Q99 / 160 · AP EAMCET 2003 · Mathematics

If the coefficient of $(2 r+1)$ th term and $(r+2)$ th term in the expansion of $(1+x)^{43}$ are equal, then $r$ is equal to :

  • A
    12
  • Correct answer
    B
    14
  • C
    16
  • D
    18

Solution

Given that, Coefficient of $(2 r+1)$ th term $=$ co-efficient of $(r+2)$ th term $\Rightarrow \quad{ }^{43} C_{2 r}={ }^{43} C_{r+1}$ $\Rightarrow \quad 2 r+(r+1)=43$ or $\quad 2 r=r+1$ $\Rightarrow \quad r=14$ or $r=1$ thus $r=14$

Hence, the correct answer is option: 'B'.

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