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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-05-INS-01
Systems of Linear Inequalities — Assignment
Chapter: Linear Inequalities
Topic: Systems of Linear Inequalities in Two Variables
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • 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.
The solution of a system of inequalities is:
  • A.a line
  • B.the common region
  • C.empty
  • D.a ray
2.
The feasible region is the intersection of:
  • A.the lines
  • B.the half-planes
  • C.the axes
  • D.the points
3.
$x\ge0$ and $y\ge0$ together give:
  • A.a line
  • B.the first quadrant
  • C.a point
  • D.the x-axis
4.
A bounded region is enclosed on:
  • A.one side
  • B.all sides
  • C.no side
  • D.two sides
5.
Corner points are:
  • A.midpoints
  • B.vertices of the region
  • C.the centre
  • D.on the axes only
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Does $(1,1)$ satisfy both $x+y\le4$ and $x\ge0$?
7.
Name the region given by $x\ge0,\ y\ge0$.
8.
Is the region $x+y\le2,\ x\ge0,\ y\ge0$ bounded?
9.
Give a point satisfying both $x\ge2$ and $y\ge3$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the corner points of $x\ge0,\ y\ge0,\ x+y\le4$.
11.
Does $(1,2)$ satisfy $x+y\le4,\ x\ge0,\ y\ge0$?
12.
Describe the region common to $x\ge1$ and $y\le3$.
13.
Find the corner points of $x\ge0,\ y\ge0,\ x+y\le6$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Solve graphically and give the corner points: $x+y\le4,\ x+y\ge1,\ x\ge0,\ y\ge0$.
15.
Find the corner points of the feasible region $2x+y\le10,\ x+3y\le15,\ x\ge0,\ y\ge0$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) the common region
  2. (B) the half-planes
  3. (B) the first quadrant
  4. (B) all sides
  5. (B) vertices of the region
Section B — Short Answer (2 marks)
  1. Yes.
  2. The first quadrant.
  3. Yes.
  4. e.g. $(2,3)$.
Section C — Short Answer (3 marks)
  1. $(0,0),(4,0),(0,4)$.
  2. Yes.
  3. The strip $x\ge1$ lying on/below $y=3$.
  4. $(0,0),(6,0),(0,6)$.
Section D — Long Answer (5 marks)
  1. Corners $(1,0),(4,0),(0,4),(0,1)$.
  2. $(0,0),(5,0),(3,4),(0,5)$.
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