Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of  are in the ratio 5:1

If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of (1+x)^{n+5} are in the ratio 5:10:14, then the largest coefficient in this expansion is:
Option: 1 462
Option: 2 330
Option: 3 792
Option: 4 252

Answers (1)

best_answer

Let n + 5 = N

\\\mathrm{N}_{\mathrm{C}_{\mathrm{r}-1}}: \mathrm{N}_{\mathrm{C}_{\mathrm{r}}}: \mathrm{N}_{\mathrm{C}_{\mathrm{rt}}}=5: 10: 14 \\ \Rightarrow \frac{\mathrm{N}_{\mathrm{C}_{\mathrm{r}}}}{\mathrm{N}_{\mathrm{C}_{\mathrm{r}-1}}}=\frac{\mathrm{N}+1-\mathrm{r}}{\mathrm{r}}=2 \\ \frac{\mathrm{N}_{\mathrm{C}_{\mathrm{r}+1}}}{\mathrm{~N}_{\mathrm{C}_{\mathrm{r}}}}=\frac{\mathrm{N}-\mathrm{r}}{\mathrm{r}+1}=\frac{7}{5} \\ \Rightarrow \mathrm{r}=4, \mathrm{~N}=11 \\ \Rightarrow(1+\mathrm{x})^{11} \\ \text { Largest coefficient }={ }^{11} \mathrm{C}_{6}=462

Posted by

himanshu.meshram

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main Maths 2025: Five tips to score high marks in ‘toughest’ subject; most important chapters
anam-khan

JEE Main 2025 exam city intimation slip for session 1 soon at jeemain.nta.nic.in
anam-khan

Focus on modern physics, formulas to solve tricky problems; 5 tips to tackle JEE Main physics 2025

Latest Question