$A$ tank is filled up to a height $h$ with a liquid and is placed on a platform of height $h$ from the ground. To get the maximum range $x_m$,a small hole is punched at a distance of $y$ from the free surface of the liquid. Then:

Assertion $(A)$: The aqueous solution of $CH_3COONa$ is alkaline in nature. Reason $(R)$: Acetate ion undergoes anionic hydrolysis. The correct answer is

The values of a function $f(x)$ at different values of $x$ are given in the table below:

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$f(x)$	$2$	$3$	$6$	$11$	$18$	$27$

Then,the approximate area (in square units) bounded by the curve $y=f(x)$ and the $x$-axis between $x=0$ and $x=5$,using the Trapezoidal rule,is

If $\int \frac{\sin x}{\cos x(1+\cos x)} d x=f(x)+c$,then $f(x)$ is equal to

Which group of organisms was the first to exist on Earth among the given options?

The following observations were taken for determining the surface tension $T$ of water by the capillary method:
Diameter of capillary,$D = 1.25 \times 10^{-2} \ m$
Rise of water,$h = 1.45 \times 10^{-2} \ m$
Using $g = 9.80 \ m/s^2$ and the simplified relation $T = \frac{rhg}{2} \times 10^3 \ N/m$,the possible error in surface tension is closest to ......... $\%$