Different Types of Intervals in Inequality

Q.

Find the general solution for the following equation:

cos 3x+ cos x - cos 2x = 0

Q.

Solve $12+1\frac{5}{6}x\le 5+3x$ when

$\left(i\right)xϵN$

$\left(ii\right)xϵR$

Draw the graph of the solution set in each case.

Q. If $x\in (-2,6]$, then $(x^2-2)$ lies in

1. $[-2,34]$
2. $[2,34]$
3. $(-2,34]$
4. $(2,34]$

Q. 1.Solve 24x < 100, when(i)xis a natural number.(ii) x is an integer.

Q. 3.Solve 5x - 3<7, when(i) x is an integer.(ii) x is a real number.

Q.

In the following, X will be:

1. 

2. 

3. 

4. 

Q. 2. Solve- 12x> 30, when(i)xis a natural number.(ii) x is an integer.

Q. 13. 4x+3y s60, y 22x, x23, x, y2(0

Q. x(5x-2) (7x-3)스>20. 2

Q.

Solve the inequalities in Exercieses 7 to 10 and represent the solution graphically on number line:

$5(2x-7)-3(2x+3)\le 0,2x+19\le 6x+47$

Q.

Solve the inequalities in Exercieses 7 to 10 and represent the solution graphically on number line:

2(x-1)< x+5, 3(x+2)>2-x

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. 18. 5x 3 2 3x 5

Q. 7. 2x+y26

Q. 5. 2x - y >1, x 2y-1

Q. x (5x-2) (7x-3)4.15.

Q. 2. 3x + 2ys 12, x2 1, y 2 2

Q. 4.Solve 3x +8 >2, when(i) x is an integer.(ii) x is a real number.

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.

Solve

$\frac{x-3}{x+1}<0,xϵR$

Q. If $x\in [-3,2]$, then $2x+7$ lies in

1. $[-1,9]$
2. $[1,11]$
3. $[-1,11]$
4. $[1,10]$

Q. A material has Poisson's ratio $0.5$. If a uniform rod made of the material suffers a longitudinal strain of $2\times {10}^{-3}$, what is the percentage increase in volume?

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

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. 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. 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. $(80,96)$

Q. If $x\in R$ and $x+\frac{x}{2}+\frac{x}{4}<7$, then $x$ lies in

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

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

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

Q. 10. 5 (2r 7) 3 (2x +3) s0, 2x 19 s6x47

Q. 17. 3x -2<2x 1

Q. 4. y82 2x