TS EAMCET · Maths · Binomial Theorem
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
- B 14
- C 16
- D 18
Answer & Solution
Correct Answer
(B) 14
Step-by-step Solution
Detailed explanation
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 \(r=14\)
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