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Linear Inequations Mathematics - Linear Inequations

ICSE - STD 10 - Mathematics (ICSE - English Medium). 57 questions in this chapter.

Question types

Linear Inequations question types

57 questions across 5 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.

57
Questions
5
Question groups
5
Question types
Sample Questions

Linear Inequations questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 9[2 Mark Question Answer]2 Marks
One-third of a bamboo pole is buried in mud, one-sixth of it is in water and the part above the water is greater than or equal to 3 metres. Find the length of the shortest pole.
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Q 11[3 marks sum]3 Marks
Solve the inequation and represent the solution set on the number line.
$
-3+x \leq \frac{8 x}{3}+2 \leq \frac{14}{3}+2 x \text {, Where } x \in I
$
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Q 13[3 marks sum]3 Marks
Solve the following inequation and represent the solution set on the number line:
$
4 x-19<\frac{3 x}{5}-2 \leq-\frac{2}{5}+x, x \in R
$
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Q 14[3 marks sum]3 Marks
A = {x : 11x – 5 > 7x + 3, x ∈R} and B = {x : 18x – 9 ≥ 15 + 12x, x ∈R}. Find the range of set A ∩ B and represent it on a number line
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Q 15[3 marks sum]3 Marks
Solve the inequation : $-2 \frac{1}{2}+2 x \leq \frac{4 x}{3} \leq \frac{4}{3}+2 x, x \in W$. Graph the solution set on the number line.
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Q 16[4 marks sum]4 Marks
Given: P {x : 5 < 2x – 1 ≤ 11, x∈R)
Q{x : – 1 ≤ 3 + 4x < 23, x∈I) where
R = (real numbers), I = (integers)
Represent P and Q on number line. Write down the elements of P ∩ Q.
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Q 17[4 marks sum]4 Marks
Solve the following inequation and represent the solution set on the number line:
$
-3<-\frac{1}{2}-\frac{2 x}{3} \leq \frac{5}{6}, x \in R
$
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Q 18MCQ1 Mark
If $x \in R$, the solution set of $6 \leq-3(2 x-4)<12$ is
  • A
    $\{x: x \in R, 0\}$
  • ✓
    $\{x: x \in R, 0 \leq x<1\}$
  • C
    $\{0,1\}$
  • D
    none of these

Answer: B.

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Q 19MCQ1 Mark
If $x \in I$, then the solution set of the inequation $1<3 x+5 \leq 11$ is
  • ✓
    $\{-1,0,1,2\}$
  • B
    $\{-2,-1,0,1\}$
  • C
    $\{-1,0,1\}$
  • D
    $\left\{x: x \in R ,-\frac{4}{3} < x \leq 2\right\}$

Answer: A.

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Q 20MCQ1 Mark
If $x \in W$, then the solution set of the inequation $5-4 x \leq 2-3 x$ is
  • A
    $\{1,2,3\}$
  • B
    $\{0,1,2,3\}$
  • ✓
    $\{x: x \in R, x \leq 3\}$
  • D
    $\{3,4,5, \ldots\}$

Answer: C.

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Q 21MCQ1 Mark
If $x \in W$, then the solution set of the inequation $3 x+11 \geq x+8$ is
  • A
    $\{-2,-1,0,1,2, \ldots\}$
  • B
    $\{-1,0,1,2, \ldots\}$
  • ✓
    $\{0,1,2,3, \ldots\}$
  • D
    $\left\{x: x \in R , x \geq-\frac{3}{2}\right\}$

Answer: C.

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Q 22MCQ1 Mark
If $x \in\{-3,-1,0,1,3,5\}$, then the solution set of the inequation $3 x-2 \leq 8$ is
  • A
    $\{-3,-1,1,3\}$
  • ✓
    $\{-3,-1,0,1,3\}$
  • C
    $\{-3,-2,-1,0,1,2,3\}$
  • D
    $\{-3,-2,-1,0,1,2\}$

Answer: B.

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