The number of hydroxide ions produced by one molecule of sodium carbonate $(Na_2CO_3)$ on hydrolysis is

If the curves $x^2 - 6x + y^2 + 8 = 0$ and $x^2 - 8y + y^2 + 16 - k = 0$ $(k > 0)$ touch each other at a point,then the largest value of $k$ is

$A$ chloro compound of Vanadium has a spin-only magnetic moment of $1.73 \, BM$. This Vanadium chloride has the formula:

If $\frac{3x+2}{(x+1)(2x^2+3)} = \frac{A}{x+1} + \frac{Bx+C}{2x^2+3}$,then $A-B+C =$

Fresnel diffraction is produced due to light rays falling on a small obstacle. The intensity of light at a point on a screen beyond an obstacle depends on

The freezing point depression of a $0.001 \ m$ aqueous solution of $[Pt(NH_3)_4 Cl_4]$ is $0.0054^{\circ} C$. If $K_f$ for water is $1.80 \ K \ kg \ mol^{-1}$,determine the correct formula of the complex.