CAT Modulus Practice Questions With Solutions

Let $0 \leq a \leq x \leq 100$ and $f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\mid$. Then the maximum value of f(x) becomes 100 when a is equal to

The largest real value of a for which the equation $\mid x + a \mid + \mid x - 1 \mid = 2$ has an infinite number of solutions for x is

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

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

For a real number x the condition $\mid3x-20\mid+\mid3x-40\mid=20$ necessarily holds if

If $3x+2\mid y\mid+y=7$ and $x+\mid x \mid+3y=1$ then $x+2y$ is:

In how many ways can a pair of integers (x , a) be chosen such that $x^{2}-2\mid x\mid+\mid a-2\mid=0$ ?

The product of the distinct roots of $\mid x^2 - x - 6 \mid = x + 2$ is

The shortest distance of the point $(\frac{1}{2},1)$ from the curve y = I x -1I + I x + 1I is

Let $f(x) =2x-5$ and $g(x) =7-2x$. Then |f(x)+ g(x)| = |f(x)|+ |g(x)| if and only if