MCA Entrance Previous Year Question Bank

$2C_0+\frac{2^2}{2}{C}_1+\frac{2^3}{3}{C}_2+\cdots +\frac{2^{11}}{11}{C}_{10}=$

Numerical value of the expression $\left|\frac{3x^3+1}{2x^2+2}\right|$ for $x=-3$ is:

Find the $6^{\text{th}}$ term in the expansion of $(1-2x^2{)}^{1/2}$:

If $f(x)=x^n$, then the value of the expression $f(1)+\frac{f^{\prime }(1)}{1!}+\frac{f^{\prime \prime }(1)}{2!}+\cdots +\frac{f^n(1)}{n!}$ is equal to:

The sum of ${}^{20}{C}_8{+}^{20}{C}_9{+}^{21}{C}_{10}{+}^{22}{C}_{11}{-}^{23}{C}_{11}$ is:

If $(1+x{)}^n=a_0+a_{1}x+a_2{x}^2+\cdots +a_n{x}^n$, then $\left(1+\frac{a_1}{a_0}\right)\left(1+\frac{a_2}{a_1}\right)\left(1+\frac{a_3}{a_2}\right)\dots \left(1+\frac{a_n}{a_{n-1}}\right)$ is equal to:

If $x$ is so small that $x^2$ and higher powers of $x$ can be neglected, then $\frac{(9+2x{)}^{1/2}(3+4x)}{(1-x{)}^{1/5}}$ is approximately equal to:

If $n$ and $r$ are integers such that $1\le r\le n$, then the value of $n{(}^{n-1}{C}_{r-1})$ is:

If $(1+x-2x^2{)}^6=1+a_{1}x+a_2{x}^2+...+a_{12}{x}^{12}$, then $a_2+a_4+...+a_{12}$ is?

The coefficient of $x^{50}$ in the expression $(1+x{)}^{1000}+2x(1+x{)}^{999}+3x^2(1+x{)}^{998}+\cdots +1001x^{1000}$ is: