MCA Entrance Previous Year Question Bank

Let a set $A=A_1\cup A_2\cup \cdots \cup A_k$, where $A_i\cap A_j=\varphi$ for $i\ne j,1\le i,j\le k$. Define the relation $R$ from $A$ to $A$ by $R=\{(x,y):y\in A_i\text{ if and only if }x\in A_i,1\le i\le k\}$. Then, $R$ is:

Let $P(S)$ denote the power set of $S=\{1,2,3,\dots ,10\}$. Define the relations $R_1$ and $R_2$ on $P(S)$ as $A{R}_{1}B$ if $(A\cap B^C)\cup (B\cap A^C)=\varphi$ and $A{R}_{2}B$ if $A\cup B^C=B\cup A^C,\forall A,B\in P(S)$. Then:

Let $f:\mathbb{R}-\{0,1\}\to \mathbb{R}$ be a function such that $f(x)+f\left(\frac{1}{1-x}\right)=1+x$ Then $f(2)$ is equal to:

Let $R$ be a relation on $\mathbb{R}$, given by $R=\{(a,b):3a-3b+\sqrt{7}\text{ is an irrational number}\}$. Then $R$ is:

Among the relations

S = \{(a, b): a, b \in \mathbb{R} - \{0\}, 2 + \frac{a}{b} > 0 \} and

$T=\{(a,b):a,b\in \mathbb{R},a^2-b^2\in \mathbb{Z}\}$.

If the domain of the function $f(x)=\frac{[x]}{1+x^2}$, where $[x]$ is the greatest integer $\le x$, is $[2,6)$, then its range is:

Let $A=\{1,2,3,5,8,9\}$. Then the number of possible functions $f:A\to A$ such that $f(m\cdot n)=f(m)\cdot f(n)$ for every $m,n\in A$ with $m\cdot n\in A$ is equal to ________.

Let $S=\{1,2,3,4,5,6\}$. Then the number of one-one functions $f:S\to P(S)$, where $P(S)$ denote the power set of $S$, such that $f(n)\subset f(m)$ where n < m is

The minimum number of elements that must be added to the relation $R=\{(a,b),(b,c)\}$ on the set $\{a,b,c\}$ so that it becomes symmetric and transitive is:

Let $A=\{1,2,3,4\}$ and $R$ be a relation on the set $A\times A$ defined by $R=\{((a,b),(c,d)):2a+3b=4c+5d\}$. Then, the number of elements in $R$ is ________.