Binomial Theorem - Algebra - Mathematics Previous Year Questions

The coefficient of x⁸ in the polynomial (x \(-\) 1) (x \(-\) 2) ..... (x \(-\) 10)

The value of \({}^{47}{C_4} + \sum\limits_{r = 1}^5 {{}^{52 - r}{C_3}}\) is equal to

$${{{C_1}} \over {{C_0}}} + 2{{{C_2}} \over {{C_1}}} + 3{{{C_3}} \over {{C_2}}} + 4{{{C_4}} \over {{C_3}}} + ....20{{{C_{20}}} \over {{C_{19}}}} =$$

The number of terms in the expansion of \({(1 + 5\sqrt {2x} )^9} + {(1 - 5\sqrt {2x} )^9}\) is

If the sum of the coefficients in the expansion of (x + y)ⁿ is 1024, then the value of the greatest coefficient in the expansion is

The sum of the coefficients of all odd degree terms in the expansion of \(\left(x+\sqrt{x^3-1}\right)^5 +\left(x-\sqrt{x^3-1}\right)^5, x>1\) is

\(\sum_\limits{\substack{i, j=0 \\ i \neq j}}^n{ }^n C_i{ }^n C_j\) is equal to

If ${ }^n C_{n-r}+3 \cdot{ }^n C_{n-r+1}+3 \cdot{ }^n C_{n-r+2} +{ }^n C_{n-r+3}={ }^x C_r$, then the value of $x$ is

What is the coefficient of $x^{50}$ in $(1+x)^{41}\left(1-x+x^2\right)^{40}$.