MCA Entrance Previous Year Question Bank

Let $3,6,9,12,\dots$ up to $78$ terms and $5,9,13,17,\dots$ up to $59$ terms be two series. Then, the sum of the terms common to both the series is equal to ________.

The sum of the infinite series $1+\frac{5}{6}+\frac{12}{6^2}+\frac{22}{6^3}+\frac{35}{6^4}+\frac{51}{6^5}+\frac{70}{6^6}+\dots$ is equal to:

Let $\{a_n{\}}_{n=0}^{\infty }$ be a sequence such that $a_0=a_1=0$ and $a_{n+2}=2a_{n+1}-a_n+1$ for all $n\ge 0$. Then, ${\sum }_{n=2}^{\infty }\frac{a_n}{7^n}$ is equal to:

The sum of the common terms of the following three arithmetic progressions:

$3,7,11,15,\dots ,399$

$2,5,8,11,\dots ,359$ and

$2,7,12,17,\dots ,197$

is equal to:

The sum ${\sum }_{n=1}^{\infty }\frac{2n^2+3n+4}{(2n)!}$ is equal to:

Let $a_1=8,a_2,a_3,\dots ,a_n$ be an A.P. If the sum of its first four terms is $50$ and the sum of its last four terms is $170$, then the product of its middle two terms is:

The sum to 10 terms of the series $\frac{1}{1+1^2+1^4}+\frac{2}{1+2^2+2^4}+\frac{3}{1+3^2+3^4}+\dots \text{ is}$

The sum $1^2-2\cdot 3^2+3\cdot 5^2-4\cdot 7^2+5\cdot 9^2-\cdots +15\cdot 29^2$ is ________.

Let $a_1,a_2,a_3,\dots$ be an A.P. If $a_7=3$, the product $a_1{a}_4$ is minimum and the sum of its first $n$ terms is zero, then $n!-4a_{n(n+2)}$ is equal to:

Let $a_1,a_2,...,a_n$ be in A.P. If $a_5=2a_7$ and $a_{11}=18$, then find the value of: $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+...+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$