CAT Graphs Practice Questions With Solutions

Suppose k is any integer such that the equation $2x^{2}+kx+5=0$ has no real roots and the equation $x^{2}+(k-5)x+1=0$ has two distinct real roots for x. Then, the number of possible values of k is

Let r be a real number and $f(x) = \begin{cases}2x -r & ifx \geq r\\ r &ifx < r\end{cases}$. Then, the equation $f(x) = f(f(x))$ holds for all real values of $x$ where

The number of integers n that satisfy the inequalities $\mid n - 60 \mid < \mid n - 100 \mid < \mid n - 20 \mid$ is

$f(x) = \frac{x^2 + 2x - 15}{x^2 - 7x - 18}$ is negative if and only if

If r is a constant such that $\mid x^2 - 4x - 13 \mid = r$ has exactly three distinct real roots, then the value of r is

The number of real-valued solutions of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is:

How many disticnt positive integer-valued solutions exist to the equation $(x^{2}-7x+11)^{(x^{2}-13x+42)}=1$ ?

Let k be a constant. The equations $kx + y = 3$ and $4x + ky = 4$ have a unique solution if and only if

The quadratic equation $x^2 + bx + c = 0$ has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of $b^2 + c$?

Suppose, $\log_3 x = \log_{12} y = a$, where $x, y$ are positive numbers. If $G$ is the geometric mean of x and y, and $\log_6 G$ is equal to