The reaction of propane with bromine in the presence of $UV$ light predominantly forms

$1+\frac{1+2}{2 !}+\frac{1+2+2^2}{3 !}+\ldots$ is equal to

If $z$ and $\omega$ are two non-zero complex numbers such that $|z\omega| = 1$ and $\text{arg}(z) - \text{arg}(\omega) = \frac{\pi}{2}$,then $\bar{z}\omega$ is equal to

The value of $\lambda$ such that $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$ represents a pair of straight lines is:

The equation of the plane passing through $(1, 1, 1)$ and $(1, -1, -1)$ and perpendicular to $2x - y + z + 5 = 0$ is

In a cyclic process,the work done by the system is