Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If for positive integers  the coefficient of the  <img alt="(3 r)^{t h}" src="https

If for positive integers r>1, n>2 the coefficient of the  (3 r)^{t h} and (r+2)^{\text {th }} powers of x  in the expansion of (1+x)^{2 n} are equal, then 

Option: 1

n = 2r


Option: 2

n = 3r


Option: 3

n = 2r+1


Option: 4

None of these


Answers (1)

best_answer

In the expansion of (1+x)^{2n}, the general term ={ }^{2 n} C_k, 0 \leq k \leq 2 n

As given for r>1, n>2,{ }^{2 n} C_{3 r}={ }^{2 n} C_{r+2}

\\\Rightarrow Either 3 r=r+2\\ or\ 3 r=2 n-(r+2)\ \ \ \ ( { }^n C_r={ }^n C_{n-r} )\\ \Rightarrow r=1\ or\ \ n=2 r+1 \Rightarrow n=2 r+1,\ \ (2 r>1)

Posted by

avinash.dongre

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

NTA JEE Main 2026 session 1 admit card likely today; download link generated but not active yet
anam-khan

JEE Main 2026: IIT Guwahati CSE cut-off drops; BTech biosciences still least competitive
anam-khan

JEE Main Admit Card 2026 (OUT) LIVE: Session 1 hall ticket link active now; NTA announces shift timings

Latest Question