Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If the coefficient of  <img alt="x^7 \text { in }\left(a x^2+\frac{1}{b

If the coefficient of  x^7 \text { in }\left(a x^2+\frac{1}{b x}\right)^{11}is equal to the coefficient of x^{-7} \text { in }\left(a x-\frac{1}{b x^2}\right)^{11}then ab =

Option: 1

1


Option: 2

1/2


Option: 3

2


Option: 4

3


Answers (1)

best_answer

For coefficient of  x^7 \text { in }\left(a x^2+\frac{1}{b x}\right)^{11} ; n=11, \alpha=2, \beta=1, m=7

r=\frac{11.2-7}{2+1}=\frac{15}{3}=5

Coefficient of  x^7 \text { in } T_6={ }^{11} C_5 a^6 \cdot \frac{1}{b^5}x^7 \text { in } T_6={ }^{11} C_5 a^6 \cdot \frac{1}{b^5}......(1) and for coefficient of x^{-7} \text { in }\left(a x-\frac{1}{b x^2}\right)^{11} ; n=11, \alpha=1, \beta=2, m=-7 ; \quad r=\frac{11.1+7}{3}=6

 Coefficient of  x^{-7} \text { in } T_7={ }^{11} C_6 \cdot a^5 \cdot \frac{1}{b^6}.....(2)

From equation (1) and (2), we get

ab=1

 

Posted by

Devendra Khairwa

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 2025: BTech ECE cut-offs for female candidates go up at top NITs
anam-khan

JEE Main 2025 Session 2 City Slip (OUT) Live: Admit card likely on March 29 at jeemain.nta.nic.in; cut-offs
anam-khan

AESL expands Aakash Digital 2.0 to offer AI-powered coaching for NEET, JEE, Olympiads

Latest Question