Inequalities Involving Modulus Function

Q.

Solve the linear equation:

$\frac{(3t-2)}{4}-\frac{(2t+3)}{3}=\frac{2}{3}-t$

Q.

What is the square root of $0.9$?

Q.

What is dodging number?

Q. If the equation $|x+1|+|x-3|=k$ has exactly two solution then $k$ lies in

1. $(4,\infty )$
2. $[4,\infty )$
3. $R$
4. $(-\infty ,4)$

Q.

For what values of $x,$ the numbers $-1,x,$ $-\frac{3}{4}$ are in GP?

1. $\frac{3}{2}$

2. $\sqrt{\frac{3}{4}}$

3. $\sqrt{\frac{3}{2}}$

4. $\frac{3}{\sqrt{2}}$

Q. The complete set of values of $x$ for which the inequality ${\log }_x\left(\frac{4x+5}{6-5x}\right)<-1$ holds good, is

1. $(1,\frac{6}{5})$
2. $(0,1)$
3. $(\frac{1}{2},1)$
4. $(0,1)\cup (1,\frac{6}{5})$

Q. Evaluate lim_x->-1[1+x+x²+....+x¹⁰]

Q.

On a winter day the temperature at a place in Himachal Pradesh was $\text{-16°C}$. Convert it in degree Fahrenheit ($\text{°F}$) by using the formula. $\frac{C}{5}=\frac{F-32}{9}$

Q.

Zero degree Celsius is the same temperature as?

Q. If $||x-3|+4|\ge 2$, then $x$ belongs to

1. $\varphi$
2. $[-5,\infty )$
3. $(-\infty ,-5]\cup [1,\infty )$
4. $R$

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

1. $(0,2)$
2. $(2,\infty )$
3. $[0,2]$
4. $[0,\infty )$

Q. If $f\left(x\right)=\sqrt{x^2+6x+9}-\sqrt{x^2-6x+9}$, then the value of $f\left(\frac{456}{123}\right)-f(-\frac{456}{123})$ is

Q.

If $3\le 3t-18\le 18$, then which one of the following is correct?

1. $15\le 2t+1\le 20$

2. $8\le t<12$

3. $8\le t+1\le 13$

4. $21\le 3t\le 24$

5. $t\le 7ort\ge 12$

Q.

If $x$ satisfies the inequations $2x-7<11\text{and}3x+4<-5$, then $x$ lies in the interval

1. $\left(-\infty ,3\right)$

2. $\left(-\infty ,2\right)$

3. $\left(-\infty ,-3\right)$

4. $\left(-\infty ,\infty \right)$

5. $\left(3,\infty \right)$

Q. How to solve limit x approachs infinity sinx/x

Q.

If $\frac{|x-2|}{x-2}\ge 0$ , then

1. $xϵ[2,\infty )$

2. $xϵ(2,\infty )$

3. $xϵ[-\infty ,2)$

4. $xϵ(-\infty ,2]$

Q.

Given matrix $A=\left[\begin{array}{cc}\frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}\\ -\frac{1}{\sqrt{2}}& -\frac{1}{\sqrt{2}}\end{array}\right]$ is type of

1. Unitary

2. Orthogonal

3. Nilpotent

4. Involuntary

Q.

Why cant you take the logarithm of a negative number?

Q. If $\text{sgn}\left(\frac{x-2}{x+1}\right)\le \frac{x-1}{2}$, then $x\in$

1. $[-1,\infty )$
2. $(-1,2)\cup (3,\infty )$
3. $(-1,2]\cup [3,\infty )$
4. $(-1,\infty )$

Q.

Solve the following system of equations in R.
|4-x|+1<3

Q.

Solve the given inequality for real x: 37 ­– (3x + 5) ≥ 9x – 8(x – 3)

Q.

Let $f\left(x\right)=x^2+xg\left(1\right)+g\left(2\right)$ and $g\left(x\right)=x^2+xf\left(2\right)+f\left(3\right)$, then:

1. $f\left(1\right)=4+f\left(2\right)$

2. $g\left(2\right)=g\left(1\right)+4$

3. $g\left(2\right)+f\left(3\right)=8$

4. None of these

Q.

Given that $\frac{d}{dx}f\left(x\right)=f\left(x\right).$ The relationship $f(a+b)=f\left(a\right)+f\left(b\right)$ is valid if $f\left(x\right)$ is equal to

1. $x$

2. $x^2$

3. $x^3$

4. $x^4$

Q. Complete solution set of $|x^2-5x+7|+|x^2-5x-14|=21$ is -

1. $[-2,7]$
2. $(-\infty ,-2]\cup [7,\infty )$
3. $[7,\infty )$
4. $(-\infty ,-2]$

Q.

Write the solution set of values of x satisfying $|x-1|\le 3and|x-1|\le 1$.

Q. The solution set of the inequality $||x|-1<1-x,2\forall xϵR$ is equal to

1. $(0,\infty )$
2. $(-1,\infty )$
3. $(-1,1)$
4. $(-\infty ,0)$

Q. The number of integral values of $x,$ satisfying the inequality $\frac{(|x|+3)(4-|x|)}{x^2-|x|}>0$ is

Q.

The solution set of the inequation $|x+2|\le 5$ is

1. [-5, 5]

2. (-7, 3)

3. [-7, 3]

4. (-7, 5)

Q. If $|x^2+x-4|=|x^2-4|+|x|$, then $x\in$

1. $[0,2]$
2. $(0,2)$
3. $[-2,0]\cup [2,\infty )$
4. $[-2,\infty )$

Q.

Solve the following equation:
$\frac{3x-1}{4}=11$