The order of the differential equation of the family of all concentric circles centered at $(h, k)$ is

Select the incorrect statement from the following.

If the coefficients $a$ and $b$ of a quadratic expression $x^2+ax+b$ are chosen from the sets $A=\{3,4,5\}$ and $B=\{1,2,3,4\}$ respectively, then the probability that the equation $x^2+ax+b=0$ has real roots is

For all values of $\theta$,the values of $3-\cos \theta+\cos \left(\theta+\frac{\pi}{3}\right)$ lie in the interval :

The characteristics of a molecular probe are:
$I$. Very long molecule
$II$. Double-stranded
$III$. $DNA$ or $RNA$
$IV$. Complementary to a part of desired gene
The correct pair is:

Two small drops of mercury,each of radius $R$,coalesce to form a single large drop. The ratio of the total surface energies before and after the change is