## RS Aggarwal Class 10 Solutions Chapter 1 Real Numbers MCQS

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 1 Real Numbers MCQS.

**Other Exercises**

- RS Aggarwal Solutions Class 10 Chapter 1 Real Numbers Ex 1A
- RS Aggarwal Solutions Class 10 Chapter 1 Real Numbers Ex 1B
- RS Aggarwal Solutions Class 10 Chapter 1 Real Numbers Ex 1C
- RS Aggarwal Solutions Class 10 Chapter 1 Real Numbers Ex 1D
- RS Aggarwal Solutions Class 10 Chapter 1 Real Numbers Ex 1E
- RS Aggarwal Solutions Class 10 Chapter 1 Real Numbers MCQs
- RS Aggarwal Solutions Class 10 Chapter 1 Real Numbers Test Yourself

**Choose the correct answer in each of the following questions.**

**Question 1.**

Which of the following is a pair of co-primes.

(a) (14, 35)

(b) (18, 25)

(c) (31, 93)

(d) (32, 62)

**Solution:**

**(b)** We know that HCF of two co-prime number is 1

HCF of 14, 35 is 7

HCF of 18, 25 is 1

HCF of 31, 93 is 31

HCF of 32, 60 is 4

Required co-prime number is (18, 25)

**Question 2.**

If a = (2^{2} x 3^{3} x 5^{4}) and b = (2^{3} x 3^{2} x 5) then HCF (a, b) = ?

(a) 90

(b) 180

(c) 360

(d) 540

**Solution:**

**(b)** a = (2^{2} x 3^{3} x 5^{4}), b = (2^{3} x 3^{2} x 5)

HCF = 2^{2} x 3^{2} x 5 = 2 x 2 x 3 x 3 x 5 = 180

**Question 3.**

HCF of (2^{3} x 3^{2} x 5), (2^{2} x 3^{3} x 5^{2}) and (2^{4} x 3 x 5^{3} x 7) is

(a) 30

(b) 48

(c) 60

(d) 105

**Solution:**

**(c)** HCF of 2^{3} x 3^{2} x 5, 2^{2} x 3^{3} x 5^{2}, 2^{4} x 3 x 5^{3} x 7

HCF = 2^{2} x 3 x 5 = 2 x 2 x 3 x 5 = 60

**Question 4.**

LCM of (2^{3} x 3 x 5) and (2^{4} x 5 x 7) is

(a) 40

(b) 560

(c) 1120

(d) 1680

**Solution:**

**(d)** LCM of 2^{3} x 3 x 5, 2^{4} x 5 x 7 = 2^{4} x 3 x 5 x 7

=2 x 2 x 2 x 2 x 3 x 5 x 7

= 1680

**Question 5.**

The HCF of two numbers is 27 and their LCM is 162. If one of the number is 54, what is the other number:

(a) 36

(b) 45

(c) 9

(d) 81

**Solution:**

**(d)** HCF of two numbers = 27

LCM = 162

One number = 54

**Question 6.**

The product of two numbers is 1600 and their HCF is 5. The LCM of the numbers is

(a) 8000

(b) 1600

(c) 320

(d) 1605

**Solution:**

**(c)** Product of two numbers = 1600

HCF = 5

**Question 7.**

What is the largest number that divides each one of 1152 and 1664 exactly:

(a) 32

(b) 64

(c) 128

(d) 256

**Solution:**

**(c)** Largest number that divides each one of 1152 and 1664

HCF of 1152 and 1664 =128

**Question 8.**

What is the largest number that divides 70 and 125, leaving remainders 5 and 8 respectively

(a) 13

(b) 9

(c) 3

(d) 585

**Solution:**

**(a)** Largest number that divides 70 and 125 leaving remainders as 5 and 8 respectively.

Required number = 70 – 5 = 65

and 125 – 8= 117

HCF of 65, 117 = 13

**Question 9.**

What is the largest number that divides 245 and 1029, leaving remainder 5 in each case?

(a) 15

(b) 16

(c) 9

(d) 5

**Solution:**

**(b)** Largest number that divides 245 and 1029 leaving remainder as 5 in each case. .

Required number = 245 – 5 = 240 and 1029 – 5 = 1024

Now, HCF of 240 and 1020 = 16

**Question 10.**

The simplest form of

(a)

(b)

(c)

(d)

**Solution:**

**(d)**

**Question 11.**

Euclid’s division lemma states that for any positive integer a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy:

(a) 1 < r < b

(b) 0 < r ≤ b

(c) 0 ≤ r < b

(d) 0 < r < b

**Solution:**

**(c)** In a = bq + r

r must satisfy i.e. 0 ≤ r < b

**Question 12.**

A number when divided by 143 leaves 31 as remainder. What will be the remainder when the same number is divided by 13?

(a) 0

(b) 1

(c) 3

(d) 5

**Solution:**

**(d)** Let the given number when divided by 143 gives q as quotient and 31 as remainder.

Number = 143q + 31

= (13 x 11) q + 31

= 13 x 11 q+ 13 x 2 + 5

= 13 (110 + 2) + 5

The number where divided by 73, gives 5 as remainder.

**Question 13.**

Which of the following is an irrational number?

(a)

(b) 3.1416

(c)

(d) 3.141141114…

**Solution:**

**(d)** 3.141141114… is irrational because it is non terminating non-repeating.

**Question 14.**

π is

(a) an integer

(b) a rational number

(c) an irrational number

(d) none of these

**Solution:**

**(c)** π is an irrational number.

**Question 15.**

is

(a) an integer

(b) a rational number

(c) an irrational number

(d) none of these

**Solution:**

**(b)** is a rational number as it is non-terminating repeating decimal.

**Question 16.**

2.13113111311113… is

(a) an integer

(b) a rational number

(c) an irrational number

(d) none of these

**Solution:**

**(c)** 2.13113111311113… is an irrational number.

It is non-terminating non-repeating decimal.

**Question 17.**

The number 3.24636363… is

(a) an integer

(b) a rational number

(c) an irrational number

(d) none of these

**Solution:**

**(b)** 3.24636363…

=

It is non-terminating repeating decimal.

It is a rational number.

**Question 18.**

Which of the following rational numbers is expressible as a terminating decimal?

(a)

(b)

(c)

(d)

**Solution:**

**(c)** = is a rational because it has terminating decimal as q = 5^{4} which is in form of 2^{m} x 5^{n}.

**Question 19.**

The decimal expansion of the rational number will terminate after

(a) one decimal place

(b) two decimal places

(c) three decimal places

(d) four decimal places

**Solution:**

**(b)**

**Question 20.**

The decimal expansion of the number will terminate after

(a) one decimal place

(b) two decimal places

(c) three decimal places

(d) four decimal places

**Solution:**

**(d)**

**Question 21.**

The number 1.732 is

(a) an irrational number

(b) a rational number

(c) an integer

(d) a whole number

**Solution:**

**(b)** 1.732 is a rational number.

As it is terminating decimal.

**Question 22.**

a and b are two positive integers such that the least prime factor of a is 3 and the least prime factor of b is 5. Then, the least prime factor of (a + b) is

(a) 2

(b) 3

(c) 5

(d) 8

**Solution:**

**(a)** Least prime factor of a positive integer a is 3 and b is 5

2 is neither a factor of a nor of b

a and b are odd

Then (a + b) = even

(Sum of two odd numbers is even)

(a + b) is divisible by 2

Which is the least prime factor.

**Question 23.**

√2 is

(a) a rational number

(b) an irrational number

(c) a terminating decimal

(d) a nonterminating repeating decimal

**Solution:**

**(b)** √2 is an irrational number.

**Question 24.**

is

(a) a fraction

(b) a rational number

(c) an irrational number

(d) none of these

**Solution:**

**(c)**

**Question 25.**

(2 + √2 ) is

(a) an integer

(b) a rational number

(c) an irrational number

(d) none of these

**Solution:**

**(c)** 2 + √2 is an irrational number as sum of a rational and an irrational is an irrational

**Question 26.**

What is the least number that is divisible by all the natural numbers from 1 to 10 (both inclusive)?

(a) 100

(b) 1260

(c) 2520

(d) 5040

**Solution:**

**(c)** LCM of 1 to 10 = 2 x 2 x 2 x 3 x 3 x 5 x 7 = 2520

Hope given RS Aggarwal Solutions Class 10 Chapter 1 Real Numbers MCQS are helpful to complete your math homework.

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