RD Sharma Class 9 Solutions Chapter 1 MCQS (Updated for 2024)

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1.) Can we write 0 in the form of p/q?

a. Yes

b. No

c. Cannot be explained

d. None of the above

Answer: a

Explanation: 0 is a rational number and hence it can be written in the form of p/q.

Example: 0/4 = 0

2.) The three rational numbers between 3 and 4 are:

a. 5/2, 6/2, 7/2

b. 13/4, 14/4, 15/4

c. 12/7, 13/7, 14/7

d.11/4, 12/4, 13/4

Answer: b

Explanation: There are many rational numbers between 3 and 4

To find 3 rational numbers, we need to multiply and divide both the numbers by 3+1 = 4

Hence, 3 x (4/4) = 12/4 and 4 x (4/4) = 16/4

Thus, three rational numbers between 12/4 and 16/4 are 13/4, 14/4, and 15/4.

3.) In between any two numbers, there are:

a. Only one rational number

b. Two rational numbers

c. Infinite rational numbers

d. No rational number

Answer: c

Explanation: Take the reference from question number 2 explained above.

4.) Every rational number is:

a. Whole number

b. Natural number

c. Integer

d. Real number

Answer: d

5.) √9 is  __________ number.

a. A rational

b. An irrational

c. Neither rational nor irrational

d. None of the above

Answer: a

Explanation: √9 = 3

Hence, √9 is a rational number.

6.) Which of the following is an irrational number?

a. √16

b. √(12/3)

c. √12

d. √100

Answer: c

Explanation: √12 cannot be simplified to a rational number.

7.) 3√6 + 4√6 is equal to:

a. 6√6

b. 7√6

c. 4√12

d. 7√12

Answer: b

Explanation: 3√6 + 4√6 = (3 + 4)√6 = 7√6

8.) √6 x √27 is equal to:

a. 9√2

b. 3√3

c. 2√2

d. 9√3

Answer: a

Explanation: √6 x √27 = √(6  x 27) = √(2 x 3 x 3 x 3 x 3) = (3 x 3)√2 = 9√2

9.) Which of the following is equal to x³?

a. x⁶ – x³

b. x⁶.x³

c. x⁶/x³

d. (x⁶)³

Answer: c

Explanation: x⁶/x³ = x^{6 – 3} = x³

10.) Which of the following is an irrational number?

a. √23

b. √225

c. 0.3796

d. 7.478478

Answer: a

Explanation: √23 = 4.79583152331…

Since the decimal expansion of the number is non-terminating and non-recurring. Hence, it is an irrational number.

11.) Which of the following is an irrational number?

a. 0.14

b. $0.14\overline{16}$

c. $0.\overline{1416}$

d. 0.4014001400014…

Answer: d

Explanation: 0.4014001400014…is an irrational number as it is non-terminating and non-repeating.

12.) 2√3+√3 = 

a. 6

b. 2√6

c. 3√3

d. 4√6

Answer:  c

Explanation: 2√3+√3 = (2+1)√3= 3√3.

13.) Find the value of $\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}$, if √2 = 1.4142.

a. 5.8282

b. 0.1718

c. 0.4142

d. 2.4142

Answer: c

Explanation:

$\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}$ = $\sqrt{\frac{1.4142-1}{1.4142+1}}$

=$\sqrt{\frac{0.4142}{2.4142}}$

= 0.4142

14.) The number obtained by rationalizing the denominator of $\frac{1}{\sqrt{7}-2}$ is

a. (√7+2)/3

b. (√7-2)/3

c. (√7+2)/5

d. (√7+2)/45

Answer: a

Explanation:

$\frac{1}{\sqrt{7}-2}=\frac{1}{\sqrt{7}-2}\times \frac{\sqrt{7}+2}{\sqrt{7}+2}=\frac{\sqrt{7}+2}{(\sqrt{7}{)}^2-(2{)}^2}=\frac{\sqrt{7}+2}{3}$

15.) Which of the following is rational?

a. 4/0

b. 0/4

c. √3

d. π

Answer: b

Explanation: 0/4 is a rational number that is equal to 0. Whereas π and √3 are irrational numbers and 4/0 is meaningless.

16.) The irrational number between 2 and 2.5 is 

a. √11

b. √5

c. √22.5

d. √12.5

Answer: b

Explanation: The irrational number between 2 and 2.5 is √5 because the approximate value of √5 is 2. 23606…

17.) The value of √10 times √15 is equal to

a. 5√6

b. √25

c. 10√5

d. √5

Answer: a

Explanation: √10×√15 =(√2.√5)×(√3. √5) = 5√6.

18.) The decimal representation of the rational number is

a. Always terminating

b. Either terminating or repeating

c. Either terminating or non-repeating

d. Neither terminating nor repeating

Answer: b

Explanation: As per the definition of a rational number, its decimal representation is either terminating or repeating.

19.) Which of the following is a rational number?

a. 0

b. 2√3

c. 2+√3

d. π

Answer: a

Explanation: 0 is a rational number, and it can be written as 0/1 or 0/2 or 0/3 etc. Whereas 2√3, 2+√3, and π are irrational numbers.

20.) Which of the following is an irrational number?

a. √(4/9)

b. √12/√3

c. √7

d. √81

Answer: c

Explanation: √7 is an irrational number. Because other options given are simplified into a rational number.

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