An object is projected with a velocity of $20 \ m/s$ making an angle of $45^{\circ}$ with the horizontal. The equation for the trajectory is $h = Ax - Bx^2$,where $h$ is the height,$x$ is the horizontal distance,and $A$ and $B$ are constants. The ratio $A:B$ is $(g = 10 \ m/s^2)$.

Match the corresponding entries of Column-$I$ with Column-$II$. [Where $m$ is the magnification produced by the mirror]

Column-$I$	Column-$II$
$1. m = -2$	$a$. Convex mirror
$2. m = -\frac{1}{2}$	$b$. Concave mirror
$3. m = +2$	$c$. Real Image
$4. m = +\frac{1}{2}$	$d$. Virtual image

$\int \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right) d x$ is equal to

$\cos 36^{\circ} - \cos 72^{\circ}$ is equal to

An infinite number of electric charges each equal to $5 \text{ nC}$ (magnitude) are placed along the $X$-axis at $x=1 \text{ cm}, x=2 \text{ cm}, x=4 \text{ cm}, x=8 \text{ cm} \dots$ and so on. In this setup, if the consecutive charges have opposite signs, then the electric field in $\text{N/C}$ at $x=0$ is: $\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text{ N} \cdot \text{m}^2/\text{C}^2\right)$

Name the plant growth regulator which,when sprayed on sugarcane crops,increases the length of the stem and thus increases the yield of sugarcane.