MCA Entrance Previous Year Question Bank

$T_n$ represents the no. of triangles formed from a polygon having $n$ vertices. If $T_{n+1}-T_n=21$, then $n$ is equal to:

12 members were present at a board meeting. Each member shook hands will all of the other memebers before and after the meeting. How many hand shakes were there?

Twelve villages in a district are divided into 3 zones with 4 villages per each zone. The telephones department of the district intends to connect the villages with telephone lines such that every two villages in the same zone are connected with three direct lines and every two villages belonging to different zones are connected with two direct lines. How many direct lines are required?

The number of one-to-one functions from $\{1,2,3\}$ to $\{1,2,3,4,5\}$ is:

The number of different license plates that can be formed in the format 3 English letters ($A,\dots ,Z$) followed by 4 digits ($0,1,\dots ,9$) with repetitions allowed in letters and digits is equal to:

The number of words that can be formed by using the letters of the word 'MATHEMATICS' that start as well as end with $T$ is:

The number of ways of forming different nine digit numbers from the number 223355888 by rearranging its digits, so that the odd digits occupy even positions is:

If $\vec{a}=(\vec{i}+2\vec{j}-3\vec{k})$ and $\vec{b}=(3\vec{i}-\vec{j}+2\vec{k})$ then the angle between $(\vec{a}+\vec{b})$ and $(\vec{a}-\vec{b})$ is?

9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is

If a and b are greatest values of ${}^{2n}$C${}_1$ and ${}^{2n-1}$C${}_1$ respectively, then