Please refer to the **MCQ Questions for Class 10 Maths Real Numbers **with Answers. The following Real Numbers Class 10 Maths MCQ Questions have been designed based on the current academic year syllabus and examination guidelines for Class 10. Our faculty has designed MCQ Questions for Class 10 Maths with Answers for all chapters as per your NCERT Class 10 Mathematics book.

## Real Number Class 10 MCQ Questions with Answers

Please see below Real Number Class 10 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question** For some integer q, every even integer is of the form

(a) q

(b) q +1

(c) 2q

(d) 2q +1

**Answer**

C

**Question**. The least number that is divisible by all the numbers from 1 to 5 (both inclusive) is

(a) 20

(b) 30

(c) 60

(d) 120

**Answer**

C

**Question** The decimal expression of the rational number 44/2 ^{5}x3 will terminate after

(a) one decimal place

(b) two decimal places

(c) three decimal places

(d) more than three decimal places

**Answer**

C

**Question**. For some integer m, every odd integer is of the form

(a) m

(b) m +1

(c) 2m

(d) 2m +1

**Answer**

D

**Question**. The largest number which divides 85 and 77, leaving remainders 5 and 7 respectively is

(a) 5

(b) 20

(c) 35

(d) 10

**Answer**

D

**Question**. n_{2} −1 is divisible by 8, if n is

(a) an integer

(b) a natural number

(c) an odd integer

(d) an even integer

**Answer**

C

** Question.** The decimal expansion of the rational number 47/2×2

^{5 }will terminate after

(a) one decimal place

(b) two decimal places

(c) three decimal places

(d) none of these 1

**Answer**

B

** Question.** If two positive integers a and b can be expressed as a = x

^{2}y

^{5}and b = x

^{3}y

^{2}; x , y being prime numbers, then L.C.M. (a, b) is

(a) x2 y2

(b) x

^{3}y

^{3}

(c) x

^{5}y

^{2}

(d) x

^{5}y

^{3}

**Answer**

D

** Question.** The largest number which divides 71 and 97 leaving remainder 11 and 7 respectively is

(a) 15

(b) 20

(c) 60

(d) 30 2

**Answer**

D

** Question.** For some integer m, every odd integer is of the form

(a) m

(b) m +1

(c) 2m +1

(d) 2m 1

**Answer**

C

** Question.** Euclid division Lemma states that if a and b are any two positive integers, then there exist unique integers q and r such that

(a) a = bq + r , 0 < r £ b

(b) a= bq + r, 0 £ r< b

(c) a bq r = + n, 0 < q £ b

(d) a= bq + rn, 0 £ r< b 1

**Answer**

B

** Question.** The sum or difference of a rational and an irrational number is

(a) always irrational

(b) always rational

(c) rational or irrational

(d) none of these 1

**Answer**

B

**Question. Euclid’s division lemma states that for two positive integers 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

**Answer**

C

**Question. The largest number which exactly divides 70, 80, 105, 160 is **

(a) 10

(b) 7

(c) 5

(d) none of these

**Answer**

C

**Question. The decimal expansion of the rational number 47/2 ^{3} 5^{2} will terminate after **(a) one decimal place

(b) two decimal places

(c) three decimal places

(d) more than three decimal places

**Answer**

C

**Question √5 is **

(a) an integer

(b) an irrational number

(c) a rational number

(d) none of these

**Answer**

B

**Question. The product of three consecutive integers is divisible by **

(a) 5

(b) 6

(c) 7

(d) none of these

**Answer**

B

**Question. The decimal expansion of number 29/2 ^{2}x5x7 is **

(a) terminating

(b) non-terminating repeating

(c) non-terminating non-repeating

(d) none of these

**Answer**

B

**Question. The decimal expansion of the rational number 33/2 ^{2}5 will terminate after **

(a) one decimal place

(b) two decimal places

(c) three decimal places

(d) more than three decimal places

**Answer**

B

**Question The decimal expansion of irrational number is **

(a) terminating

(b) non-terminating repeating

(c) non-terminating non-repeating

(d) none of these

**Answer**

C

**Question. The least number that is divisible by first five even numbers is **

(a) 60

(b) 80

(c) 120

(d) 160

**Answer**

C

**Question. The product of two consecutive integers is divisible by **

(a) 2

(b) 3

(c) 5

(d) 7

**Answer**

A

**Question. If two positive integers a and b are written as a = x 4 y2 and b = x 2 y3, a, b are prime numbers, then HCF (a, b) is **

(a) x 4 y3

(b) xy

(c) x 2 y3

(d) x 2 y2

**Answer**

D

**Question. LCM of x 2 – 4 and x ^{ 4} -16 is **

(a) (x –

^{2})(x +2)

(b) (x

^{2}+ 4)(x -2)

(c) (x

^{2}– 4) (x +2)

(d) (x

^{2}+ 4)(x

^{2}– 4)

**Answer**

D

**Question. If two positive integers a and b are written as a = xy2 and b = x 3 y, a, b are prime numbers, then LCM (a, b) is **

(a) x 2 y2

(b) xy

(c) x 3 y2

(d) none of these

**Answer**

C

**Question. The product of LCM and HCF of two numbers m and n is **

(a) m + n

(b) m – n

(c) m´ n

(d) none of these

**Answer**

C

**Question. HCF of (x ^{3} -3x +2) and (x ^{2} – 4x +3) is **

(a) (x -2)

^{3}

(b) (x -1)(x +2)

(c) (x -1)

(d) (x -1)(x -3)

**Answer**

C

**Question The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is **

(a) 10

(b) 100

(c) 504

(d) 2520

**Answer**

D

**Question. For some integer m, every even integer is of the form **

(a) m

(b) m+1

(c) 2 m

(d) 2m+1

**Answer**

C

**Question. The largest number which divides 615 and 963 leaving remainder 6 in each case is **

(a) 82

(b) 95

(c) 87

(d) 93

**Answer**

C

**Question. If the HCF of 65 and 117 is expressible in the form 65m –117, then the value of m is **

(a) 4

(b) 2

(c) 11

(d) 3

**Answer**

B

**Question. When 256 is divided by 17, remainder would be **

(a) 16

(b) 1

(c) 14

(d) none of these

**Answer**

B

**Question. The largest number which divides 318 and 739 leaving remainder 3 and 4 respectively is **

(a) 110

(b) 7

(c) 35

(d) 105

**Answer**

D

**Question. 6.6 ^{–} is **

(a) an integer

(b) a rational number

(c) an irrational number

(d) none of these

**Answer**

B

**Question. √7 is **

(a) an integer

(b) an irrational number

(c) rational number

(d) none of these

**Answer**

B

**Question. The decimal expansion of the rational number 14587/1250 will terminate after **

(a) one decimal place

(b) two decimal places

(c) three decimal places

(d) four decimal places

**Answer**

D

**Question. The product of a non-zero rational and an irrational number is **

(a) always rational

(b) always irrational

(c) one

(d) rational or irrational

**Answer**

B

**Question. The product of two irrational numbers is **

(a) always irrational

(b) always rational

(c) one

(d) rational or irrational

**Answer**

D

**Question. If n is an even natural number, then the largest natural number by which n(n +1)(n +2) is divisible is **

(a) 24

(b) 6

(c) 12

(d) 9

**Answer**

A

**Question. For any natural number n, (2n +1)2 -1 is always divisible by ______ **

(a) 2

(b) 4

(c) 8

(d) All the above

(e) None of these

**Answer**

D

**Question. If LCM and HCF of two numbers are 324 and 18 respectively, then how many such pairs of numbers are possible? **

(a) 0

(b) 1

(c) 2

(d) 3

(e) None of these

**Answer**

C

**Question. The largest number that will divide 398, 606 and 474 leaving remainders 7, 11 and 15 respectively is ________ **

(a) 52

(b) 26

(c) 17

(d) 18

(e) None of these

**Answer**

C

**Question. The largest number which divides 1288 and 2915 and leaves the remainders 1 and 8 respectively, is H and it satisfies the expression, H = 45m + 288n. Find the value of m + n. **

(a) 11

(b) 15

(c) 13

(d) 10

(e) None of these

**Answer**

A

**Question. If p= √11+ √5, q= √14+ √2 and r= √13+ √3 then which one of the following holds true? **

(a) p > q > r

(b) p < q < r

(c) p > r > q

(d) p < r < q

(e) None of these

**Answer**

C

**Question. Which of the following statements is always true? **

(a) The sum or difference of a rational and an irrational number is rational.

(b) Every irrational number is a surd.

(c) The product or quotient of a non-zero rational number and an irrational number is irrational.

(d) All the above

(e) None of these

**Answer**

C

**Question. If u= ^{16}√7 + ^{16}√5 , u = √7 + √5 , w = ^{8}√7 + ^{8}√5 , x = ^{16}√7 – ^{16}√5 , and y = ^{4}√7 + ^{4}√5 , then which one of the following is a rational number? **

(a) uvxy

(b) uvwxy

(c) uxwy

(d) vwxy

(e) None of these

**Answer**

B

**Question. The number of ways, in which 576 can be resolved into two factors, is ________ **

(a) 8

(b) 9

(c) 10

(d) 11

(e) None of these

**Answer**

D

**Question. Four runners P, Q, R and S start running around a circular track simultaneously. If they complete one round in 16, 12, 24, 18 minutes respectively, after how much time they will meet next? **

(a) 2 hours 20 minutes

(b) 2 hours

(c) 3 hours 18 minutes

(d) 2 hours 24 minutes

(e) None of these

**Answer**

D

**Question. The number of ways, in which 360 can be resolved in two factors, is ______ **

(a) 24

(b) 18

(c) 12

(d) 15

(e) None of these

**Answer**

C

**Question**. For some integer q, every odd integer is of the form

(a) q

(b) q +1

(c) 2q

(d) 2q +1

**Answer**

D

**Question. n ^{2} -1 is divisible by 8, if n is **

(a) an integer

(b) a natural number

(c) an odd integer

(d) an even integer

**Answer**

B

**Question. When 256 is divided by 17, remainder would be **

(a) 16

(b) 1

(c) 14

(d) none of these

**Answer**

B

**Question**. If x and y are prime numbers, then HCF of x^{3}y^{2} and x y 2 is

(a) x^{3} y^{2}

(b) x^{2} y^{2}

(c) x y^{2}

(d) xy

**Answer**

C

**Question. If 0.2317 is expressed in the form of p/q where ‘p’ and ‘q’ are co-prime and also ‘q’ is in the form 2n x 5m what are the values of ‘m’ and ‘n’ respectively? **

(a) 4 and 3

(b) 4 and 5

(c) 4 and 4

(d) 3 and 4

**Answer**

C

**Question. Choose the methods that can be used to find the H.C.F. of any two numbers. ****(i) Euclid’s division lemma****(ii) Prime factorization****(iii) Division of the numbers****(iv) Product of numbers**

(a) (i) and (iv) only

(b) (i), (ii) and (iii) only

(c) (i), (iii) and (iv) only

(d) (ii), (iii) and (iv) only

**Answer**

B

**Question. A positive number ‘n’ when divided by 8 leaves a remainder 5. What is the remainder when 2n + 4 is divided by 8? **

(a) 8

(b) 1

(c) 6

(d) 0

**Answer**

C

**Question. Which of the following is a correct statement **

(a) π is a natural number.

(b) π is an irrational number.

(c) π is not defined.

(d) The value of π is 22/7 .

**Answer**

B

**Question. The L.C.M. and H.C.F. of marks scored by Ajit and Amar in a math test are 5040 and 12 respectively. If Amar’s score is 144, what is Ajit’s score? **

(a) 288

(b) 132

(c) 564

(d) 420

**Answer**

D

**Question. Which of the following is true about 17x 41x 43x 61 x 43? **

(a) It is a prime number.

(b) It is a composite number.

(c) It is an odd number.

(d) Both (a) and (c)

**Answer**

B

**Question. The factor tree shows the prime factorization of 1314. **

**Find the respective values of ‘a’ and ‘b’.**

(a) 3, 37

(b) 3, 73

(c) 73, 3

(d) 9, 73

**Answer**

B

**Question. The remainder when a number is divided by 143 is 31.What is the remainder when the same number is divided by 11? **

(a) 5

(b) 7

(c) 6

(d) 9

**Answer**

D

**Question. If 4 divides 1728, which of the following statements is true? **

(a) 4 divides 12.

(b) 6 divides 1728.

(c) 2 divides 1728.

(d) 4 divides 144.

**Answer**

A

**Question. Three ropes are 7 m, 12 m 95 cm and 3 m 85 cm long. What is the greatest possible length which can be used to measure these ropes? **

(a) 35 cm

(b) 55 cm

(c) 1 m

(d) 65 cm

**Answer**

A

**Question**. If (−1) +(−1)n 4n = 0, then n is

(a) any positive integer

(b) any odd natural number

(c) any even natural number

(d) any negative integer

**Answer**

B

**True or False :**

** Question.** The product of two consecutive positive integers is divisible by 2.

**Answer**

**True**

** Question.** 3 × 5 × 7+ 7 is a composite number. 2 × 2 = 4

**Answer**

**True**

**Question. 7/2 ^{4}X5 has non-terminating decimal expansion. **

**Answer**

F

**Question. The largest number which exactly divides 12 and 60 is 4. **

**Answer**

F

**Question. Every composite number can be factorised as a product of primes and this factorisation is unique, apart from the order in which the prime factor occurs. **

**Answer**

T

**Question. 17/18 has terminating decimal expansion **

**Answer**

F

**Question. Any positive odd integer is of the form 6 p +1 or 6 p+3 or 6 p+5, where p is some integer. **

**Answer**

T

**Question. The decimal expansion of √5 is non-terminating recurring. **

**Answer**

F

**Question. The least number which is exactly divisible by 8 and 12 is 24. **

**Answer**

T

**Question. If LCM and HCF of 18 and x are 36 and 6 respectively, then x =12. **

**Answer**

T

**Question. Prime factorisation of 300 is 2 ^{2} ×3×5^{2 }**

**Answer**

T

**Question. √72/√50 is an irrational number. **

**Answer**

F

**Question. If p/q is a rational number, such that the prime factorisation of q is of the form 2 ^{n} 5^{m} where n, m are non-negative integers, then p/q has a decimal expansion which terminates **

**Answer**

F

**One Word Questions :**

**Question. State whether the product of two consecutive integers is even or odd.**

**Answer**

Even

**Question. What will be the HCF of two prime numbers?**

**Answer**

1

**Question. Give two irrational numbers whose product is rational.**

**Answer**

2 + **√**3 and 2 – **√**3

**Question. Is 1 a prime number? Justify your answer.**

**Answer**

No

**Question. Can you write prime factorisation of a prime number? Justify your answer**

**Answer**

No

**Question. Is p a rational number?**

**Answer**

No, it is irrational

Question. Is √75/√12 a rational number?

**Answer**

Yes, rational

**Question. Is there any prime number which is even?**

**Answer**

Yes, 2

**Question. Which number is neither prime nor composite?**

**Answer**

1

**Question. Which two types of numbers constitute real numbers?**

**Answer**

Rational and irrational

**Question. Is 1.203003000300003 …….. a rational number? Give reason.**

**Answer**

No, as it is non-terminating non-repeating

**Question. After how many decimal places the decimal expansion of the rational number 23/2×5 ^{2} will terminate?**

**Answer**

Two

** Question.** (i) Use Euclid’s division algorithm to find the HCF of 81 and 237.

**(ii) Prove that for any prime positive integer p, p is an irrational number. 3 × 2 = 6**

**Answer**

3

** Question.** (i) Prove that the product of three consecutive positive integers is divisible by 6.

**(ii) Using prime factorisation method, find the HCF and LCM of 72, 120 and verify that LCM × HCF = product of the two numbers.**

**Answer**

**HCF 24, LCM 360**

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