Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Examples

Example 1

Example 2 Important

Example 3 Important

Example 4

Question 1 Important Deleted for CBSE Board 2024 Exams

Question 2 Important Deleted for CBSE Board 2024 Exams

Question 3 Deleted for CBSE Board 2024 Exams

Question 4 Important Deleted for CBSE Board 2024 Exams

Question 5 Deleted for CBSE Board 2024 Exams

Question 6 Important Deleted for CBSE Board 2024 Exams

Question 7 Important Deleted for CBSE Board 2024 Exams

Question 8 Deleted for CBSE Board 2024 Exams

Question 9 Important Deleted for CBSE Board 2024 Exams

Question 10 Important Deleted for CBSE Board 2024 Exams

Question 11 Important Deleted for CBSE Board 2024 Exams You are here

Question 12 Deleted for CBSE Board 2024 Exams

Question 13 Important Deleted for CBSE Board 2024 Exams

Chapter 7 Class 11 Binomial Theorem

Serial order wise

Last updated at May 29, 2023 by Teachoo

Example 15 Find the term independent of x in the expansion of (āš„ " + " 1/(2 āš„))^18, x > 0. Calculating general term of expansion We know that general term of (a + b)n is Tr+1 = nCr (a)nār . (a)n For general term of expansion (āš„ " + " 1/(2 āš„))^18 Putting n = 18 , a = āš„ , b = 1/(2 āš„) ā“ Tr + 1 = 18Cr (āš„)18 ā r (1/(2 āš„))^š = 18Cr (ćš„")" ć^(1/3 Ć (18 ā š)) (1/2 "Ć" 1/āš„)^š = 18Cr (ćš„")" ć^((18 ā š)/3 ) (1/2)^š (1/āš„)^š = 18Cr (ćš„")" ć^((18 ā š)/3 ) 1/2^š (1/š„^(1/3) )^š = 18Cr (ćš„")" ć^((18 ā š)/3 ) 1/2^š 1/š„^(š/3) = 18Cr (ćš„")" ć^((18 ā š)/3 ) 1/2^š š„^((āš)/3) = 18Cr (ćš„")" ć^((18 ā š)/3 ) š„^((āš)/3) 1/2^š = 18Cr (ćš„")" ć^((18 ā š)/3 ā š/3) 1/2^š = 18Cr (ćš„")" ć^((18 ā š ā š)/3 ) 1/2^š = 18Cr (ćš„")" ć^((18 ā 2š)/3 ) 1/2^š ā“ Tr + 1 = 18Cr (ćš„")" ć^((18 ā 2š)/3 ) 1/2^š We need to find the term independent of x So, power of x is 0 š„^((18 ā2š)/3) = x0 Comparing power (18 ā 2š)/3 = 0 18 ā 2r = 0 18 = 2r 18/2 = r 9 = r r = 9 Putting r = 9 in (1) Tr+1 = 18Cr (ćš„")" ć^((18 ā 2š)/3 ) 1/2^š T9+1 = 18C9 .š„^((18 ā3(9))/3). 1/29 = 18C9 .x0. 1/29 = 18C9 . 1/29 Hence, the term which is independent of x is 10th term = T10 = 18C9 . š/šša