The maximum and minimum values of the function $f: R \rightarrow R$ defined by $f(x)=5 \cos x+3 \cos \left(x+\frac{\pi}{3}\right)+8$ for all $x \in R$,are respectively

Each category of taxonomic hierarchy is referred to as a unit of . . . . . . .

Match the following columns correctly:

Column-$I$	Column-$II$
$A$. Tapetum	$i$. Degenerates during development
$B$. Intine	$ii$. Resistant organic material
$C$. Vegetative cell	$iii$. Pollen tube
$D$. Sporopollenin	$iv$. Provides nourishment to pollen grains

The adsorption isotherm for a gas is given by the relation $x = \frac{ap}{1 + bp}$,where $x$ is moles of gas adsorbed per gram of the adsorbent,$p$ is the pressure of the gas,and $a$ and $b$ are constants. Then $x$:

If $\int \frac{7x^8+8x^7}{(1+x+x^8)^2} dx = f(x) + c$,then $f(x)$ is equal to

$A$ parallel plate capacitor of capacity $C_0$ is charged to a potential $V_0$. $(i)$ The energy stored in the capacitor when the battery is disconnected and the plate separation is doubled is $E_1$. (ii) The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is $E_2$. Then,the value of $E_1 / E_2$ is: