JEE Mains · Maths · STD 11 - 7. binomial theoram
Let the coefficients of three consecutive terms \(T_r, T_{r+1}\) and \(T_{r+2}\) in the binomial expansion of \((a+b)^{12}\) be in a G.P. and let \(p\) be the number of all possible values of \(r\). Let \(q\) be the sum of all rational terms in the binomial expansion of \((\sqrt[4]{3}+\sqrt[3]{4})^{12}\). Then \(\mathrm{p}+\mathrm{q}\) is equal to :
- A \(283\)
- B \(287\)
- C \(295\)
- D \(299\)
Answer & Solution
Correct Answer
(A) \(283\)
Step-by-step Solution
Detailed explanation
Coefficient of \(\begin{aligned} & T_r, T_{r+1}, T_{r+2} \rightarrow G P \\ & \Rightarrow\left({ }^{12} C_r\right)^2={ }^{12} C_{r-1} \cdot{ }^{12} C_{r+1} \end{aligned}\) \(\Rightarrow\left({ }^{12} C_r\right)^2={ }^{12} C_{r-1} \cdot{ }^{12} C_{r+1}\) but no three consecutive…
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