MCA Entrance Previous Year Question Bank

Let $f:R\to R$ be a function defined by $f(x)=(x-3{)}^{n_1}(x-5{)}^{n_2},n_1,n_2\in N$. Then, which of the following is NOT true?

A wire of length 22m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is:

The sum of the absolute maximum and minimum values of the function $f(x)=|x^2-5x+6|-3x+2$ in the interval $[-1,3]$ is equal to:

A wire of length $20$ m is to be cut into two pieces. A piece of length $l_1$ is bent to make a square of area $A_1$ and the other piece of length $l_2$ is made into a circle of area $A_2$. If $2A_1+3A_2$ is minimum then $(\pi l_1):l_2$ is equal to:

If the functions $f(x)=\frac{x^2}{3}+2bx+\frac{a{x}^2}{2}$ and $g(x)=\frac{x^2}{3}+ax+b{x}^2$, where $a\ne 2b$, have a common extreme point, then the value of $a+2b+7$ is equal to:

If the equation of the normal to the curve $y=\frac{x-a}{(x+b)(x-2)}$ at the point $(1,-3)$ is $x-4y=13$, then the value of $a+b$ is equal to:

Let the function $f(x)=2x^3+(2p-7)x^2+3(2p-9)x-6$ have a maxima for some value of x < 0 and a minima for some value of x > 0. Then, the set of all values of $p$ is

Let $f:(0,1)\to \mathbb{R}$ be a function defined by $f(x)=\frac{1}{1-e^{-x}},\text{and}g(x)=f(-x)-f(x)$ Consider two statements:

(I) $g$ is an increasing function in $(0,1)$

(II) $g$ is one-one in $(0,1)$

Let $x=2$ be a local minima of the function: $f(x)=2x^4-18x^2+8x+12,x\in (-4,4)$ If $M$ is local maximum value of the function $f$ in $(-4,4)$, then $M=$

The set of all $a\in \mathbb{R}$ for which the equation $x|x-1|+|x+2|+a=0$ has exactly one real root is: