Mathematics -Study Plan-21 September 2008 for IIT JEE 2010

21 September 2008 Mathematics Binomial theorem Study session 10
Based on the Text: Objective Mathematics by R D Sharma


Do objective type exercises

41 to 60


Do practice exercises (at the end of the chapter) 26 to 30


Past JEE question with solution

1. Let n be a positive integer. If the coefficients of 2nd, 3rd, and 4th terms in the expansion of (1 + x)ⁿ are in A.P. then the value of n is ________________ .
(JEE 1994)


Answer: 7

Solution:

The question requires concepts from binomial theorem and concept from arithmetic progression.

Coefficients of 2nd, 3rd, and 4th terms in the expansion of (1 + x)ⁿ are
ⁿC₁, ⁿC₂, ⁿC₃

According to arithmetic progression properties, three terms can be taken as a-d, a, and a+d. Hence sum of first and third terms = 2*second term

=> 2(ⁿC₂) = ⁿC₁ + ⁿC₃

=> 2 n(n-1)/2 = n + [n(n-1)(n-2)/6]

=> n-1 = 1 +[(n² – 3n+2)/6]

=> n² – 3n+2 = 6n-12
=> n² – 9n+14 = 0
=> (n-2)(n-7) = 0

Since 4th term will be there only when n>2, n is equal to 7.


JEE question for practice


1. If the binomial expansion of (a-b)ⁿ, n≥5, the sum of the 5th and 6th terms is zero. The a/b equals

a. (n-5)/6
b. (n-4)/5
c. 5/(n-4)
d. 6/(n-5)

(JEE 2001)

Permutations

Answer true or false questions 11 to 19


Any doubt regarding the chapter raise it in the JEE academy orkut community.


http://www.orkut.co.in/Community.aspx?cmm=39291603