XI Revision assignment Binomial theorem

                 DCM PRESIDENCY SCHOOL, LUDHIANA

                          MATHS – ASSIGNMENT, CLASS- 11^TH TOPIC -  BINOMIAL THEOREM

1.  Find the number of terms in the following expansion;

      a)   (1+2x+x²)²⁰  b) [(3x+y)⁸ –(3x-y)⁸]

2.   Using binomial theorem expand :       a)  (1 + x +x²)³  b)  (10.1)⁵

3.   Using binomial theorem , prove that  2³ⁿ -7n -1 is divisible by 49, n€N.

4.  Find the 11^th  term from the end of the expansion  (2x – 1/x²)²⁵.

5.  Find the coffiecients of x³² and x^-17  in the expansion (x⁴- 1/x³)¹⁵

6.  If the fourth term in the expansion (ax+ 1/x)ⁿ  is 5/2, then find the value of a and n.

7.  Using the binomial , prove that 6ⁿ -5n always leave the remainder 1 , when divisible by 25.

8.  Prove that the coefficient of the middle term in the expansion of (1 +x)²ⁿ is equal to the sum of the        coefficient of middle term of the expansion (1+x)^2n-1

9.  In the binomial expansion of (1+x)ⁿ, the coefficient of the 5^th ,6^th , and 7^th terms are in A. P . Find all  values of n for which this can happen.

10.  The coefficient of three consecutive term in the expansion(1+x)ⁿ be 76, 95, 76, find n.