# Recent questions tagged absolute-value

1
The number of distinct pairs of integers $(m,n)$ satisfying $|1 + mn| < |m + n| < 5$ is
1 vote
2
If $3x + 2|y| + y = 7$ and $x + |x| + 3y = 1,$ then $x + 2y$ is $\frac{8}{3}$ $1$ $– \frac{4}{3}$ $0$
1 vote
3
For a real number $x$ the condition $|3x – 20| + |3x – 40| = 20$ necessarily holds if $9 < x < 14$ $6 < x < 11$ $7 < x < 12$ $10 < x < 15$
1 vote
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 $8$ $12$ $10$ $6$
1 vote
6
The area of the region satisfying the inequilities $\left | x \right |-y\leq 1,y\geq 0$ and $y\leq 1$ is
1 vote
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 $1$ $0$ $\sqrt{2}$ $\sqrt{\dfrac{3}{2}}$
1 vote
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 by $\text{S}$ equals ________
11
The product of the distinct roots of $|x^{2}-x-6|=x+2$ is $-8$ $-24$ $-4$ $-16$
1 vote
12
The number of solutions to the equation $|x|(6x^{2}+1)=5x^{2}$ is _________
1 vote
13
If $a, b$ and $c$ are three real numbers, then which of the following is not true? $\mid a+b \mid\leq \mid a \mid+\mid b \mid$ $\mid a – b \mid \leq \mid a \mid + \mid b\mid$ $\mid a-b \mid \leq \mid a \mid -\mid b \mid$ $\mid a-c \mid \leq \mid a-b \mid+\mid b-c \mid$
The area bounded by the three curves $|x + y| = 1, |x| = 1$, and $|y| = 1$, is equal to $4$ $3$ $2$ $1$
If $x^2 + y^2 = 0.1$ and $|x – y| = 0.2$, then $| x | + | y |$ is equal to $0.3$ $0.4$ $0.2$ $0.6$
In the $\text{X-Y}$ plane, the area of the region bounded by the graph $|x+y| + |x-y| =4$ is $8$ $12$ $16$ $20$