Two wires $A$ and $B$ are of the same material. Their lengths are in the ratio $1:2$ and their diameters are in the ratio $2:1$. When stretched by forces $F_A$ and $F_B$ respectively,they experience an equal increase in their lengths. Then the ratio $F_A/F_B$ is:

If $p \rightarrow (\sim p \vee q)$ is false,then the truth values of $p$ and $q$ are,respectively

In the $Hoop$ process for the refining of $Al$,the molten materials form three different layers and remain separate during electrolysis because ..........

Let $f(x)$ be a non-negative continuous function such that the area bounded by the curve $y = f(x)$,$x$-axis and the ordinates $x = \frac{\pi}{4}$ and $x = \beta > \frac{\pi}{4}$ is $\left( \beta \sin \beta + \frac{\pi}{4} \cos \beta + \sqrt{2} \beta \right)$. Then $f\left( \frac{\pi}{2} \right)$ is

$A$ real value of $x$ will satisfy the equation $\left( \frac{3 - 4ix}{3 + 4ix} \right) = \alpha - i\beta$ (where $\alpha, \beta$ are real),if

$A$ bag contains $5$ black balls,$4$ white balls,and $3$ red balls. If a ball is selected at random,the probability that it is a black or red ball is