MCQ

MCQ 11 Mark

If $|x−1| x - 1 > 5,$ then :

A
$\text{x}\in(-4,6)$
B
$\text{x}\in[-4,6]$
✓
$\text{x}\in(-\infty,-4)\cup(6,\infty)$
D
$\text{x}\in(-\infty,-4)\cup[6,\infty)$

Answer

Correct option: C.

$\text{x}\in(-\infty,-4)\cup(6,\infty)$

$|x−1| > 5$
$\Rightarrow x − 1 > 5$ or $x − 1 < −5$
$\Rightarrow x > 5 + 1$ or $x < −5 + 1$
$\Rightarrow x > 6$ or $x < −4$
$\Rightarrow\text{x}\in(-\infty,-4)\cup(6,\infty)$

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MCQ 21 Mark

If $− 3x + 17 < -13,$ then :

✓
$\text{x}\in(10,\infty)$
B
$\text{x}\in[10,\infty)$
C
$\text{x}\in(-\infty,10]$
D
$\text{x}\in[-10,10)$

Answer

Correct option: A.

$\text{x}\in(10,\infty)$

$− 3x + 17 < −13$
Subtracting $17$ on both sides, we get
$\Rightarrow −3x + 17 − 17 < −13 − 17$
$\Rightarrow −3x < − 30$
Dividing $−3$ on both sides, we get
$\Rightarrow\frac{-3\text{x}}{-3}>\frac{-30}{-3}$
$\Rightarrow\text{x}>10$
$\Rightarrow\text{x}\in(10,\infty)$

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MCQ 31 Mark

If $\frac{|\text{x}-2|}{\text{x}-2}\geq0,$ then :

A
$\text{x}\in[2,\infty)$
✓
$\text{x}\in(2,\infty)$
C
$\text{x}\in(-\infty,2)$
D
$\text{x}\in(-\infty,2]$

Answer

Correct option: B.

$\text{x}\in(2,\infty)$

$|\text{x}+2|\leq5$
$\Rightarrow-5\leq\text{x}+2\leq5$
$\Rightarrow-5-2\leq\text{x}+2-2\leq5-2$
$\Rightarrow-7\leq\text{x}\leq3$
$\Rightarrow\text{x}\in[-7,3]$
$\text{x}\in(2,\infty)$

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MCQ 41 Mark

If $x$ is a real number and $|x| < 5,$ then :

A
$\text{x}\geq5$
✓
$-5<\text{x}<5$
C
$\text{x}\leq-5$
D
$-5\leq\text{x}\leq5$

Answer

Correct option: B.

$-5<\text{x}<5$

If $x$ is a real number.
$|x| < 5$
$\Rightarrow -5 < x < 5$

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MCQ 51 Mark

If $\text{|x}+2|\leq9,$ then :

A
$\text{x}\in(-7,11)$
B
$\text{x}\in[-11,7]$
✓
$\text{x}\in(-\infty,-7)\cup(11,\infty)$
D
$\text{x}\in(-\infty,-7)\cup[11,\infty)$

Answer

Correct option: C.

$\text{x}\in(-\infty,-7)\cup(11,\infty)$

$|\text{x}+2|\leq9$
$\Rightarrow-9\leq\text{x}+2\leq9$
$\Rightarrow-9-2\leq\text{x}+2-2\leq9-2$
$\Rightarrow-11\leq\text{x}\leq7$
$\Rightarrow\text{x}\in[-11,7]$
$\text{x}\in(-\infty,-7)\cup(11,\infty)$

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MCQ 61 Mark

If $|\text{x}+3|\geq10,$ then :

A
$\text{x}\in(-12,7]$
B
$\text{x}\in(-13,7)$
C
$\text{x}\in(\infty,-13)\cup(7,\infty)$
✓
$\text{x}\in(-\infty,-13]\cup[7,\infty)$

Answer

Correct option: D.

$\text{x}\in(-\infty,-13]\cup[7,\infty)$

$|\text{x}+3|\geq10$
$\Rightarrow\text{x}+3\geq10$ or $\text{x}+3;\leq-10$
$\Rightarrow\text{x}\geq10-3$ or $\text{x}\leq-10-3$
$\Rightarrow\text{x}\geq7$ or $\ \text{x}\leq-13$
$\Rightarrow\text{x}\in(-\infty,-13)\cup[7,\infty)$

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MCQ 71 Mark

The solution set of the inequation $|\text{x}+2|\leq5$ is :

A
$(-7, 5)$
✓
$[-7, 3]$
C
$[-5, 5]$
D
$(-7, 3)$

Answer

Correct option: B.

$[-7, 3]$

$|\text{x}+2|\leq5$
$\Rightarrow-5\leq\text{x}+2\leq5$
$\Rightarrow-5-2\leq\text{x}+2-2\leq5-2$
$\Rightarrow-7\leq\text{x}\leq3$
$\Rightarrow\text{x}\in[-7,3]$

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MCQ 81 Mark

If $x < 7,$ then :

A
$-\text{x}<-7$
B
$-\text{x}\leq-7$
✓
$-\text{x}>-7$
D
$-\text{x}\geq-7$

Answer

Correct option: C.

$-\text{x}>-7$

$x < 7$
subtracting $x$ on both sides, we get
$\Rightarrow x − x < 7 − x$
$\Rightarrow 0 < 7 − x$
subtracting $7$ on both sides, we get
$\Rightarrow 0 − 7 < 7 − x − 7$
$\Rightarrow −7 < − x$
$\Rightarrow − x > −7$

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MCQ 91 Mark

If $x$ and $a$ are real numbers such that $a > 0$ and $|x| > a,$ then :

A
$\text{x}\in(-\text{a},\infty)$
B
$\text{x}\in[-\infty,\text{a}]$
C
$\text{x}\in(-\text{a},\text{a})$
✓
$\text{x}\in(-\infty,-\text{a})\cup(\text{a},\infty)$

Answer

Correct option: D.

$\text{x}\in(-\infty,-\text{a})\cup(\text{a},\infty)$

If $x$ and $a$ are real numbers such that $a > 0$.
$|x| > a$
$\Rightarrow x > a$ or $x < −a$
$\Rightarrow\text{x}\in(-\infty,-\text{a})\cup(\text{a},\infty)$

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MCQ 101 Mark

The linear inequality representing the solution set given in Fig. is :

A
$\text{|x|}<5$
B
$\text{|x|}>5$
✓
$\text{|x|}\geq5$
D
$\text{|x|}\geq5$

Answer

Correct option: C.

$\text{|x|}\geq5$

As according to the graph,
$x$ lies between $(-\infty,-5]$ and $[5,\infty)$
$\Rightarrow\text{x}\geq5$ or $\text{x}\leq-5$
$\Rightarrow|\text{x}|\geq5$

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MCQ 111 Mark

Given that $x, y$ and $b$ are real numbers and $x < y, \ b > 0,$ then :

✓
$\frac{\text{x}}{\text{b}}<\frac{\text{y}}{\text{b}}$
B
$\frac{\text{x}}{\text{b}}\leq\frac{\text{y}}{\text{b}}$
C
$\frac{\text{x}}{\text{b}}>\frac{\text{y}}{\text{b}}$
D
$\frac{\text{x}}{\text{b}}\geq\frac{\text{y}}{\text{b}}$

Answer

Correct option: A.

$\frac{\text{x}}{\text{b}}<\frac{\text{y}}{\text{b}}$

Given that $x, y$ and $b$ are real numbers and $x < y, \ b > 0.$
Both sides of an inequality can be multiplied or divided by the same positive number.
$\therefore\frac{\text{x}}{\text{b}}<\frac{\text{y}}{\text{b}}$

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MCQ 121 Mark

The inequality representing the following graph is :

A
$\text{|x|}<3$
✓
$\text{|x|}\leq3$
C
$\text{|x|}>3$
D
$\text{|x|}\geq3$

Answer

Correct option: B.

$\text{|x|}\leq3$

As according to the graph,
$x$ lies between $−3$ and $3$
$\Rightarrow-3\leq\text{x}\leq3$
$\Rightarrow|\text{x}|\leq3$

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