If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+..........+{{C}_{n}}{{x}^{2}},\] then \[C_{0}^{2}+C_{1}^{2}+C_{2}^{2}+C_{3}^{2}+......+C_{n}^{2}\] = [MP PET 1985; Karnataka CET 1995; MNR 1999]

If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+..........+

1.	If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+..........+{{C}_{n}}{{x}^{2}},\] then \[C_{0}^{2}+C_{1}^{2}+C_{2}^{2}+C_{3}^{2}+......+C_{n}^{2}\] = [MP PET 1985; Karnataka CET 1995; MNR 1999]
A.	\[\frac{n!}{n!n!}\]
B.	\[\frac{(2n)!}{n!n!}\]
C.	\[\frac{(2n)!}{n!}\]
D.	None of these
Answer» C. \[\frac{(2n)!}{n!}\]

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If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+..........+{{C}_{n}}{{x}^{2}},\] then \[C_{0}^{2}+C_{1}^{2}+C_{2}^{2}+C_{3}^{2}+......+C_{n}^{2}\] = [MP PET 1985; Karnataka CET 1995; MNR 1999]

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