$ collides elastically with an atom of mass number $A$. If the collision is head-on and the initial kinetic energy of the neutron is $E$,then the final kinetic energy of the neutron after the collision is

The lines $2x + 3y = 6$ and $2x + 3y = 8$ cut the $X$-axis at $A$ and $B$,respectively. $A$ line $L$ drawn through the point $(2, 2)$ meets the $X$-axis at $C$ in such a way that the abscissae of $A, B,$ and $C$ are in arithmetic progression. Then,the equation of the line $L$ is