Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too!

The total number of terms in the expansion

Question:

The total number of terms in the expansion of $(x+a)^{100}+(x-a)^{100}$ after simplification is

(A) 50

(B) 202

(C) 51

(D) none of these

Solution:

(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.

Leave a comment

None
Free Study Material