Saturday, September 20, 2008

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


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)


Answer true or false questions 11 to 19

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

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