Vidaara.orgClass 11 · Mathematics
CodeVID-M11-05-INT-01
Linear Inequalities in Two Variables — Assignment
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 region of a linear inequality in two variables is:
- A.a line
- B.a half-plane
- C.a ray
- D.a point
2.
For a strict inequality $(<)$, the boundary line is:
- A.solid
- B.dashed
- C.absent
- D.doubled
3.
Does $(0,0)$ satisfy $x+y\le5$?
- A.Yes
- B.No
- C.only on line
- D.cannot tell
4.
The region $y\ge0$ is:
- A.below the x-axis
- B.above (and on) the x-axis
- C.left of y-axis
- D.right of y-axis
5.
The region $x\le3$ is:
- A.right of $x=3$
- B.left of (and on) $x=3$
- C.above $x=3$
- D.a point
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Does $(1,1)$ satisfy $2x+y\le4$?
7.
Is the boundary line included for $x+y\ge2$?
8.
Does the origin satisfy $x+y\le4$?
9.
Write "the region above the x-axis" as an inequality.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Determine whether $(2,3)$ satisfies $3x-2y<5$.
11.
For $2x+y\ge6$, state which of $(0,0)$ and $(3,1)$ satisfies it.
12.
Describe the region given by $x\ge0,\ y\ge0$.
13.
Does the boundary of $x-y\le0$ pass through the origin, and which region is the solution?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Describe the region $2x+3y\le12,\ x\ge0,\ y\ge0$ and give its corner points.
15.
A mix uses $x$ units of A and $y$ of B with $2x+y\ge8$ and $x+2y\ge10$. Write the constraints (with non-negativity) and check whether $(4,3)$ satisfies both.
Answer Key
Section A — Multiple Choice Questions
- (B) a half-plane
- (B) dashed
- (A) Yes
- (B) above (and on) the x-axis
- (B) left of (and on) $x=3$
Section B — Short Answer (2 marks)
- Yes ($3\le4$).
- Yes (solid line).
- Yes.
- $y>0$.
Section C — Short Answer (3 marks)
- Yes ($0<5$).
- $(3,1)$ satisfies it; $(0,0)$ does not.
- The first quadrant.
- Yes; the region $y\ge x$ (on/above $y=x$).
Section D — Long Answer (5 marks)
- A triangle with corners $(0,0),(6,0),(0,4)$.
- $2x+y\ge8,\ x+2y\ge10,\ x,y\ge0$; $(4,3)$ satisfies both.
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