Different Types of Intervals in Inequality

Q.

If $z$ is any complex number satisfying $\left|z-3-2i\right|\le 2$, then the minimum value of $\left|2z-6+5i\right|$ is

1. $2$

2. $1$

3. $3$

4. $5$

Q.

When $\frac{1}{a}+\frac{1}{c}+\frac{1}{\left(a-b\right)}+\frac{1}{\left(c-b\right)}=0$ and $b\ne a+c$, then $a,b,c$ are in

1. AP

2. GP

3. HP

4. None of these

Q.

If sum of two numbers is $3$, then maximum value of the product of first and the square of second is

1. $4$

2. $3$

3. $2$

4. $1$

Q. A solution of $9\%$ acid is to be diluted by adding $3\%$ acid solution to it. The resulting mixture is to be more than $5\%$ but less than $7\%$ acid. If there is $460$ litres of the $9\%$ solution, how many litres of $3\%$ solution will have to be added?

Q.

There are $12$ volleyball players in all in a college, out of which a team of $9$ players is to be formed. If the captain always remains the same, then in how many ways can the team be formed

1. $36$

2. $108$

3. $99$

4. $165$

Q. If $x<2$, then $\frac{1}{x}$ lies in the interval

1. $(-\infty ,\frac{1}{2})$
2. $(-\infty ,0)\cup (\frac{1}{2},\infty )$
3. $(-\infty ,0)\cup (0,\frac{1}{2})$
4. $(\frac{1}{2},\infty )$

Q. Solution set of $\frac{3x-4}{2}\ge \frac{x+1}{4}-1$ is

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

Q. If $-3<\frac{2x-1}{3}\le 5$, then $x$ lies in the interval

1. $(-4,8]$
2. $[-4,8)$
3. $(-4,8)$
4. $[-4,8]$

Q. If $x<2$, then $\frac{1}{x}$ lies in the interval

1. $(-\infty ,\frac{1}{2})$
2. $(-\infty ,0)\cup (\frac{1}{2},\infty )$
3. $(-\infty ,0)\cup (0,\frac{1}{2})$
4. $(\frac{1}{2},\infty )$

Q.

Solve the following linear in equations in R.

Solve :12x < 50, then

(i) $xϵR$ (ii) $xϵZ$ (iii) $xϵN$

Q. If $xϵR$, the solution set of the equation
$4^{-x+0.5}-{7.2}^{-x}-4<0$ is equal to

1. $(2,\frac{7}{2})$
2. $(-2,\infty )$
3. $(2,\infty )$
4. $(-\infty ,\infty )$

Q.

The difference between integers $x$ and $-6$ is $-5$ .

Find the value of $x$.

Q.

When a number is divided by $8$, the result is $–3$. The number is _________.

Q. Number of integral solutions of $-5\le \frac{5-3x}{2}\le 8$ is

1. $7$
2. $6$
3. $8$
4. $9$

Q.

You make homemade lip balm, about $11\%$ of the lip balm is made from beeswax.

You make $4\frac{2}{5}$ teaspoons of the lip balm.

About how many teaspoons of beeswax do you need?

Round your answer to the nearest ${10}^{th}$.

Q. The number of pairs of consecutive even natural numbers whose sum is less than $16$ is

1. $4$
2. $6$
3. $5$
4. $3$

Q.
The intervals of concavity and convexity of $f\left(x\right)=e^{-x^2}$ are

1. Convex : $(-\infty ,-\frac{\sqrt{2}}{2})\cup (\frac{\sqrt{2}}{2},\infty )$
2. Concave:$(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$
3. Concave : $(-\infty ,-\frac{\sqrt{2}}{2})\cup (\frac{\sqrt{2}}{2},\infty )$
4. Convex:$(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$

Q. The velocity $v($in $\text{m/s})$ of a train in time $t($in $\text{sec})$ is given by $v=52+7t$. The minimum time $t($in $\text{sec})$ when its velocity is atleast $73\text{m/s}$ is

1. $2$
2. $3$
3. $4$
4. $2.5$

Q.

The straight lines $x+y=0,5x+y=4$ and $x+5y=4$ form

1. an isosceles triangle

2. an equilateral triangle

3. a scalene triangle

4. a right angles triangle

Q. The common solution set of $3x-7<5+x$ and $11-5x\le 1$ is

1. $(2,6)$
2. $[2,6)$
3. $[2,6]$
4. $(2,6]$

Q.

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it.The resulting mixture is to be more than 4% but less than 6% boric acid.If there are 640 liters of the 8% solution, how many liters of 2% solution will have to be added ?

Q. If $(x+2),3,5$ are the lengths of sides of a triangle, then $x$ lies in

1. $(0,6)$
2. $(-4,6)$
3. $(-1,6)$
4. $(1,6)$

Q. I.Q. of a person is given by $I=\frac{M}{C}\times 100$, where $M$ is mental age and $C$ is chronological age. If $80\le I\le 140$ for a group of $12$ years old children, then the range of their mental age is

1. $[9.6,16.8]$
2. $(9.6,16.8)$
3. $[9,16]$
4. $(9,16)$

Q.

A total of $1400kg$ of potatoes were sold in three days. On the first day, $100kg$ less potatoes were sold than on the second day, and on the third day, ${\left(\frac{3}{5}\right)}^{th}$ of the amount sold on the first day. How many kilograms of potatoes were sold on each day?

Q.

If the replacement set is the set of integers lying between $-4$ and $8$, then find the solution set of $14-5x\ge 3x-40$. Also, represent the solution set on number line.

Q.

The minimum value of $2x+3y$ where $xy=6$ is

1. $12$

2. $9$

3. $8$

4. $6$

Q. Number of integral solutions of $-5\le \frac{5-3x}{2}\le 8$ is

1. $7$
2. $6$
3. $8$
4. $9$

Q.

If $f$ and $g$ are differentiable functions such that $f\left(2\right)=3,f\left(2\right)=1,f\left(3\right)=7,g\left(2\right)=-5$ and $g\left(2\right)=2$, then find the numbers indicated in problem $\left(f\circ f\right)\left(2\right)$.

Q. If $5x-3\ge 3x-5$ and $x\in R^{-}$, then $x\in$

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

Q. If $9x=5(y–32)$ and $x\in (30,35)$, then $y$ lies in the interval

1. $(86,95)$
2. $(85,96)$
3. $(80,95)$
4. $(80,96)$