Test: Inequalities - ACT MCQ

# Test: Inequalities - ACT MCQ

Test Description

## 10 Questions MCQ Test - Test: Inequalities

Test: Inequalities for ACT 2024 is part of ACT preparation. The Test: Inequalities questions and answers have been prepared according to the ACT exam syllabus.The Test: Inequalities MCQs are made for ACT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Inequalities below.
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Test: Inequalities - Question 1

### If Ram has x rupees and he pay 40 rupees to shopkeeper then find range of x if amount of money left with Ram is at least 10 rupees is given by inequation ________.

Detailed Solution for Test: Inequalities - Question 1

Amount left is at least 10 rupees i.e. amount left ≥ 10.
x - 40 ≥ 10 => x ≥ 50.

Test: Inequalities - Question 2

### ax2 + bx + c > 0 is __________

Detailed Solution for Test: Inequalities - Question 2
• Since it has highest power of x ‘2’ and has inequality sign so, it is called quadratic inequality.
• It is not numerical inequality as it does not have numbers on both sides of inequality.
• It does not have two inequality signs so it is not double inequality.
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Test: Inequalities - Question 3

### x > 5 is __________

Detailed Solution for Test: Inequalities - Question 3

Since a variable ‘x’ is compared with number ‘5’ with inequality sign so it is called literal inequality.

Test: Inequalities - Question 4

If Ram has x rupees and he pay 40 rupees to shopkeeper then find range of x if amount of money left with Ram is at most 10 rupees is given by inequation _________

Detailed Solution for Test: Inequalities - Question 4

Amount left is at most 10 rupees i.e. amount left ≤ 10.
x - 40 ≤ 10 => x ≤ 50.

Test: Inequalities - Question 5

ax+ bx + c ≥ 0 is a strict inequality.

Detailed Solution for Test: Inequalities - Question 5

Since it has equality sign along with inequality sign so it is a slack inequality not strict inequality.

Test: Inequalities - Question 6

ax + b > 0 is ___________

Detailed Solution for Test: Inequalities - Question 6
• Since it has highest power of x ‘1’ and has inequality sign so, it is called linear inequality.
• It is not numerical inequality as it does not have numbers on both sides of inequality.
• It does not have two inequality signs so it is not double inequality.
Test: Inequalities - Question 7

7 > 5 is _____________

Detailed Solution for Test: Inequalities - Question 7

Since here numbers are compared with inequality sign so, it is called numerical inequality.

Test: Inequalities - Question 8

If x + 2y ≤ 3, x > 0 and y > 0, then one of the solution is

Detailed Solution for Test: Inequalities - Question 8

Given

x + 2y ≤ 3

x > 0 and y > 0

Calculation

We need to satisfy the equation x + 2y ≤ 3 from the options

Option: 1  x = -1 and y = 2

This will be incorrect as we have x and y > 0

In 1st option x is less than 0, so we can't take this

Option: 2  x = 2, y = 1

2 + 2 ≤ 3 , which is incorrect.

Option: 3  x = 1, y = 1

1 + 2 ≤  3

3 ≤ 3, which is correct.

∴ The correct answer is x = 1, y = 1

Test: Inequalities - Question 9

Calculate the least whole number, which when subtracted from both the terms of the ratio 5 : 6 gives a ratio less than 17 : 22.

Detailed Solution for Test: Inequalities - Question 9

Given:

Initial ratio = 5 ∶ 6

Final ratio should be less than 17 ∶ 22

Calculation:

Let the least whole number that is needed to be subtracted be a.

According to the question,

(5 - a)/(6 - a) < 17/22

⇒ 5 × 22 - 22a < 17 × 6 - 17a

⇒ 110 - 22a < 102 - 17a

⇒ 110 - 102 < - 17a + 22a

⇒ 8 < 5a

⇒ 8/5 = 1.6 < a

∴ The least whole number must be 2.

Test: Inequalities - Question 10

If 2x + 5 > 2 + 3x and 2x - 3 ≤ 4x - 5, then x can take which of the following values?

Detailed Solution for Test: Inequalities - Question 10

2x + 5 > 2 + 3x

5 – 2 > 3x – 2x

3 > x          .......(1)

2x - 3 ≤ 4x - 5

5 – 3 ≤ 4x – 2x

1 ≤ x          .......(2)

From (1) and (2)

x = 1 or 2

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