A compound contains three elements X, Y and Z. The oxidation number...

The sum of all oxidation values must be equal to zero. Let, number of atoms of X, Y and Z are respectively a, b and c.

Then, $( + 3 ) \text{a} + ( + 5 ) \text{b} + ( - 2 ) \text{c} = 0$

Or

$3\text{a} + 5\text{b} - 2\text{c} = 0$

Now, putting values of a, b and c for all the given options, which will give sum equal to zero, will be our formula.

(a) For, ${\text{X}}_{2}\text{Y}\text{Z}$

$\text{a} = 2$

$\text{b} = 1$

$\text{c} = 1$

Thus, $3\text{a} + 5\text{b} - 2\text{c} = 0$

$3 \times 2 + 5 - 2 \ne 0$

(b) For, $\text{X}\text{Y}{\text{Z}}_{3}$

$\text{a} = 1, \text{b} = 1, \text{c} = 3$

$3\text{a} + 5\text{b} - 2\text{c} = 0$

$3 + 5 - 6 \ne 0$

(c) ${\text{X}}_{3}{( \text{Y}{\text{Z}}_{4} )}_{3}$

$\text{a} = 3, \text{b} = 3, \text{c} = 12$

$3\text{a} + 5\text{b} - 2\text{c} = 0$

$( 3 \times 3 + 5 \times 3 ) - ( 2 \times 12 ) = 0$

$9 + 15 - 24$

$24 - 24 = 0$

(d) ${\text{X}}_{2}{\text{Y}}_{2}\text{Z}$

$\text{a} = 2, \text{b} = 2, \text{c} = 1$

$3\text{a} + 5\text{b} - 2\text{c} = 0$

$( 3 \times 2 ) + ( 5 \times 2 ) - ( 2 \times 1 ) = 0$

$6 + 10 - 2 \ne 0$

Hence, option (c) is the correct answer.