A) 302
B) 301
C) 202
D) 101
Correct Answer: C
Solution :
Given expansion is \[{{(1+x)}^{101}}{{(1-x+{{x}^{2}})}^{100}}\] \[=(1+x){{(1-x)}^{100}}{{(1-x+{{x}^{2}})}^{100}}\] \[=(1+x){{[(1-x)(1-x+{{x}^{2}})]}^{100}}\] \[=(1+x)[{{(1-{{x}^{3}})}^{100}}]\] Expansion \[={{(1+{{x}^{3}})}^{100}}\]will have 100 + 1 = 101 terms So, \[=(1+x){{(1-{{x}^{3}})}^{100}}\]will have \[2\times 101=202\] termsYou need to login to perform this action.
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