Haryana Police Constable Model Paper 2

Concept:
Binomial expansion:
The binomial expansion of the sum a and b to the power n is:
${\left(\mathrm{a}+\mathrm{b}\right)}^{\mathrm{n}}={}^{\mathrm{n}}{\mathrm{C}}_1{\mathrm{a}}^{\mathrm{n}}{\mathrm{b}}^0+{}^{\mathrm{n}}{\mathrm{C}}_2{\mathrm{a}}^{\mathrm{n}-1}{\mathrm{b}}^1+...+{}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{n}}{\mathrm{a}}^0{\mathrm{b}}^{\mathrm{n}}$
Calculation:
We will substitute a = ${\mathrm{x}}^2$ and b = ${\mathrm{y}}^2$ .
We can write the first bracket as follows:
${\left(\mathrm{a}+\mathrm{b}\right)}^{25}={}^{25}{\mathrm{C}}_1{\mathrm{a}}^{25}{\mathrm{b}}^0+{}^{25}{\mathrm{C}}_2{\mathrm{a}}^{24}{\mathrm{b}}^1+...+{}^{25}{\mathrm{C}}_{25}{\mathrm{a}}^0{\mathrm{b}}^{2}5$
Similarly, we can write the second bracket as follows:
${\left(\mathrm{a}+\mathrm{b}\right)}^{25}={}^{25}{\mathrm{C}}_1{\mathrm{a}}^{25}{\mathrm{b}}^0-{}^{25}{\mathrm{C}}_2{\mathrm{a}}^{24}{\mathit{b}}^1+...+{}^{25}{\mathrm{C}}_{25}{\mathrm{a}}^0{\mathrm{b}}^{2}5$
If we add both the equations we observe that all the even terms will get cancelled and we will only left with the odd-numbered terms.
There are total 13 terms in the first bracket and identical 13 terms from the second bracket.
Therefore, total number of terms in the expression will be 13.