M.C.Q (1 Marks)

MCQ 11 Mark

If $x$ is a real number and $|x| < 3,$ then:

A
$\text{x}\geq3$
✓
$-3<\text{x}<3$
C
$\text{x}\leq-3$
D
$-3\leq\text{x}\leq3$

Answer

Correct option: B.

$-3<\text{x}<3$

Given that $|x| < 3$
$\Rightarrow -3 < x < 3 | x | < a$
$\Rightarrow -a < x < a.$

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MCQ 21 Mark

If $x < 5,$ then.

A
$-\text{x} < – 5 $
B
$-\text{x}\leq-5$
✓
$-\text{x} > – 5 $
D
$-\text{x}\leq-5$

Answer

Correct option: C.

$-\text{x} > – 5 $

If $x > 5$ then $- x > - 5.$

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MCQ 31 Mark

Solution of a linear inequality in variable $x$ is represented on number line.

✓
$\text{x}\in\big(-\infty,\frac{7}{2}\big)$
B
$\text{x}\in\big(-\infty,\frac{7}{2}\big]$
C
$\text{x}\in\big(\frac{7}{2},-\infty\big)$
D
$\text{x}\in\big(\frac{7}{2},\infty\big)$

Answer

Correct option: A.

$\text{x}\in\big(-\infty,\frac{7}{2}\big)$

The given graph all real values of $x$ greater than and equal $\frac{7}{2}$ on real number line.
So, $\text{x}\in\big(-\infty,\frac{7}{2}\big)$

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MCQ 41 Mark

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

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

Answer

Correct option: B.

$\text{x}\in[-11, 7]$

Given that $|\text{x}+2|\leq9$
$\Rightarrow-9\leq\text{x}+2\leq9$
$\Rightarrow-9-2\leq\text{x}\leq9-2[|\text{x}\leq\text{a}|]$
$\Rightarrow-11\leq\text{x}\leq7$
$\Rightarrow\text{x}\in[-11, 7]$

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MCQ 51 Mark

If $|x - 1| > 5,$ 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) $

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

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MCQ 61 Mark

$x$ and $b$ are real numbers. If $b > 0$ and $|x| > b,$ then:

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

Answer

Correct option: D.

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

Given that $|x| > b, b > 0$
$\Rightarrow x < -b$ or $x > b$
$\Rightarrow\text{x}\in(-\infty,-\text{b})\cup(\text{b,}\infty)$

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MCQ 71 Mark

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

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

Answer

Correct option: C.

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

Given that $x < y, b < 0$
$\Rightarrow\frac{\text{x}}{\text{b}}>\frac{\text{y}}{\text{b}},\text{b}<0$

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MCQ 81 Mark

If $– 3x + 17 < – 13,$ then:

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

Answer

Correct option: A.

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

Given that $- 3x + 17 < - 13$
$\Rightarrow - 3x < - 17 - 13$
$\Rightarrow -3x < - 30$
$\Rightarrow 3x > 30$
$\Rightarrow x > 10$
$\Rightarrow\text{x}\in(10, \infty)$

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Maths M.C.Q (1 Marks)

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