MCA Entrance Previous Year Question Bank

Let $R$ be a relation defined on $\mathbb{N}$ as $aRb$, if $2a+3b$ is a multiple of $5,a,b\in \mathbb{N}$. Then $R$ is:

Let $S=\{1,2,3,5,7,10,11\}$. The number of non-empty subsets of $S$ that have the sum of all elements a multiple of $3$, is:

Let $A=\{1,3,4,6,9\}$ and $B=\{2,4,5,8,10\}$. Let $R$ be a relation defined on $A\times B$ such that $R=\{((a_1,b_1),(a_2,b_2)):a_1\le b_2\text{ and }{b}_1\le a_2\}$. Then, the number of elements in the set $R$ is:

An organisation awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals were awarded to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?