If the difference between the roots of $x^2+ax+b=0$ and $x^2+bx+a=0$ is the same,and $a \neq b$,then:

In a hypothetical system,a particle of mass $m$ and charge $-3q$ is moving around a very heavy particle having charge $q$. Assuming Bohr's model to be true for this system,the orbital velocity of mass $m$ when it is in its ground state is:

$X$ is a non-volatile solute and $Y$ is a volatile solvent. The following vapour pressures are observed by dissolving $X$ in $Y$:
| $X / \text{mol L}^{-1}$ | $Y / \text{mm of Hg}$ |
| :--- | :--- |
| $0.10$ | $p_1$ |
| $0.25$ | $p_2$ |
| $0.01$ | $p_3$ |
The correct order of vapour pressures is:

$25 \ mL$ of $3.0 \ M \ HNO_3$ are mixed with $75 \ mL$ of $4.0 \ M \ HNO_3$. If the volumes are additive,the molarity of the final mixture would be $......... \ M$.

$\int (1+x-x^{-1}) e^{x+x^{-1}} dx$ is equal to :