CA Foundation Paper 3

Inequalities MCQ

Chapter 3 • 10 Questions from ICAI Study Material

Questions

10

Est. Time

8 min

Source

ICAI Book

Sample Questions: Inequalities

Preview 8 of 10 MCQs from Chapter 3

1. An employer recruits experienced (x) and fresh workmen (y) for his firm under the condition that he cannot employ more than 9 people. x and y can be related by the inequality

A) x + y != 9
B) x + y <= 9, x >= 0, y >= 0 ✓
C) x + y >= 9, x >= 0, y >= 0
D) none of these

2. On the average an experienced person does 5 units of work while a fresh one 3 units of work daily but the employer has to maintain an output of at least 30 units of work per day. This situation can be expressed as

A) 5x + 3y <= 30
B) 5x + 3y > 30
C) 5x + 3y >= 30, x >= 0, y >= 0 ✓
D) none of these

3. The rules and regulations demand that the employer should employ not more than 5 experienced hands to 1 fresh one and this fact can be expressed as

A) y >= x/5 ✓
B) 5y <= x
C) 5y >= x
D) none of these

4. The union however forbids him to employ less than 2 experienced person to each fresh person. This situation can be expressed as

A) x <= y/2
B) y <= x/2 ✓
C) y >= x/2
D) x > 2y

5. A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below: Food I: A=2, B=1, C=1, D=2 Food II: A=1, B=1, C=2, D=3 Assuming x units of food I is to be mixed with y units of food II the situation can be expressed as

A) 2x + y <= 9, x + y <= 7, x + 2y <= 10, 2x + 3y <= 12, x > 0, y > 0
B) 2x + y >= 30, x + y <= 7, x + y <= 10, x + 2y >= 10, 2x + 3y >= 12, x >= 0, y >= 0
C) 2x + y >= 9, x + y >= 7, x + 2y >= 10, 2x + 3y >= 12, x >= 0, y >= 0 ✓
D) 2x + y >= 9, x + y >= 7, x + 2y >= 10, 2x + 3y >= 12

6. The common region (shaded part) shown in a diagram with L1: 2x + y = 9, L2: x + y = 7, L3: x + 2y = 10, L4: x + 3y = 12 refers to

A) 2x + y <= 9, x + y <= 7, x + 2y <= 10, x + 3y <= 12, x > 0, y > 0
B) 2x + y <= 9, x + y <= 9, x + 3y >= 12, x >= 0, y >= 0
C) 2x + y >= 9, x + y >= 7, x + 2y >= 10, x + 3y >= 12, x >= 0, y >= 0 ✓
D) none of these

7. The region indicated by the shading in the graph is expressed by inequalities

A) x1 + x2 <= 2, 2x1 + 2x2 >= 8, x1 >= 0, x2 >= 0 ✓
B) x1 + x2 <= 2, x2x1 + x2 <= 4, 2x1 + 2x2 >= 8
C) x1 + x2 >= 2, 2x1 + 2x2 >= 8
D) x1 + x2 <= 2, 2x1 + 2x2 > 8

8. A firm makes two types of products: Type A and Type B. The profit on product A is Rs.20 each and that on product B is Rs.30 each. Both types are processed on three machines M1, M2 and M3. The time required in hours by each product and total time available in hours per week on each machine are as follows: M1: Product A=3, Product B=3, Available=36 M2: Product A=5, Product B=2, Available=50 M3: Product A=2, Product B=6, Available=60 The constraints can be formulated taking x1 = number of units A and x2 = number of unit of B as

A) x1 + x2 <= 12, 5x1 + 2x2 <= 50, 2x1 + 6x2 <= 60
B) 3x1 + 3x2 >= 36, 5x1 + 2x2 >= 50, 2x1 + 6x2 >= 60, x1 >= 0, x2 >= 0
C) 3x1 + 3x2 <= 36, 5x1 + 2x2 <= 50, 2x1 + 6x2 <= 60, x1 >= 0, x2 >= 0 ✓
D) none of these