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CBSE Questions for Class 11 Engineering Maths Linear Inequalities Quiz 1 - MCQExams.com
CBSE
Class 11 Engineering Maths
Linear Inequalities
Quiz 1
Which equation has the solution shown on the number line?
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$$1\leq x < 4$$.
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$$x < 1$$
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$$x\neq 1$$
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$$x < 0$$
Explanation
The red line represents all the numbers that satisfy the equation $$1\leq x < 4$$.
Ordered pair that satisfy the equation $$x + y + 1 < 0$$ is:
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$$(0, -1)$$
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$$(-2 , 0)$$
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$$(2, - 4)$$
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Both (B) and (C)
Explanation
Given inequation is $$x+y+1<0$$
From option A, $$0+\left ( -1 \right )+1 <0 $$
$$ \Rightarrow 0<0 $$ which is false
Hence, $$(0,-1)$$ is not a solution.
From option B, $$-2+0+1 <0 $$
$$ \Rightarrow -1<0 $$ which is true
Hence, $$(-2,0)$$ there is a solution
From option C, $$2-4+1 <0 $$
$$ \Rightarrow -1<0 $$ which is true.
Hence, $$(2,-4)$$ is a solution
Hence, Option B and C are the solutions.
Which of the following number line represents the solution of the inequality
$$15 < 4x + 3 \le 31$$ ?
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0%
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Explanation
$$15 < 4x + 3 \le 31$$ ........... (Given)
$$\implies 15-3 < 4x+3-3 \leq 31-3$$
$$\implies 12 < 4x \leq 28$$
$$\implies 3 < x \le 7$$ ......... (Divided by $$4$$)
Hence, option C is correct.
Which equation has the solution shown on the number line?
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$$x \geq 1$$
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$$x \geq -6$$
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$$x\neq 1$$
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$$x < 0$$
Explanation
The red line represents all the numbers that satisfy the equation $$x \geq -6$$.
If you multiply an inequality by a negative number, when should you reverse the inequality symbol?
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Always
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Never
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Sometimes
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Only if the negative number is a fraction
Explanation
If we take $$x\leq y$$ then $$-x\geq -y$$ always.
Thus, the inequality gets reversed always when multiplied by negative number.
Hence, option A is correct.
Which equation has the solution shown on the number line?
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$$-3\leq x < 0 $$.
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$$3\leq x < 6 $$.
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$$x\neq 1$$
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$$x < 0$$
Explanation
The red line represents all the numbers that satisfy the equation $$-3\leq x < 0 $$.
Find solution of following inequality also show it graphically.
$$x<5,x\in W$$.
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Explanation
Given, $$x<5$$ and $$x \in W$$
Natural numbers are counting numbers whose set is $$W=\{0,1,2,3,...\}$$
Therefore,$$\{0,1,2,3,4\}$$ represents
$$x<5$$
Option A graph has
$$\{0,1,2,3,4\}$$ solution set.
Solve the following inequality and show it graphically:
$$-2<x+3<5,x\in Z$$
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Explanation
Given, $$-2<x+3<5$$
Subtracting $$3$$ from all sides, we get
$$-2-3<x+3-3<5-3$$
$$-5<x<2$$
Thus $$x$$ will contain all the points between $$-5$$ and $$2$$ except point $$-5$$ and $$2$$.
Which of the following number line represents the solution of the inequality $$2x+1 \ge 9$$?
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0%
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Explanation
Given, $$ 2x+1 \geq 9$$
$$\Rightarrow 2x \geq 9-1$$
$$\Rightarrow 2x\geq 8$$
$$\Rightarrow x \geq 4$$
$$\therefore$$Solution $$=$$ $$x \geq 4$$
Hence, option $$A$$ is the answer.
Find the solution of following inequality, also show it graphically:
$$x<4,x\in R$$
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0%
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Explanation
$$x<4$$ and $$x\in R$$
means x takes all real values less than 4.(but not 4)
So It is interval $$(-\infty,4)$$
The graph is option C.
Which equation has the solution shown on the number line?
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$$x \geq 1$$
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$$x \geq -6$$
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$$x\leq 6$$
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$$x < 0$$
Explanation
The red line represents all the numbers that satisfy the equation $$x \leq 6$$.
Which of the following could be the graph of all values of $$x$$ that satisfy the inequality $$2-5x\le -\cfrac{6x-5}{3}$$
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Explanation
$$2-5x\le\dfrac{-(6x-5)}{3}$$
$$\Rightarrow 6-15x\le\, -6x+5$$
$$\Rightarrow 1\le 9x$$
$$\Rightarrow \dfrac{1}{9} \le x$$
$$\Rightarrow x\ge \dfrac{1}{9} $$
Solve the inequality: $$-3x + 4 < -8$$
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$$x>4$$
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$$x<4$$
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$$x>-4$$
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None of these
The above diagram shows a number line.
The above number line represents the solution for
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$$-3\leq x$$ and $$x> 4$$
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$$-3< x< 4$$
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$$-3\leq x< 4$$
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$$-3< x$$ and $$x\leq 4$$
Explanation
From the given diagram, the number line is representing the value $$\ge -3 $$ and $$< 4$$.
Hence, C will be correct answer.
A pack of coffee powder contains a mixture of x gms of coffee and y gms of choco. The amount of coffee powder is greater than that of chocolate and each pack weights at least 10 g. Which of the following inequalities describe the given condition?
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$$x < y$$
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$$x+y\geq 10$$
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$$x+y\leq 10$$
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$$x > y$$
Explanation
The coffee powder is greater than choco
hence, $$x > y$$
each pack is at least 10 gm
hence, $$x + y \ge 10$$
The shaded region is represented by the inequality:
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$$\displaystyle y-2x\leq -1$$
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$$\displaystyle x-2y\leq -1$$
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$$\displaystyle y-2x\geq -1$$
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$$\displaystyle x-2y\geq -1$$
Explanation
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
$$y-2x\leq -1$$
The graph of which inequality is shown below:
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$$\displaystyle y-x\leq 0$$
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$$\displaystyle x-y\leq 0$$
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$$\displaystyle y+x\leq 0$$
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None of the above
Explanation
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
$$x+y\leq 0$$.
Which region is described by the shade in the graph given above?
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$$2x+3y=3$$
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$$2x+3y< 3$$
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$$2x+3y> 3$$
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$$-2x+3y< 3$$
Explanation
The line represents $$2x+3y=3$$
Writing it in intercept form, we get
$$\dfrac{x}{3/2}+\dfrac{y}{1}=1$$
Hence, $$x$$ intercept is $$1.5$$ units and $$y$$ intercept is $$1$$ unit.
Consider any arbitrary point in the shaded region such that it does not lie on the line $$2x+3y=3$$.
Let us consider $$(4,4)$$:
$$(4,4) $$ clearly does not lie on the line but it does lie in the shaded region.
$$2(4)+3(4)=20$$ and $$20>3$$
Therefore in the shaded region $$2x+3y>3$$
Since the line on the graph is not dotted, therefore the shaded region includes
$$2x+3y=3$$ or $$2x+3y>3$$
Hence, $$2x+3y\geq3$$
Identify the region described by the shaded part in the graph above.
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$$y=4x-6$$
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$$y\neq 4x-6$$
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$$y< 4x-6$$
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$$y> 4x-6$$
Explanation
The line represents the linear equation $$y=4x-6$$
Any other region on the given figure represents $$y\neq4x-6$$ ..$$(i)$$
Now writing the given equation in intercept form, we get
$$4x-y=6$$
$$\Rightarrow \dfrac{x}{\frac{6}{4}}-\dfrac{y}{6}=1$$
Therefore the line cuts the $$x$$-axis at $$x=\dfrac{6}{4}$$ and $$y$$-axis at $$-6$$.
Now consider an arbitrary point in the shaded region $$(x,y)$$ which does not lie on the line to check the inequality.
Consider point $$(10,10)$$
$$4x-6=40-6=34$$ and $$y=-6$$.
Hence, $$y<4x-6$$
Similarly, we can check the inequality for the shaded region by substituting points in that region, which do not lie on the line, and by comparing $$y$$ and $$4x-6$$
Hence, the correct answers are options B and C.
In given figure, number line represents the solution of inequality ____ .
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$$\displaystyle 2x-4<16$$
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$$\displaystyle 2x-6<10$$
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$$\displaystyle 2x-6>12$$
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$$\displaystyle 2x-4>16$$
Explanation
$$\displaystyle 2x-6<10\Rightarrow 2x< 16\Rightarrow x<8$$
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