Find the coefficient of `t^8` in the expansion of `(1+2t^2-t^3)^9`.

The coefficient of t^4 in the expansion of ((1 - t^6)/(1-t))^(3) is 3k. The value of k is _________.

(i) Find the coefficient of x^(3)y^(4)z^(2)t^(5) in the expansion of (x-y+z-t)^(14) . (ii) Find the coefficient of x^(10)y^(12)z^(8) in the expansion of (xy+yz+zx)^(15)

Find the term independent of x in the expansion of [(t^(-1)-1)x+(t^(-1)+1)^(-1)x^(-1)]^8

If the coefficients of (r-5)t h a n d(2r-1)t h terms in the expansion of (1+x)^(34) are equal, find rdot

If T_2/T_3 in the expansion of (a + b)^n and T_3/T_4 in the expansion of (a + b)^(n+3) are equal, then n is equal to

The coefficient of t^24 in (1+t^2)^2 (1+ t^12) (1+ t^24) is:

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials (iv) t^(3)-2t^(2)-15t .

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials (iv) t^(3)-2t^(2)-15t .

If the coefficients of the (n+1)^(t h) term and the (n+3)^(t h) term in the expansion of (1+x)^(20) are equal , then the value of n is a. 10 b. 8 c. 9 d. none of these