#### 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 x^{7} 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 – C_{1}(a – 1) + C_{2}(a -2) …. + (-1)^{n} C_{n} (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 x^{4r} occurs in the expansion of (x + 1/x^{2})^{4n}, prove that its coefficient is

8. If (1 + x)^{n} = C_{0} + C_{1}x + C_{2} x^{2} + C_{n}x^{n} show that