If $\cos (\alpha+\beta)=\frac{4}{5}$,$\sin (\alpha-\beta)=\frac{5}{13}$ and $\alpha, \beta$ are between $0$ and $\frac{\pi}{4}$,then $\tan 2\alpha$ is equal to

The chemical formula of feldspar is

Which group includes microorganisms that lack a defined nucleus but contain genetic material (nucleoid)?

$A$ circle passes through the point $(3, 4)$ and cuts the circle $x^2 + y^2 = a^2$ orthogonally. The locus of its centre is a straight line. If the distance of this straight line from the origin is $25$,then $a^2$ is equal to

The logical statement $(\sim(\sim p \vee q) \vee(p \wedge r)) \wedge(\sim q \wedge r)$ is equivalent to

In a $500 \ mL$ flask,the degree of dissociation of $PCl_5$ at equilibrium is $40 \%$ and the initial amount is $5 \ moles$. The value of equilibrium constant in $mol \ L^{-1}$ for the decomposition of $PCl_5$ is