MCA Entrance Previous Year Question Bank

Let $f(x)$ and $g(x)$ be two real polynomials of degree 2 and 1 respectively. If $f(g(x))=8x^2-2x$, and $g(f(x))=4x^2+6x+1$, then the value of $f(2)+g(2)$ is ________.

The domain of the function ${\cos }^{-1}\left(\frac{2{\sin }^{-1}\left(\frac{1}{4x^2-1}\right)}{\pi }\right)\text{ is :}$

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:

Let $f:R-\{2,6\}\to R$ be real valued function defined as $f(x)=\frac{x^2+2x+1}{x^2-8x+12}$. Then range of $f$ 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 ________.