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### Two salts $A_2 X$ and MX have the same value of ....

Two salts $A_2 X$ and MX have the same value of solubility product of $4.0 \times 10^ {-12}$. The ratio of their molar solubilities i.e. $\frac{{S({A_2}X)}}{{S(MX)}} =$ _ _ _ _ . (Round off to the nearest integer)

Solution

We have, $4.0 \times {10^{ - 12}} = 4[S{({A_2}X)]^3}$

$\Rightarrow S({A_2}X) = {10^{ - 4}}$

Also, $4.0 \times {10^{ - 12}} = [S{(MX)]^2}$

$\Rightarrow S(MX) = 2.0 \times {10^{ - 6}}$

The ratio, $\frac{{S({A_2}X)}}{{S(MX)}} = \frac{{{{10}^{ - 4}}}}{{2.0 \times {{10}^{ - 6}}}} = 50$

### Sum of the coefficients in the expansion of $(x+y)^n$ ....

If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$