JEE Mains · Maths · STD 11 - 7. binomial theoram
If the coefficients of the three successive terms in the binomial expansion of \((1 + x)^n\) are in the ratio \(1 : 7 : 42,\) then the first of these terms in the expansion is
- A \(8^{th}\)
- B \(6^{th}\)
- C \(7^{th}\)
- D \(9^{th}\)
Answer & Solution
Correct Answer
(C) \(7^{th}\)
Step-by-step Solution
Detailed explanation
\(\frac{^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}}{1}=\frac{^{\mathrm{n}} \mathrm{C}_{\mathrm{r}+1}}{7}=\frac{^{\mathrm{n}} \mathrm{C}_{\mathrm{r}+2}}{42}\) By solving we get \(r=6\) so, it is \(7^{\text {th }}\) term
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