The total number of terms in the expansion

(C) 51

Explanation:

Given $(x+a)^{100}+(x-a)^{100}$

$=\left({ }^{100} C_{0} x^{100}+{ }^{100} C_{1} x^{99} a+{ }^{100} C_{2} x^{98} a^{2}+\ldots\right)$

$+\left({ }^{100} C_{0} x^{100}-{ }^{100} C_{1} x^{99} a+{ }^{100} C_{2} x^{98} a^{2}+\ldots\right)$

$=2\left({ }^{100} C_{0} x^{100}+{ }^{100} C_{2} x^{98} a^{2}+\ldots++{ }^{100} C_{100} a^{100}\right)$

So, there are 51 terms

Hence option $c$ is the correct answer.