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Question: If coefficient of \(\frac{(2n)!}{(n)!(n + 2)!}\) and \(\frac{(2n)!}{(n - 1)!(n + 2)!}\) terms in the...

If coefficient of (2n)!(n)!(n+2)!\frac{(2n)!}{(n)!(n + 2)!} and (2n)!(n−1)!(n+2)!\frac{(2n)!}{(n - 1)!(n + 2)!} terms in the expansion of (1+x)n=C0+C1x+C2x2+...+Cnxn(1 + x)^{n} = C_{0} + C_{1}x + C_{2}x^{2} + ... + C_{n}x^{n} are equal, then value of r is.

A

5

B

6

C

4

D

3

Answer

5

Explanation

Solution

∵ 6mu(55−11)(55+11)=4\because\mspace{6mu}(5\sqrt{5} - 11)(5\sqrt{5} + 11) = 4

But 55−11=455+115\sqrt{5} - 11 = \frac{4}{5\sqrt{5} + 11}

⇒ ∵0<55−11<1⇒0<(55−11)2n+1<1\because 0 < 5\sqrt{5} - 11 < 1 \Rightarrow 0 < (5\sqrt{5} - 11)^{2n + 1} < 1.