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7.Binomial Theorem
hard
If the coefficients of the three consecutive terms in the expansion of $(1+ x )^{ n }$ are in the ratio $1: 5: 20$, then the coefficient of the fourth term is $............$.
A
$3654$
B
$1827$
C
$5481$
D
$2436$
(JEE MAIN-2023)
Solution
$\frac{{ }^n C_r}{{ }^n C_{r-1}}=5 \quad \frac{{ }^n C_{r+1}}{{ }^n C_r}=4$
$\frac{ n – r +1}{ r }=5 \quad n =5 r +4 \ldots(2)$
$n=6 r-1 \ldots(1)$
$\therefore n=29, r=5$
$\text { Coeff of } 4^{\text {th }} \text { term }={ }^{29} C _3$
$=3654$
Standard 11
Mathematics
