In the expansion of `(1+x+x^3+x^4)^10,` the coefficient of `x^4` is `^40C_4` b. `^10 C_4` c. `210` d. `310`

In the expansion of (1-2x+3x^2 -4x^3+…."to")^4 coefficient of x^2 is

In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be a. 4n b. 4n-3 c. 4n+1 d. none of these

In the expansion of (x-1/(3x^2))^9, the term independent of x is a. T_3 b. T_4 c. T_5 d. none of these

If the sum of the binomial coefficients in the expansion of (x+ 1/x)^n is 64, then the term independent of x is equal to (A) 10 (B) 20 (C) 30 (D) 40

Statement-1: The coefficient of a^(3)b^(4)c^(3) in the expansion of (a-b+c)^(10) is (10!)/(3!4!3!) Statement-2: The coefficient of x^(p)y^(q)z^(r) in the expansion of (x+y+z)^(n) is (n!)/(p!q!r!) for all integer n.

Consider the following statements S_(1) : The total of terms in (x^(2)+2x+4)^(10) is 21 S_(2): The coefficient of x^(10) in (x^(2)+(1)/(x))^(20) is .^(20)C_(10) . S_(3) : The middle term in the expansion of (1+x)^(12) is .^(12)C_(6)x^(6) S_(4) : If the coefficients of fifth and ninth term in the expansion of (1+x)^(n) are same, then n=12 Now identify the correct combination of true statements.

The coefficient of x^4 in the expansion of {sqrt(1+x^2)-x}^(-1) in ascending powers of x , when |x|<1,i s a. 0 b. 1/2 c. -1/2 d. -1/8

If in the expansion of (x^4-1/(x^3))^(15),\ x^(-17) occurs in rth term, then a. r=10 b. r=11 c. r=12 d. r=13

Coefficient of x^(11) in the expansion of (1+x^2)^4(1+x^3)^7(1+x^4)^(12) is 1051 b. 1106 c. 1113 d. 1120

Find the coefficient of x^4 in the expansion of (x/2-3/x^2)^10 .