MgSO₄ on reaction with NH₄OH and Na₂HPO₄ forms a white crystalline precipitate. What is its formula?

75.2 g of C₆H₅OH (phenol) is dissolved in a solvent of K_f = 14. If the depression in freezing point is 7 K then find the % of phenol that dimerises.

We have taken a saturated solution of AgBr. K_sp of AgBr is 12 $$\times$$ 10^-14. If 10^-7 mole of AgNO₃ are added to 1 litre of this solution find conductivity (specific conductance) of this solution in terms of 10^-7 S m^-1 units. Given, molar conductance of Ag⁺, Br^- and $$NO_3^-$$ are 6 $$\times$$ 10^-3 Sm² mol^-1, 8 $$\times$$ 10^-3 Sm² mol^-1 and 7 $$\times$$ 10^-3 Sm² mol^-1

Let $$\overrightarrow a = \widehat i + 2\widehat j + \widehat k,\,\overrightarrow b = \widehat i - \widehat j + \widehat k$$ and $$\overrightarrow c = \widehat i + \widehat j - \widehat k.$$ A vector in the plane of $$\overrightarrow a $$ and $$\overrightarrow b $$ whose projection on $$\overrightarrow c $$ is $${1 \over {\sqrt 3 }},$$ is