If the function $f$ defined by $f(x) = K(x - x^2)$ for $0 < x < 1$ and $f(x) = 0$ otherwise,is the probability density function (p.d.f.) of a random variable $X$,then the value of $P(X < \frac{1}{2})$ is

The height of the cone of maximum volume inscribed in a sphere of radius $R$ is

Fraunhofer lines are produced by the absorption of light in

$A$ $100 \ mL$ solution of $0.1 \ N$ $HCl$ was titrated with $0.2 \ N$ $NaOH$ solution. The titration was discontinued after adding $30 \ mL$ of $NaOH$ solution. The remaining titration was completed by adding $0.25 \ N$ $KOH$ solution. The volume of $KOH$ required for completing the titration is $............ \ mL$.

Which of the following is basic in nature?

The expression $[(p \wedge \sim q) \vee q] \vee (\sim p \wedge q)$ is equivalent to