Real Numbers Study Guide for Competitive Exams

Real Numbers

Q. If a = 2 and b = 3, what is the value of a^2 + b^2?

A. 5
B. 7
C. 13
D. 12

Solution

a^2 = 4 and b^2 = 9, so 4 + 9 = 13.

Correct Answer: C — 13

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Q. If the sum of two numbers is 12 and their product is 32, what are the numbers?

A. 4 and 8
B. 6 and 6
C. 2 and 10
D. 3 and 9

Solution

The numbers are 4 and 8, as 4 + 8 = 12 and 4 × 8 = 32.

Correct Answer: A — 4 and 8

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Q. If x = -3, what is the value of |x| + x?

A. 0
B. -3
C. -6
D. -9

Solution

|-3| = 3, so |x| + x = 3 - 3 = 0.

Correct Answer: B — -3

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Q. If x = -5, what is the value of |x|?

A. -5
B. 0
C. 5
D. 10

Solution

The absolute value |x| of -5 is 5.

Correct Answer: C — 5

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Q. If x = 3 and y = 4, what is the value of x² + y²?

A. 25
B. 20
C. 15
D. 12

Solution

x² + y² = 3² + 4² = 9 + 16 = 25.

Correct Answer: A — 25

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Q. If x = 4, what is the value of 2x - 3? (2022)

A. 5
B. 6
C. 7
D. 8

Solution

2x - 3 = 2(4) - 3 = 8 - 3 = 5.

Correct Answer: C — 7

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Q. If x = 4, what is the value of 3x - 2? (2019)

A. 10
B. 12
C. 14
D. 16

Solution

3x - 2 = 3(4) - 2 = 12 - 2 = 10.

Correct Answer: B — 12

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Q. What is the absolute value of -7? (2023)

A. -7
B. 0
C. 7
D. 14

Solution

The absolute value of -7 is 7.

Correct Answer: C — 7

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Q. What is the sum of the roots of the equation x² - 5x + 6 = 0? (2022)

A. 5
B. 6
C. 7
D. 8

Solution

The sum of the roots is given by -b/a = 5/1 = 5.

Correct Answer: A — 5

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Q. What is the value of (3/4) + (1/2)?

A. 1
B. 5/4
C. 3/2
D. 7/4

Solution

Convert 1/2 to 2/4, then (3/4) + (2/4) = 5/4.

Correct Answer: B — 5/4

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Q. What is the value of (−1) × (−1) × (−1)? (2021)

A. 1
B. 0
C. −1
D. −3

Solution

Multiplying three negative ones gives −1.

Correct Answer: C — −1

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Q. What is the value of (−1)^3?

A. 1
B. 0
C. −1
D. −3

Solution

(−1)^3 = −1.

Correct Answer: C — −1

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Q. What is the value of 3 + 4 × 2?

A. 14
B. 11
C. 10
D. 8

Solution

According to BODMAS, 4 × 2 = 8, so 3 + 8 = 11.

Correct Answer: B — 11

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Q. What is the value of √(144) + √(64)?

A. 16
B. 20
C. 18
D. 22

Solution

√(144) = 12 and √(64) = 8, so 12 + 8 = 20.

Correct Answer: C — 18

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Q. Which of the following is an irrational number?

A. √4
B. √2
C. 0.25
D. 1

Solution

√4 = 2, 0.25 = 1/4, and 1 is rational. √2 is irrational.

Correct Answer: B — √2

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Q. Which of the following is equal to 0.125?

A. 1/8
B. 1/4
C. 1/2
D. 1/16

Solution

0.125 is equal to 1/8.

Correct Answer: A — 1/8

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Q. Which of the following is not a rational number? (2023)

A. 1/2
B. 0
C. √3
D. 3

Solution

√3 is an irrational number, while 1/2, 0, and 3 are rational.

Correct Answer: C — √3

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Q. Which of the following numbers is a perfect square?

A. 10
B. 15
C. 25
D. 30

Solution

25 is a perfect square (5^2).

Correct Answer: C — 25

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Real Numbers

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