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

Let $f:\mathbb{R}\to \mathbb{R}$ be a function defined by $f(x)={\log }_{\sqrt{m}}\{\sqrt{2}(\sin x-\cos x)+m-2\}$ for some $m$, such that the range of $f$ is $[0,2]$. Then the value of $m$ is:

The number of functions $f:\{1,2,3,4\}\to \{a\in \mathbb{Z}:|a|\le 8\}$ satisfying $f(n)+\frac{1}{n}f(n+1)=1,\forall n\in \{1,2,3\}$ is

Let $f(x)=2x^n+\lambda ,\lambda \in \mathbb{R},n\in \mathbb{N}$, and $f(4)=133,f(5)=255$. Then the sum of all the positive integer divisors of $(f(3)-f(2))$ is

For some $a,b,c\in \mathbb{N}$, let $f(x)=ax-3$ and $g(x)=x^b+c,x\in \mathbb{R}$. If $(f\circ g{)}^{-1}(x)={\left(\frac{x-7}{2}\right)}^{\frac{1}{3}}$ then $(f\circ g)(ac)+(g\circ f)b$ is equal to

If the domain of the function $f(x)={\log }_e(4x^2+11x+6)+{\sin }^{-1}(4x+3)+{\cos }^{-1}\left(\frac{10x+6}{3}\right)$ is $(\alpha ,\beta ]$, then $36|\alpha +\beta |$ is equal to:

For $x\in \mathbb{R}$, two real valued functions $f(x)$ and $g(x)$ are such that, $g(x)=\sqrt{x}+1$ and $fog(x)=x+3-\sqrt{x}$. Then, $f(0)$ is equal to:

Let $D$ be the domain of the function $f(x)={\sin }^{-1}\left({\log }_{3x}\left(\frac{6+2{\log }_{3}x}{-5x}\right)\right)$. If the range of the function $g:D\to R$ defined by $g(x)=x-[x]$, ($[x]$ is the greatest integer function), is $(\alpha ,\beta )$, then ${\alpha }^2+\frac{5}{\beta }\text{ is equal to}$