If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to

The area (in square unit) of the region enclosed by the curves $y=x^2$ and $y=x^3$ is

The efficiency of a Carnot engine is $50\%$ and the temperature of the sink is $500\,K$. If the temperature of the source is kept constant and its efficiency is raised to $60\%$,then the required temperature of the sink will be .... $K$.

Correct order of solubility is

Which one of the following plots is correct for a first order reaction?

Which two orbitals are located along the axis and not between the axis?