Practice Questions for Algebra - Inequalities & Modulus

1. CRE 1 - Basics | Algebra - Inequalities & Modulus

Which of the following sets represents the set of all real numbers lying between 3 and 11 excluding 3 and 11?

(a)
[3, 11]
(b)
(3, 11)
(c)
[3, 11)
(d)
(3, 11]
(e)
(-∞, 3) ∪ (11, ∞)

2. CRE 1 - Basics | Algebra - Inequalities & Modulus

Which of the following sets represents the set of all real numbers lying between 3 and 11 excluding 3 but including 11?

(a)
[3, 11]
(b)
(3, 11)
(c)
[3, 11)
(d)
(3, 11]
(e)
(-∞, 3) ∪ (11, ∞)

3. CRE 1 - Basics | Algebra - Inequalities & Modulus

If a and b are two negative numbers, the which of the following is not always negative

(a)
a + b
(b)
a - b
(c)
b - a
(d)
a²b³
(e)
Both (b) and (c)

4. CRE 1 - Basics | Algebra - Inequalities & Modulus

If a, b and c are three distinct positive numbers, then (a - b)(b - c)(c - a) is always

Type 1 for Positve
Type 2 for Negative
Type 3 for Cannot be determined

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5. CRE 1 - Basics | Algebra - Inequalities & Modulus

If p, q, r and s are real numbers then which of the following is always true?

(a)
If p > q and r > s, then pr > qs
(b)
If p > q and r > s, then p - r > q - s
(c)
If p > q and q > r, then p > q > r
(d)
All of these

6. CRE 1 - Basics | Algebra - Inequalities & Modulus

What is the value of |(4 - 3)(3 - 6)(2 - 1)|?

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7. CRE 1 - Basics | Algebra - Inequalities & Modulus

If x, y and z are all negative numbers, then x³y²z is

Type 1 for Positive
Type 2 for Negative
Type 3 for Cannot be determined

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8. CRE 1 - Basics | Algebra - Inequalities & Modulus

If x is a positive number, then the least possible value of x + $\frac{1}{x}$ is?

(a)
1
(b)
2
(c)
3
(d)
4
(e)
Cannot be determined

Answer: Option B

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Explanation :

Let us consider two numbers x and $\frac{1}{x}$ .

Now, we know for two positive numbers, AM ≥ GM

⇒ $\frac{x + \frac{1}{x}}{2}$ ≥ $\sqrt{x \times \frac{1}{x}}$

⇒ x + $\frac{1}{x}$ ≥ 2 $\sqrt{1}$

⇒ x + $\frac{1}{x}$ ≥ 2

∴ The least possible value of x + $\frac{1}{x}$ is 2.

Hence, option (b).

9. CRE 1 - Basics | Algebra - Inequalities & Modulus

Find the range of x if 2x + 4 > 10

(a)
(-3, 3)
(b)
(0, 3)
(c)
(3, ∞)
(d)
(-∞, 3)

10. CRE 1 - Basics | Algebra - Inequalities & Modulus

When an inequality is multiplied with a negative number:

(a)
the direction of the inequality is not affected i.e., remains the same
(b)
the direction of the inequality changes
(c)
the direction of the inequality may or may not change depending on the value of the number
(d)
Cannot be determined.

CRE 1 - Basics | Algebra - Inequalities & Modulus

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