A body of mass '$m$' is projected with a speed '$u$' making an angle of $45^{\circ}$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $\frac{\sqrt{2} m u^3}{X g}$. The value of '$X$' is _________.

If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which $\mathrm{C}$ and $\mathrm{S}$ do not come together, is $(6 !) \mathrm{k}$, then $\mathrm{k}$ is equal to :

During the qualitative analysis of $\mathrm{SO}_{3}^{2-}$ using dilute $\mathrm{H}_{2} \mathrm{SO}_{4}, \mathrm{SO}_{2}$ gas is evolved which turns $\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$ solution (acidified with dilute $\mathrm{H}_{2} \mathrm{SO}_{4}$) :

The minimum number of elements that must be added to the relation $\mathrm{R}=\{(\mathrm{a}, \mathrm{b}),(\mathrm{b}, \mathrm{c})\}$ on the set $\{a, b, c\}$ so that it becomes symmetric and transitive is :

A capacitor of capacitance 500 $\mu$F is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in LC circuit will be _______ A.

Three point charges of magnitude $5 \mu \mathrm{C}, 0.16 \mu \mathrm{C}$ and $0.3 \mu \mathrm{C}$ are located at the vertices $A, B, C$ of a right angled triangle whose sides are $A B=3 \mathrm{~cm}, B C=3 \sqrt{2} \mathrm{~cm}$ and $C A=3 \mathrm{~cm}$ and point $A$ is the right angle corner. Charge at point $\mathrm{A}$ experiences ____________ $\mathrm{N}$ of electrostatic force due to the other two charges.

What is the major product of the following reaction?

Which statement is not true with respect to nitrate ion test?