Linear Inequalities Test -6

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Linear Inequalities Test -6

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Weekly Quiz Competition

Question 1
1 / -0

A pack of coffee powder contains a mixture of x grams of coffee and y grams of choco. The amount of coffee is greater than that of choco and each coffee powder pack is atmost 10 grams. Which of the following inequations describe the conditions given ?

A
x + y < 12 ; x > y

B
x + y < 10 ; x < y

C
x + y ≤ 10 ; x > y

D
none of these

Solution

Given in the mixture ,amount of coffee= x grams

Amount of choco=y grams

Amount of coffee is greater than that of choco ⇒ x > y

Each coffee powder pack is atmost 10 grams ⇒ x + y ≤ 10
Question 2
1 / -0

If a, b ,c are real numbers such that a > b , c > 0, then

A
ac ≥ bc

B
ac > bc

C
ac < bc

D
none of these.

Solution

The inequality remains same if both sides of an inequality are multiplied by the same positive real number.
Question 3
1 / -0

If a , b , c are real numbers such that a ≥ b , c > 0, then

A
ac > bc

B
ac < bc

C
ac ≥ bc

D
none of these

Solution

The inequality remains same if both sides of an inequality are multiplied by the same positive real number.
Question 4
1 / -0

Graph of the system of inequations x ≥ 0 , y ≤ 0 is

A
second quadrant

B
first quadrant

C
third quadrant

D
4^th quadrant

Solution

The solution region of x ≥ 0 will be the half of XY –plane which lies on the right of y – axis , including the points on y – axis [ First and Fourth quadrants ]

The solution region of y ≤ 0 will be the half of XY –plane which lies under x – axis , including the points on x – axis [ Third and Fourth quadrants ]

Hence the solution region of x ≥ 0 , y ≤ 0 will be the the intersection of the above two regions ,which is the fourth quadrant.
Question 5
1 / -0

Which equation has the solution shown on the number line?

A
$$x \geq 1$$

B
$$x \geq -6$$

C
$$x\leq 6$$

D
$$x < 0$$

Solution

The red line represents all the numbers that satisfy the equation $$x \leq 6$$.
Question 6
1 / -0

Which of the following could be the graph of all values of $$x$$ that satisfy the inequality $$2-5x\le -\cfrac{6x-5}{3}$$

A

B

C

D

E

Solution

$$2-5x\le\dfrac{-(6x-5)}{3}$$

$$\Rightarrow 6-15x\le\, -6x+5$$

$$\Rightarrow 1\le 9x$$

$$\Rightarrow \dfrac{1}{9} \le x$$

$$\Rightarrow x\ge \dfrac{1}{9} $$
Question 7
1 / -0

Solve the inequality: $$-3x + 4 < -8$$

A
$$x>4$$

B
$$x<4$$

C
$$x>-4$$

D
None of these

Solution
Question 8
1 / -0

The shaded region is represented by the inequality:

A
$$\displaystyle y-2x\leq -1$$

B
$$\displaystyle x-2y\leq -1$$

C
$$\displaystyle y-2x\geq -1$$

D
$$\displaystyle x-2y\geq -1$$

Solution

The equation of the line is given as
$$y-2x=-1$$
Now the shading is away from the origin.
Hence, at y=0 and x=0 the inequality is not true.
we know
$$0>-1$$
Hence at origin, the inequality must be of the type
$$0<-1$$ ....(since inequality is not true at origin).
Hence $$y-2x<-1$$
Also the points on the line is a part of the inequality.
Hence
$$y-2x\leq -1$$
Question 9
1 / -0

The graph of which inequality is shown below:

A
$$\displaystyle y-x\leq 0$$

B
$$\displaystyle x-y\leq 0$$

C
$$\displaystyle y+x\leq 0$$

D
None of the above

Solution

The equation of the above straight line is
$$y=-x$$
or
$$x+y=0$$.
Now the shading in the above graph is towards the negative part (where x is negative).
Also the line is dark and not dotted.This indicates that the points on the line are part of the inequality.
Hence the required inequality is
$$x+y\leq 0$$.
Question 10
1 / -0

Which of the following inequations represents the shaded region?

A
$$\displaystyle 2x+y\leq 4$$

B
$$\displaystyle 2x+y\geq 4$$

C
$$\displaystyle x+2y\leq 4$$

D
$$\displaystyle x+2y\geq 4$$

Solution

The line passes through $$(0,4)$$ and $$(2,0)$$
Hence equation of the line
$$\dfrac{y}{4}+\dfrac{x}{2}=1$$
$$2x+y=4$$
Now in the above inequality graph the shading is done towards the origin.
Hence by substituting
$$x=0,y=0$$ we get an inequality which is true.
Hence the possible inequality is $$2x+y<4$$
Now the straight line is dark and not dotted. This indicates that the points on the line are a part of the inequality.
Hence the inequality can be written as
$$2x+y=4$$ or $$2x+y<4$$
$$2x+y\leq 4$$.
Question 11
1 / -0

The shaded region is represented by the inequation:

A
$$\displaystyle y\geq x$$

B
$$\displaystyle y\geq- x$$

C
$$\displaystyle y\geq \left | x \right |$$

D
$$\displaystyle y\leq \left | x \right |$$

Solution

The equations of both the lines in the above graph are
$$y=-x$$ and $$y=x$$
Hence if we put them together we get
$$y=|x|$$
Now
Let us take a point inside the shaded region.
Let it be $$(0,2)$$
Now
$$2>0$$
$$y>|x|$$
Hence the required inequality is
$$y\geq |x|$$.
Question 12
1 / -0

The locus represented by equation |z i| + |z + i| $$=$$ 1 on Argand plane

A
ellipse

B
hyperbola

C
straight line

D
no locus
Question 13
1 / -0

In given figure, number line represents the solution of inequality ____ .

A
$$\displaystyle 2x-4<16$$

B
$$\displaystyle 2x-6<10$$

C
$$\displaystyle 2x-6>12$$

D
$$\displaystyle 2x-4>16$$

Solution

$$\displaystyle 2x-6<10\Rightarrow 2x< 16\Rightarrow x<8$$
Question 14
1 / -0

The above diagram shows a number line.
The above number line represents the solution for

A
$$-3\leq x$$ and $$x> 4$$

B
$$-3< x< 4$$

C
$$-3\leq x< 4$$

D
$$-3< x$$ and $$x\leq 4$$

Solution

From the given diagram, the number line is representing the value $$\ge -3 $$ and $$< 4$$.
Hence, C will be correct answer.