$A$ random variate $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X=3) = 2 P(X=1)$ and $P(X=2) = 0.3$, then $P(X=0)$ is equal to:

If the line $x+3y=0$ is the tangent at $(0,0)$ to the circle of radius $1$,then the centre of one such circle is

The solubility of silver bromide in hypo solution is due to the formation of:

$A$ particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$. Then,its time period of vibration will be

If $\frac{1}{2} \leq x \leq 1$,then $\cos ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{1}{2} \sqrt{3-3 x^2}\right)$ is equal to

Regarding the molecular orbital $(MO)$ energy levels for homonuclear diatomic molecules, the $\text{INCORRECT}$ statement$(s)$ is$($are$)$
$(A)$ Bond order of $Ne _2$ is zero.
$(B)$ The highest occupied molecular orbital $\text{(HOMO)}$ of $F_2$ is $\sigma$-type.
$(C)$ Bond energy of $O _2^{+}$is smaller than the bond energy of $O _2$.
$(D)$ Bond length of $Li _2$ is larger than the bond length of $B _2$