Browse by Stream
QnA
Home

Get Answers to all your Questions

header-bg qa

If coefficients of T_9,\;T_{10} \text{ and } T_{11} in the expansion of (1 + x)n are in A.P. then n may be equal to

Option: 1

14


Option: 2

21


Option: 3

20


Option: 4

15


Answers (1)

best_answer

Coefficients of T_{9}=\;^nC_{8},\;T_{10}=\;^nC_{9} \; and \; T_{11}=\;^nC_{10}

As these terms are in A.P., so

2\;^nC_{9} =\;^nC_{8}+\;^nC_{10}

\\2\times\frac{n!}{(n-9)!9!}=\frac{n!}{(n-8)!8!}+\frac{n!}{(n-10)!10!}\\\\\text{Multiplying the equation by }(n-9)!9!\\\\2=\frac{9}{(n-8)}+\frac{n-9}{10}

\begin{array}{c}{20(n-8)=90+n^{2}-17 n+72} \\ {n^{2}-37 n+322=0} \\ {(n-23)(n-14)=0} \\ {n=14,23}\end{array}

hence option A is correct

Posted by

HARSH KANKARIA

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

Sigh of relief as JEE Main 2025 session 2 day 1 turns out easier than January exams
anam-khan

JEE Main 2025 April 2 shift 2 exam moderately difficult, math remains easy
anam-khan

JEE Main April 2 Exam Analysis 2025: Shift 1 maths easier compared to session 1; chemistry 'tough'

Latest Question