JEE Mains · Maths · STD 11 - 8. sequence and series
Let the coefficients of the middle terms in the expansion of \(\left(\frac{1}{\sqrt{6}}+\beta x\right)^{4},(1-3 \beta x)^{2}\) and \(\left(1-\frac{\beta}{2} x\right)^{6}, \beta>0\), respectively form the first three terms of an \(A.P.\) If \(d\) is the common difference of this \(A.P.\), then \(50-\frac{2 d}{\beta^{2}}\) is equal to.
- A \(57\)
- B \(56\)
- C \(55\)
- D \(54\)
Answer & Solution
Correct Answer
(A) \(57\)
Step-by-step Solution
Detailed explanation
\({ }^{4} C _{2} \times \frac{\beta^{2}}{6},-6 \beta,-{ }^{6} C _{3} \times \frac{\beta^{3}}{8}\) are in A.P \(\beta^{2}-\frac{5}{2} \beta^{3}=-12 \beta\) \(\beta=\frac{12}{5} \text { or } \beta=-2 \therefore \beta=\frac{12}{5}\)…
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