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:

A set contains $(2n+1)$ elements. If the number of subsets which contain at most $n$ elements is 4096, then the value of $n$ is:

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

If for $n\in N$, ${\sum }_{k=0}^{2n}(-1{)}^k{\left[\left(\genfrac{}{}{0ex}{}{2n}{k}\right)\right]}^2=A$, then the value of ${\sum }_{k=0}^{2n}(-1{)}^k(k-2n){\left[\left(\genfrac{}{}{0ex}{}{2n}{k}\right)\right]}^2$ 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:

One hundred identical coins, each with probability $p$ of showing up a head, are tossed. If 0 < p < 1 and if the probability of heads on exactly $50$ coins is equal to that of heads on exactly $51$ coins then the value of $p$, is:

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: