Multinomial Theorem

Coefficient of $t^{24}$ in ${\left(1+t^2\right)}^{12}\left(1+t^{12}\right)(1+t^{24})$ is

The coefficients of $x^2{y}^2, yz{t}^2$ and xyzt in the expansion of ${\left(x+y+z+t\right)}^4$ are in the ratio

Coefficient of $a^{8}bc$ in the expansion of ${\left(a+b+c\right)}^{10}$ is

If $a,\mathrm{ }\mathrm{b},\mathrm{ }\mathrm{c},d\mathrm{ }$ are odd natural numbers such that $a+b+c+d=20$ then the number of values of $a, b, c, d,$ is

Number of ways in which 25 identical balls can be distributed among Ram, Shyam, Sunder and Ghanshyam such that atleast 1, 2, 3, and 4 balls are given to Ram, Shyam, Sunder and Ghanshyam respectively, is-

In how many ways can Rs 16 be divided into 4 persons when none of them get less than Rs 3?

The number of terms in the expansion of ${\left(a+b+c\right)}^n$ will be

The coefficient of $a^3{b}^{4}c$ in the expansion of ${(1+a-b+c)}^9$is equal to

If ${(1-x+x^2)}^n=a_0+a_{1}x+$.....$a_{2n}{x}^{2n}$ then the value of $a_0+a_2+a_4+$....$+a_{2n}$ is

The number of terms in the expansion of ${\left(a+b+c\right)}^{10}$ is

The number of dissimilar terms of the expansion ${(a+b+c)}^{12}$ is

The number of terms in the expansion of ${\left(a+b+c\right)}^{10}$ is

If ${\left(2x^2-x-1\right)}^5=a_0+a_{1}x+a_2{x}^2+...+a_{10}{x}^{10}$, then $a_2+a_4+a_6+a_8+a_{10}$ is equal to

The coefficient of $a^8{b}^4{c}^9{d}^9$ in ${\left(abc + abd+ acd + bcd\right)}^{10}$ is

The coefficient of $x^2{y}^2, yz{t}^2$ and $xyzt$ in the expansion of ${\left(x+y+z+t\right)}^4$ are in the ratio

The sum of the coefficient in ${\left(x+2y+z\right)}^{10}$ is

If $a, b, c$ are in $\mathrm{A}.\mathrm{P}.,$ then the sum of the coefficients of ${\left\{1+{\left(a{x}^2-2bx+c\right)}^2\right\}}^{1973}$ is