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  • If for positive integers  the coefficient of the  <img alt="(3 r)^{t h}" src="https

If for positive integers r>1, n>2 the coefficient of the  (3 r)^{t h} and (r+2)^{\text {th }} powers of x  in the expansion of (1+x)^{2 n} are equal, then 

Option: 1

n = 2r


Option: 2

n = 3r


Option: 3

n = 2r+1


Option: 4

None of these


Answers (1)

best_answer

In the expansion of (1+x)^{2n}, the general term ={ }^{2 n} C_k, 0 \leq k \leq 2 n

As given for r>1, n>2,{ }^{2 n} C_{3 r}={ }^{2 n} C_{r+2}

\\\Rightarrow Either 3 r=r+2\\ or\ 3 r=2 n-(r+2)\ \ \ \ ( { }^n C_r={ }^n C_{n-r} )\\ \Rightarrow r=1\ or\ \ n=2 r+1 \Rightarrow n=2 r+1,\ \ (2 r>1)

Posted by

avinash.dongre

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