Absolute Value Function

Q. The minimum value of the expression $y=|x-2|+|x+4|+|x-6|$ is

1. $8$
2. $10$
3. $14$
4. $6$

Q. Number of value(s) of $x$ satisfying the equation $||2x-7|-3|=12$ is

Q. If $2|x+1{|}^2-|x+1|=3,$ then the sum of all real values of $x$ satisfying the equation is

1. $2$
2. $-2$
3. $\frac{1}{2}$
4. $-\frac{5}{2}$

Q. The value of $x$ satisfying the equation $15|x-7|+4=10|x-7|+4$ is

Q. The number of real solution(s) of $||x-2|-2|-2|x|=|x-3|$ is

1. $1$
2. $0$
3. $2$
4. $3$

Q. The minimum value of the expression is $y=|x+1|+|x-3|$ is

1. $0$
2. $1$
3. $5$
4. $4$

Q. If $\frac{|x+2|}{|x-4|}=3$, then the value(s) of $x$ is/are

1. $\frac{5}{2}$
2. $\frac{7}{2}$
3. $7$
4. $9$

Q. If $f\left(x\right)=|8-4x|,$ then

1. $f\left(x\right)=8-4x$ when $x\ge 2$
2. $f\left(x\right)=8-4x$ when $x\le 2$
3. $f\left(x\right)=4x-8$ when $x>2$
4. $f\left(x\right)=4x-8$ when $x<2$

Q. The sum of the solutions of the equation $|\sqrt{x}-2|+\sqrt{x}(\sqrt{x}-4)+2=0,(x>0)$ is equal to:

1. $4$
2. $9$
3. $10$
4. $12$

Q. The value(s) of $x$ satisfying $|x+3|=x^2-4x-3$ is/are

1. $-1$
2. $0$
3. $3$
4. $6$

Q. If $|4x-3|=|x+5|$, then $x$ is/are

1. $\frac{8}{3}$
2. $-\frac{2}{5}$
3. $-\frac{8}{3}$
4. $\frac{2}{5}$

Q. Number of real solutions of the equation $|||x^2-1|-1|+3|=1$ is

1. $1$
2. $2$
3. $3$
4. $0$

Q. If $|2x-1|+|2x-2|=6$, then $x\in$

1. $\{-\frac{3}{4},\frac{9}{4}\}$
2. $\{\frac{9}{4},6\}$
3. $\{\frac{3}{4},\frac{9}{4}\}$
4. $\{-\frac{3}{4},\frac{9}{4},6\}$

Q. Given that $|t|=3,$ then a possible value of $|2t-1|$ is

1. $4$
2. $8$
3. $9$
4. $7$

Q. If $x^2-5x\text{sgn}(x^2-4)+6=0,$ then number of values of $x$ satisfying it is

Q. If $p=2$ and $q=-5,$ then the distance between $p$ and $q$ along the number line is

1. $-3$
2. $3$
3. $-7$
4. $7$

Q. If $x^2-|x+3|+x=0$, then $x=$

1. $-\sqrt{3}$
2. $\sqrt{3}$
3. $3$
4. $0$

Q. If $f\left(x\right)=|2x^3+x-7|,$ then

1. $f\left(x\right)=2x^3+x-7$ when $2x^3+x-7\ge 0$
2. $f\left(x\right)=2x^3+x-7$ when $2x^3+x-7\le 0$
3. $f\left(x\right)=7-2x^3-x$ when $2x^3+x-7<0$
4. $f\left(x\right)=7-2x^3-x$ when $2x^3+x-7>0$

Q. If $b=\frac{-4}{3}$, then the absolute value of $9b$ is

Q. The minimum possible value of $|x-1|+|x-2|+\cdots +|x-100|$ is

1. $4900$
2. $2500$
3. $2550$
4. $2450$

Q. Number of value(s) of $x$ satisfying the equation $-2|x-14|+5=-6|x-15|-1$ is

Q. Solution of $|x||x+1|=2$ is

1. $\{-1,1\}$
2. $\{-2,1\}$
3. $\{-3,2\}$
4. $\{-4,-2\}$

Q. If $||x-3|-4|=3$, then there exist

1. exactly $2$ distinct values of $x$ in $[1,5]$
2. exactly $2$ distinct values of $x$ in $[-5,0]$
3. exactly $2$ distinct values of $x$ in $[1,10]$
4. exactly $4$ distinct values of $x$ in $[-5,10]$

Q. The value(s) of $x$ satisfying the equation $||x-3|-4|=3$, is/are

1. $-4$
2. $4$
3. $6$
4. $10$

Q.

If $\left|\begin{array}{ccc}{x}^2+x& 3x-1& -x+3\\ 2x+1& 2+x^2& x^3-3\\ x-3& x^2+4& 3x\end{array}\right|=a_0+a_{1}x+......+a_7{x}^7$ then the value of $a_0$ is

1. $35$

2. $24$

3. $23$

4. $22$

5. $21$

Q. If $y=(a-2)x^2+(b-3)x,$ where $a,b\in R$ is a linear function and $|a-b|=4$, then the possible value(s) of $b$ is/are

1. $1$
2. $2$
3. $-2$
4. $6$

Q. The value(s) of $x$ satisfying the equation $||x-3|-4|=3$, is/are

1. $-4$
2. $4$
3. $6$
4. $10$

Q. If $|x-7{|}^2-3|x-7|-10=0$, then value(s) of $x$ can be equal to

1. $2$
2. $5$
3. $9$
4. $12$

Q. If $a=-7$, then the distance of $a$ from zero along the number line is

Q. Number of positive solutions of the equation $||x+1|-3|=5$ is