In the circuit shown in the figure,the power dissipated as heat in the $6\,\Omega$ resistor is $6\,W$. What is the value of resistance $R$ in the circuit? $\Omega$

The ratio of the areas bounded by the curves $y = \cos x$ and $y = \cos 2x$ between $x = 0,$ $x = \pi /3$ and the $x$-axis is:

Which of the following ions can cause coagulation of proteins?

Justify that the following reactions are redox reactions:
$a$. $CuO_{(s)} + H_{2(g)} \rightarrow Cu_{(s)} + H_2O_{(g)}$
$b$. $Fe_2O_{3(s)} + 3CO_{(g)} \rightarrow 2Fe_{(s)} + 3CO_{2(g)}$
$c$. $4BCl_{3(g)} + 3LiAlH_{4(s)} \rightarrow 2B_2H_{6(g)} + 3LiCl_{(s)} + 3AlCl_{3(s)}$
$d$. $2K_{(s)} + F_{2(g)} \rightarrow 2K^{+}F^{-}_{(s)}$
$e$. $4NH_{3(g)} + 5O_{2(g)} \rightarrow 4NO_{(g)} + 6H_2O_{(g)}$

The value of $\cos^{-1}\left(\cos\frac{5\pi}{3}\right) + \sin^{-1}\left(\cos\frac{5\pi}{3}\right)$ is

The half-life period of a first-order chemical reaction is $6.93 \ min$. The time required for $99\%$ completion of the reaction is ........ minutes. $(\log 2 = 0.301)$