Let $R$ be a reflexive relation on a finite set $A$ having $n$ elements,and let there be $m$ ordered pairs in $R$. Then

The height of water in a tank is $H$. The range of the liquid emerging out from a hole in the wall of the tank at a depth $\frac{3H}{4}$ from the upper surface of water will be

If $\int \frac{d \theta}{\cos ^{2} \theta(\tan 2 \theta+\sec 2 \theta)}=\lambda \tan \theta+2 \log _{e}|f(\theta)|+C$ where $C$ is a constant of integration,then the ordered pair $(\lambda, f(\theta))$ is equal to

Acetic acid is reacted with metallic sodium to form hydrogen and $X$. When $X$ is heated with sodalime,$Y$ and sodium carbonate are formed. $Y$ is

Which of the following statements is not true?

$A$ slit of width $a$ is illuminated by red light of wavelength $6500 \,\, \mathring{A}$. The first minimum will fall at $\theta = 30^{\circ}$ if $a$ is equal to: