# Different Types of Intervals in Inequality

## Trending Questions

**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

$2$

$1$

$3$

$5$

**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

AP

GP

HP

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**

$4$

$3$

$2$

$1$

**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

$36$

$108$

$99$

$165$

**Q.**If x<2, then 1x lies in the interval

- (−∞, 12)
- (−∞, 0)∪(12, ∞)
- (−∞, 0)∪(0, 12)
- (12, ∞)

**Q.**Solution set of 3x−42≥x+14−1 is

- [1, ∞)
- (−∞, 1]
- (−∞, 1)
- (1, ∞)

**Q.**If −3<2x−13≤5, then x lies in the interval

- (−4, 8]
- [−4, 8)
- (−4, 8)
- [−4, 8]

**Q.**If x<2, then 1x lies in the interval

- (−∞, 12)
- (−∞, 0)∪(12, ∞)
- (−∞, 0)∪(0, 12)
- (12, ∞)

**Q.**

Solve the following linear in equations in R.

Solve :12x < 50, then

(i) x ϵ R (ii) x ϵ Z (iii) x ϵ N

**Q.**If xϵR, the solution set of the equation

4−x+0.5−7.2−x−4<0 is equal to

- (2, 72)
- (−2, ∞)
- (2, ∞)
- (−∞, ∞)

**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 $\u20133$. The number is _________.

**Q.**Number of integral solutions of −5≤5−3x2≤8 is

- 7
- 6
- 8
- 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

- 4
- 6
- 5
- 3

**Q.**

The intervals of concavity and convexity of f(x)=e−x2 are

- Convex : (−∞, −√22)∪(√22, ∞)
- Concave:(−√22, √22)
- Concave : (−∞, −√22)∪(√22, ∞)
- Convex:(−√22, √22)

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

- 2
- 3
- 4
- 2.5

**Q.**

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

an isosceles triangle

an equilateral triangle

a scalene triangle

a right angles triangle

**Q.**The common solution set of 3x−7<5+x and 11−5x≤1 is

- (2, 6)
- [2, 6)
- [2, 6]
- (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

- (0, 6)
- (−4, 6)
- (−1, 6)
- (1, 6)

**Q.**I.Q. of a person is given by I=MC×100, where M is mental age and C is chronological age. If 80≤I≤140 for a group of 12 years old children, then the range of their mental age is

- [9.6, 16.8]
- (9.6, 16.8)
- [9, 16]
- (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

$12$

$9$

$8$

$6$

**Q.**Number of integral solutions of −5≤5−3x2≤8 is

- 7
- 6
- 8
- 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≥3x−5 and x∈R−, then x∈

- [−1, 0)
- (−1, 0]
- (−1, 0)
- [−1, 0]

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

- (86, 95)
- (85, 96)
- (80, 95)
- (80, 96)