Which reagent is commonly used in titration to determine the hardness of water?

If the harmonic mean between the roots of $(5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0$ is $4$,then the value of $b$ is

The equation of the directrix of the parabola ${y^2} + 4y + 4x + 2 = 0$ is

Ethyl chloride reacts with sodium ethoxide to form a compound $A$. Which of the following reactions also yields $A$?

The general solution of $y^2 dx + (x^2 - xy + y^2) dy = 0$ is:

$A$ thin prism $P_1$ with angle $4^o$ and made from glass of refractive index $1.54$ is combined with another thin prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of prism $P_2$ is (in $^o$)