List of top Mathematics Questions on Binomial theorem asked in KCET

If n is even and the middle term in the expansion of \((x^2+\frac{1}{x})^n\) is 924 x⁶, then n is equal to

The total number of terms in the expansion of ${(x+a)^{47} - (x-a)^{47}}$ after simplification is

The middle term of expansion of $(\frac {10}{x}+\frac {x}{10})^{10}$ is

If $21^{st}$ and $22^{nd}$ terms in the expansion of $(1 + x)^{44}$ are equal, then $x$ is equal to

If the value of $C_0 + 2 \cdot C_1 + 3 \cdot C_2 + \dots+ (n+1) \cdot C_n=576$ ,then n is equal to

In $n$ is an odd positive integer and $(1+x +x^2 +x^3)^n =\displaystyle\sum_{r=0}^{3n} a_rx^r$ then $a_0 -a_1+a_2-a_3 +\dots -a_{3n}$ is equal to

If rth and (r + 1)th terms in the expansion of $(p + q)^n$ are equal, then $\frac {(n+1)q} {r(p+q)} $ is

In the binomial expansion of $(1+x)^{15}$ the coefficients of $x^r$ and $x^{r+3}$ are equal Then $r$ is _______

The remainder when $3^{100} \times 2^{500}$ is divided by $5$ is

The ten's digit in $1! + 4!+ 7! + 10!+12! + 13! + 15! +16! + 17!$ is divisible by

The ninth term of the expansion $\left(3x-\frac {1}{2x}\right)^8$ is

The remainder obtained when $(\lfloor 1)^2 + (\lfloor 2)^2 + (\lfloor 3)^2 + ... + (\lfloor 100)^2$ is divided by $10^2$ is ;

In the expansion of $\frac{C_1}{C_0} + 2\frac{C_2}{C_1} +3\frac{C_3}{C_2}+…………… n \frac{C_{n}}{C_{n-1}}$ is equal to