# Problems : Binomial Theorem

#### Level – I

1. Find the middle term in the expansion of

2. Find the term independent of x in the expansion of

3. Find the coefficient of x7 in

and find the relation between a and b so that their coefficients are equal.

4. If n is an in integer greater than 1 , prove that
a – C1(a – 1) + C2(a -2) …. + (-1)n Cn (a – n) = 0

5. Show that

6. If the coefficients of the 2nd, 3rd and 4th terms in the expansion of (1 + x)n are in A.P, find the value of n .

7. If x4r occurs in the expansion of (x + 1/x2)4n, prove that its coefficient is

8. If (1 + x)n = C0 + C1x + C2 x2 + Cnxn show that