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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-19-CT
Linear Inequations — Full Chapter Test
Chapter: Linear Inequations
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Multiplying an inequation by a negative number:
  • A.keeps the sign
  • B.reverses the sign
  • C.makes it $=$
  • D.removes it
2.
$x>3$ is shown by:
  • A.closed circle at $3$
  • B.open circle at $3$, arrow right
  • C.closed circle, arrow left
  • D.a solid line
3.
The solution of $2x>6$ is:
  • A.$x>3$
  • B.$x<3$
  • C.$x>6$
  • D.$x\ge3$
4.
A closed circle means the endpoint is:
  • A.excluded
  • B.included
  • C.infinite
  • D.negative
5.
The set from which solutions are chosen is the:
  • A.solution set
  • B.replacement set
  • C.null set
  • D.universal set
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Solve $3x\le12$ for $x\in\mathbb{R}$.
7.
How is $x>2$ marked at $2$?
8.
Solve $-2x<8$.
9.
How is $x\le4$ marked at $4$?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Solve $3x-2<7$ for $x\in\mathbb{N}$ and list the solution set.
11.
Describe the number-line graph of $x\le3$ ($x\in\mathbb{R}$).
12.
Solve $5-2x\ge1$.
13.
Describe the graph of $-1
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Solve $-2\le\dfrac{x-3}{2}<2$ for $x\in\mathbb{R}$.
15.
Solve $-3\le 2x-1<5$ for $x\in\mathbb{R}$ and represent the solution on a number line.

Answer Key

Section A — Multiple Choice Questions
  1. (B) reverses the sign
  2. (B) open circle at $3$, arrow right
  3. (A) $x>3$
  4. (B) included
  5. (B) replacement set
Section B — Short Answer (2 marks)
  1. $x\le4$.
  2. An open circle.
  3. $x>-4$.
  4. A closed circle.
Section C — Short Answer (3 marks)
  1. $\{1,2\}$.
  2. A closed dot at $3$ with an arrow to the left.
  3. $x\le2$.
  4. Open dot at $-1$, closed dot at $2$, segment joined.
Section D — Long Answer (5 marks)
  1. $-1\le x<7$.
  2. $-1\le x<3$ (closed at $-1$, open at $3$).
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