Mathematics -Study Plan-20 September 2008 for IIT JEE 2010

20 September 2008 Mathematics Binomial theorem Study session 9
Based on the Text: Objective Mathematics by R D Sharma


Do objective type exercises

21 to 40


Do practice exercises (at the end of the chapter) 21 to 25


Past IIT JEE questions

1. The coefficient of x⁴ in [(x/2)- (3/x²)]¹⁰ is

a. 405/256
b. 504/259
c. 450/263
d. none of these

(JEE 1983)

Answer (a)

Solution:
(r+1) th term of the expansion is given by
¹⁰C_r (x/2) ^10-r(-3/x²) ^r

= ¹⁰C_r (x) ^10-r(1/ x²)^r(1/2) ^10-r(-3) ^r

= ¹⁰C_r(-3) ^r(1/2) ^10-r(x) ^10-3r

In this term (x) ^10-3r is equal to x⁴
 10-3r = 4 or r = 2

So coefficient =
¹⁰C_r>(-3) ^r(1/2) <sup>10-r

10</sup>C₂>(-3) ²(1/2) ^10-2

= [10*9/2]*9*(1/2⁸)

= (45*9)/256
= 405/256


2. Let n be a positive integer. If the coefficient 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)



From Permutations chapter

Do the True of false type questions 1 to 10

For all difficult questions put a mark D or diff against them. Revise difficult problems more number of times so that they become easy problems after some time for you.



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


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