# Recent questions tagged absolute-value

1

The number of distinct pairs of integers $(m,n)$ satisfying $|1 + mn| < |m + n| < 5$ is

2

If $3x + 2|y| + y = 7$ and $ x + |x| + 3y = 1,$ then $x + 2y$ is$\frac{8}{3}$$1$$ – \frac{4}{3}$$0$

3

For a real number $x$ the condition $|3x – 20| + |3x – 40| = 20$ necessarily holds if$9 < x < 14$$6 < x < 11$$7 < x < 12$$10 < x < 15$

4

If $r$ is a constant such that $|x^{2} – 4x -13| = r$ has exactly three distinct real roots, then the value of $r$ is$15$$18$$17$$21$

5

The area, in $\text{sq. units},$ enclosed by the lines $x = 2, y = |x – 2| + 4,$ the X-axis and the Y-axis is equal to $8$$12$$10$$6$

6

The area of the region satisfying the inequilities $\left | x \right |-y\leq 1,y\geq 0$ and $y\leq 1$ is

7

The area of the closed region bounded by the equation $\mid x \mid+\mid y \mid= 2$ in the two-dimensional plane is $4\pi$$4$$8$$2\pi$

8

The shortest distance of the point $\left ( \frac{1}{2}, 1 \right )$ from the curve $y=\mid x-1 \mid+\mid x+1 \mid$ is $1$$0$$\sqrt{2}$$\sqrt{\dfrac{3}{2}}$

9

If $x^{2}+y^{2}= 0.1$ and $\left | x-y \right |=0.2$, then $\left | x \right |+\left | y \right |$ is equal to$0.3$$0.4$$0.2$$0.6$

10

Let $\text{S}$ be the set of all points $(x,y)$ in the $x-y$ plane such that $|x|+|y|\leq 2$ and $|x|\geq 1$. Then, the area, in square units, of the region represented b...

11

The product of the distinct roots of $|x^{2}-x-6|=x+2$ is$-8$$-24$$-4$$-16$

12

The number of solutions to the equation $|x|(6x^{2}+1)=5x^{2}$ is _________

13

If $a, b$ and $c$ are three real numbers, then which of the following is not true?$\mid a+b \mid\leq \mid a \mid+\mid b \mid$$\mid a – b \mid \leq \mid a \mid + \mid b...

14

The area bounded by the three curves $|x + y| = 1, |x| = 1$, and $|y| = 1$, is equal to$4$ $3$$2$$1$

15

If $x^2 + y^2 = 0.1$ and $|x – y| = 0.2$, then $| x | + | y |$ is equal to$0.3$$0.4$$0.2$$0.6$

16

In the $\text{X-Y}$ plane, the area of the region bounded by the graph $|x+y| + |x-y| =4$ is$8$$12$$16$$20$