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MATHS MCQ

Linear Inequations · Gujarat Board (GSEB) STD 11 Science (GSEB - English Medium). 12 questions.

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12 questions · auto-graded multiple-choice test.

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
⇒ x − 1 > 5 or x − 1 < −5
⇒ x > 5 + 1 or x < −5 + 1
⇒ 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
⇒ −3x + 17 − 17 < −13 − 17
⇒ −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:
  • ✓
    $\text{x}\in[2,\infty)$
  • B
    $\text{x}\in(2,\infty)$
  • C
    $\text{x}\in(-\infty,2)$
  • D
    $\text{x}\in(-\infty,2]$
Answer
Correct option: A.
$\text{x}\in[2,\infty)$
$\text{x}\in[2,\infty)$
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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
⇒ -5 < x < 5
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MCQ 51 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.
$\text{x}\in[-11,7]$
$|\text{x}+2|\leq9$
$\Rightarrow-9\leq\text{x}+2\leq9$
$\Rightarrow-9-2\leq\text{x}+2-2\leq9-2$
$\Rightarrow-11\leq\text{x}\leq7$
$\Rightarrow\text{x}\in[-11,7]$
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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.
$\text{x}\in(-\infty,-13]\cup[7,\infty)$
$|\text{x}+3|\geq10$
$\Rightarrow\text{x}+3\geq10\text{ or }\text{x}+3;\leq-10$
$\Rightarrow\text{x}\geq10-3\text{ or }\text{x}\leq-10-3$
$\Rightarrow\text{x}\geq7\ \text{or}\ \text{x}\leq-13$
$\Rightarrow\text{x}\in(-\infty,-13)\cup[7,\infty)$
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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
⇒ x − x < 7 − x
⇒ 0 < 7 − x
subtracting 7 on both sides, we get
⇒ 0 − 7 < 7 − x − 7
⇒ −7 < − x
⇒ − 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
⇒ 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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