If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$ and the equation having roots $\frac{1-\alpha}{\alpha}$ and $\frac{1-\beta}{\beta}$ is $px^2+qx+r=0$,then $r=$

Assertion : $\text{Trans-}2\text{-butene}$ on reaction with $Br_2$ gives $\text{meso-}2,3\text{-dibromobutane}$.
Reason : The reaction involves $\text{syn-addition}$ of bromine.

If the roots of $x^3-42 x^2+336 x-512=0$ are in increasing geometric progression,then its common ratio is (in $: 1$)

Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that each makes a complete circle in the same time $t$. The ratio of the angular speeds of the first to the second car is

$A$ six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once is:

$3.65 \ g$ of $HCl$ is dissolved in $16.2 \ g$ of water. The mole fraction of $HCl$ in the resulting solution is