Linear Inequalities Test -5

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Linear Inequalities Test -5

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Weekly Quiz Competition

Question 1

1 / -0

The table shown here contains pricing information for the chopper (a kitchen tool) that is advertised on television The price depends on how soon a customer calls after the end of the advertisement Approximately, how much more would a customer who orders 3 choppers, 23 minutes after the end of the television advertisement pay than a customer who orders 2 chopper, 17 minutes after the advertisement ?

Minutes (m) after television advertisement ends	Price per chopper (In Rs.)
$$\displaystyle 0\leq m\leq10$$	34.95
$$\displaystyle 10< m\leq20$$	39.95
$$\displaystyle 20< m\leq30$$	44.95
$$\displaystyle 30< m\leq40$$	49.95
$$\displaystyle m> 40$$	59.95

Rs 15

Rs 35

Rs 40

Rs 55

Solution

Question 2
1 / -0

The inequalities in which terms compared are never equal to each other is classified as

A
strict equality

B
strict inequality

C
strict quadres

D
differential quadrates

Solution

The inequalities in which the terms are never equal to each other are termed as $$strict$$ $$inequality$$
The inequality symbol in the strict inequality is either $$\gt$$ or $$\lt$$ i.e., it doesn't have any equality conditions.
Question 3
1 / -0

The point which does not belong to the feasible region of the LPP:
Minimize: $$Z=60x+10y$$
subject to $$3x+y \ge 18$$
$$2x+2y \ge 12$$
$$x+2y\ge 10$$
$$x,y \ge 0$$ is

A
$$(0,8)$$

B
$$(4,2)$$

C
$$(6,2)$$

D
$$(10,0)$$

Solution

We test whether the inequalitiies are satisfied or not
$$(0,8)$$, $$3(0)+8 \ge 8$$ $$8\ge 8$$ is true.
$$2(0)+2(8)=16\ge 12$$ is true.
$$0+2(8)=16 \ge 10$$ is true.
$$\therefore$$ $$(0,8)$$ is in the feasible region.
$$(4,2)$$, $$3(4)+2=14 \ge 8$$
$$2(4)+2(2)=16\ge 12$$
$$4+2(2)=8\ge 10$$ is not true
$$\therefore$$ $$(4,2)$$ is not a point in the feasible region
$$\therefore$$ (2) is correct
Question 4
1 / -0

Which of the following number line represents the solution of the inequality
$$-6x + 12 > -7x + 17$$ ?

A

B

C

D

Solution

Given, $$-6x+12>-7x+17$$
$$\Rightarrow -6x+7x>17-12$$
$$\Rightarrow x > 5$$
Hence, option A is correct.
Question 5
1 / -0

Sketch the solution to system of ineqalities
$$x\le -3$$
$$y < \frac{5}{3}x+2$$

A

B

C

D

Solution

Given, $$x\leq -3$$ and $$y<\dfrac{5}{3}x+2$$

first, draw the graph for equations $$x= -3$$ and $$y=\dfrac{5}{3}x+2$$

$$x=-3$$ is the line which is parallel to the y-axis and passes through (-3,0).
Hence, $$x\leq -3$$ includes the left side region of the line.

similarly, for $$y=\dfrac{5}{3}x+2$$
substitute y=0 we get, $$\dfrac{5}{3}x=-2 \implies x=-\dfrac{6}{5}=-1.2$$
substitute x=0 we get, $$y=2$$
therefore, $$y=\dfrac{5}{3}x+2$$ line passes through $$(-1.2,0)$$ and $$(0,2)$$.
Hence, $$y<\dfrac{5}{3}x+2$$ includes the region below the line.

Option D satisfies the above conditions.
Question 6
1 / -0

A graph and the system of inequalities are shown above. Which region of the graph could represent the solution for the system of in equations?
$$y > x$$
$$3y≤-4x+6$$

A
$$A$$

B
$$B$$

C
$$C$$

D
$$D$$

Solution

given $$y>x$$

and $$3y\leq -4x+6$$

first, draw the graph for equations $$y =x$$ and $$3y= -4x+6$$

$$y=x$$ is the line which passes through the origin as shown in the above fig
Hence, $$y>x$$ includes the above region of the line.

similarly, for $$3y= -4x+6$$
substitute y=0 we get, $$-4x+6=0 \implies x=1.5$$
substitute x=0 we get, $$3y=6 \implies y=2$$

therefore, $$3y= -4x+6$$ line passes through (1.5,0) and (0,2) as shown in fig.
Hence, $$3y\leq -4x+6$$ includes the region below the line.

the intersection region is the D region as shown in above figure.
Question 7
1 / -0

If the solution set for the system $$\begin{cases} y>x \\ y\le -\dfrac { 3 }{ 7 } x+5 \end{cases}$$ is given by the above figure, then which of the following is NOT a solution to the system?

A
$$(0,3)$$

B
$$(1,2)$$

C
$$(2,4)$$

D
$$(3,3)$$

Solution

As per the given figure, $$(0,3)$$ and $$(1,2)$$ lie in the desired region, hence these are solutions of the system.
Whereas $$(2,4)$$ and $$(3,3)$$ lie on the lines but $$(3,3)$$ does not satisfy the equation $$y>x$$.
Hence, it is not a solution to the system.
Question 8
1 / -0

Which equation has the solution shown on the number line?

A
$$-3 > x > -1$$

B
$$-5 < x < -2$$

C
$$-2 > x > 0$$

D
$$-1 > x > -6$$

Solution

Since shaded region on the graph is from $$-5$$ to $$-2$$
So solution is $$-5<x<-2$$
Hence, option B is correct.
Question 9
1 / -0

Which of the following is the correct graph for $$x\ge 3$$ or $$x\le -2$$?

A
Line A

B
Line B

C
Line C

D
Line D

E
Line E
Question 10
1 / -0

Directions For Questions

Solve the linear inequations graphically:
$$2x+3y > 2$$
$$x-y < 0$$
$$y \geq 0$$
$$x \leq 3$$

...view full instructions

Which quadrant does the solution lie in?

A
$$I$$

B
$$II$$

C
$$III$$

D
$$IV$$

Solution

Given, $$2x+3y>2$$
$$x-y<0 \implies y>x$$
$$y\geq 0$$
$$x\leq 3$$
first, draw the graph for equations $$2x+3y=2$$
$$x-y=0 \implies x=y$$
$$y= 0 \implies x-axis$$
$$x= 3$$

$$x=y$$ is the line which passes through the origin as shown in the above fig
Hence, $$y>x$$ includes the above region of the line.

$$y= 0 \implies x-axis$$. Hence, $$x\leq 3$$ includes the left region of the line.

$$x= 3 \implies $$line parallel to x-axis. Hence, $$x\leq 3$$ includes the left region of the line.

for $$2x+3y=2$$
substituting y=0, we get $$2x=2\implies x=1$$
substituting x=0, we get $$3y=2\implies y=\dfrac{2}{3}$$
Therefore, line $$2x+3y=2$$ passes through (1,0) and (0,2/3) as shown in the above figure
Hence, $$2x+3y>2$$ includes the above region of the line.

Therefore, the blue shaded region is the feasible region which is present in I quadrant as shown in the figure.