Find the coefficient of `a^3b^4c^5` in the expansion of `(b c+c a+a b)^6dot`

Find the coefficient of a^3b^4c in the expansion of (1+a-b+c)^9dot

Find the coefficient of x^4 in the expansion of (2-x+3x^2)^6dot

The coefficient of a^(5)b^(6)c^(7) in the expansion of (bc + ca + ab)^(9) is

If A_(i,j) be the coefficient of a^i b^j c^(2010-i-j) in the expansion of (a+b+c)^2010 , then

The coefficient of x^5 in the expansion of (x^2-x-2)^5 is -83 b. -82 c. -86 d. -81

The coefficient of x^(28) in the expansion of (1+x^3-x^6)^(30) is 1 b. 0 c. 30 C_6 d. ^30 C_3

If a,b,c,d be four consecutive coefficients in the binomial expansion of (1+x)^(n) , then value of the expression (((b)/(b+c))^(2)-(ac)/((a+b)(c+d))) (where x gt 0 and n in N ) is

The coefficient x^5 in the expansion of (1+x)^(21)+(1+x)^(22)++(1+x)^(30) is a. "^51 C_5 b. "^9C_5 c. "^31 C_6 -"^(21)C_6 d. "^30 C_5 + "^(20)C_5

If coefficient of a^2 b^3 c^4 in(a+b+c)^m (where n in N ) is L(L != 0), then in same expansion coefficient of a^4b^4c^1 will be (A) L (B) L/3 (C) (mL)/4 (D) L/2

If the 3rd, 4th , 5th and 6th term in the expansion of (x+alpha)^n be, respectively, a ,b ,ca n dd , prove that (b^2-a c)/(c^2-b d)=(5a)/(3c)dot