Students can refer to the following Real numbers MCQ Questions for Class 10 with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here a collection of multiple choice questions for Real Numbers Class 10 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

## Real numbers MCQ Questions for Class 10 Maths with Answers

We have provided below chapter wise MCQs questions for Class 10 Mathematics Real Numbers with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Real Numbers MCQs in Class 10 pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

#### Real numbers MCQ Questions for Class 10 Maths

**Question. For P ∈ N, 3 ^{4P} – 2^{4P} is always divisible by ____ **

(a) 15

(b) 5

(c) 13

(d) Both (b) and (c)

(e) None of these

**Answer**

D

**Question. The greatest number of 5 digits exactly divisible by 15, 24 and 36 is ____**

(a) 99620

(b) 99720

(c) 99968

(d) 99960

(e) None of these

**Answer**

B

**Question. Which one among the following statements is true?**

(a) The remainder when the square of any number is divided by 4 is 1 or 0.

(b) There is no natural number for which 4 ends with digit zero.

(c) A positive integer n is prime, if no prime p less than or equal to n divides n.

(d) All the above

(e) None of these

**Answer**

D

**Question. The unit value of 100 100 6 – 5 is ______ **

(a) 0

(b) 1

(c) 2

(d) 3

(e) None of these

**Answer**

B

**Question. For any odd natural number n,(√3) ^{4n} + (√2)^{4n}) is always divisible by ______ **

(a) 5

(b) 7

(c) 17

(d) 13

(e) None of these

**Answer**

D

**Question. If I is a positive integer then (I)2 will be in the form of ———— **

(a) 4m for some integer m

(b) 8m for some integer m

(c) 4m+1 for some integer m

(d) Both (a) and (c)

(e) None of these

**Answer**

D

**Question. Which among the following statements is not true? **

(a) The square of any odd integer is of the form 4q + 1, for some integer q.

(b) For any odd integer p, p^{2} – 1 is divisible by 8.

(c) If p and q are both odd positive integers/ then p^{2} + q^{2} is even and divisible by 4.

(d) For any natural number n, n 12 cannot end with the digit 0 or 5.

(e) None of these

**Answer**

C

**Question. For any natural number n, 2 (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 equal, then the numbers will be _________**

(a) Composite

(b) Prime

(c) Equal

(d) Co-prime

(e) None of these

**Answer**

C

**Question. If the product of two numbers is 149058 and HCF of these numbers is 21 then how many pairs of these numbers are possible? **

(a) 1

(b) 2

(c) 3

(d) 4

(e) None of these

**Answer**

B

**Question. The decimal expansion of the rational number 12879 /1250 will terminate after: **

(a) One decimal places

(b) Two decimal places

(c) Three decimal places

(d) Four decimal places

(e) None of these

**Answer**

D

**Question. Find the greatest prime factor in 527527. **

(a) 17

(b) 11

(c) 13

(d) 31

(e) None of these

**Answer**

D

**Question. If 14 (1 x 2 x 3 x 4 x 5 …………….A 10 x 14) and B 19 (1 x 2 x 3 x 4 x 5 …………….10 x 19) then which one of the following is/are correct? **

(i) B – A is a prime number.

(ii) B + A is a composite number.

(iii) A is a composite number.

(iv) B is a prime number.

(a) Both (i) and (ii)

(b) Both (ii) and (iii)

(c) Both (iii) and (iv)

(d) All (i), (ii), (iii) and (iv)

(e) None of these

**Answer**

B

**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. The value of (27) ^{3p} – (13)^{3p} ends in ______ (where p is a natural number)**

(a) 0

(b) 4

(c) 6

(d) Either (b) or (c)

(e) None of these

**Answer**

D

**Question. If P 1 3 5 7………….21 andQ 2 4 6 8 10…………22 then HCF of P and Q is ________**

(a) 12375

(b) 14175

(c) 825

(d) 925

(e) None of these

**Answer**

B

**Question. In a seminar, the numbers of participants in science, English and Mathematics are 144, 180 and 192 respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject. **

(a) 38

(b) 40

(c) 43

(d) 45

(e) None of these

**Answer**

C

**Question. Without actually performing the Song division, choose which among the following rational numbers will not have a terminating decimal expansion. **

(a) 123 /16

(b) 351 /2^{7} x 5^{8} x 7^{18}

(c) 32 / 28 x 59

(d) 833 /49 2

(e) None of these

**Answer**

B

**Question. The largest number that divides 588, 1999 and 1650 leaving 3, 10 and 12 respectively is ______**

(a) 117

(b) 109

(c) 27

(d) 43

(e) None of these

**Answer**

A

**Question. If p is a single digit natural number and the unit digits of 4 p and p are same, then how many possibilities p can assume?**

(a) 2

(b) 3

(c) 4

(d) 5

(e) None of these

**Answer**

B

**Question. The sum of exponents of prime factors in the primefactorisation of 196 is **

(a) 3

(b) 4

(c) 5

(d) 2

**Answer**

B

**Question. The rational number of the form p/ q , q ≠ 0, p and q are positive integers , which represents 0. ^{−}134 i.e., (0.1343434….) is **

(a) 134/ 999

(b) 134/ 990

(c) 133/ 999

(d) 133/ 990

**Answer**

D

**Question. When 2256 is divided by 17, then remainder would be **

(a) 1

(b) 16

(c) 14

(d) None of these

**Answer**

A

**Question. The sum of three non-zero prime numbers is 100. One of them exceeds the other by 36. Then, the largest number is **

(a) 73

(b) 91

(c) 67

(d) 57

**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. 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 3 decimal places

**Answer**

B

**Question. The least number which is a perfect square and is divisible by each of 16, 20 and 24 is **

(a) 240

(b) 1600

(c) 2400

(d) 3600

**Answer**

D

**Question. Consider the following statements: For any integer n, ****I. n ^{2} + 3 is never divisible by 17.**

**II. n**

^{2}+ 4 is never divisible by 17.**Then,**

(a) both I and II are true

(b) both I and II are false

(c) I is false and II is true

(d) I is true and II is false

**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) 6

(b) 8

(c) 12

(d) 24

**Answer**

D

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

(a) 13

(b) 9

(c) 3

(d) 585

**Answer**

A

**Question. The least number which when divided by 15, leaves a remainder of 5, when divided by 25, leaves a remainder of 15 and when divided by 35, leaves a remainder of 25, is **

(a) 515

(b) 525

(c) 1040

(d) 1050

**Answer**

A

**Question. The number 3 ^{13} – 3^{10} is divisible by **

(a) 2 and 3

(b) 3 and 10

(c) 2, 3 and 10

(d) 2, 3 and 13

**Answer**

D

**Question. Which of the following statement is true? **

(a) Every point on the number line represents a rational number.

(b) Irrational numbers cannot be represented by points on the number line.

(c) 22/ 7 is a rational number.

(d) None of these.

**Answer**

D

**Question. Which of the following will have a terminating decimal expansion? **

(a) 77/ 210

(b) 23/ 30

(c) 125 /441

(d) 23/ 8

**Answer**

D

**Question. Which of the following statement(s) is/are not correct? **

(a) 7^{3}/5^{4} is a non-terminating repeating decimal.

(b) If a = 2 +√ 3 and b = √2 –√ 3 , then a + b is irrational.

(c) If 19 divides a^{3}, then 19 divides a, where a is a positive integer.

(d) Product of L.C.M. and H.C.F. of 25 and 625 is 15625.

**Answer**

A

**Question. A rectangular metal piece of dimensions 360 cm by 280 cm is cut into some identical small squares. If the side of each square has the largest possible length, find the number of square pieces formed. **

(a) 126

(b) 20

(c) 40

(d) 63

**Answer**

D

**Question. Three bulbs are connected in such a manner that they glow for every 24 seconds, 36 seconds and 54 seconds respectively. All of them glow at once at 8 a.m. When will they again glow simultaneously? **

(a) 8:30:36 a.m.

(b) 8:03:36 a.m.

(c) 8:36:03 a.m.

(d) 8:36:30 a.m.

**Answer**

B

**Question. Euclid’s division lemma: For any two positive integers ‘a’ and ‘b’, there exist unique integers ‘q’ and ‘r’ such that a = bq + r . ****What is the condition that ‘r’ must satisfy?**

(a) 0 ≤ r ≤ b

(b) 0 < r ≤ b

(c) 0 ≤ r < b

(d) 0 < r < b

**Answer**

C

**Question. Find The largest number which divides the numbers 120, 224 and 256. **

(a) 8

(b) 6

(c) 4

(d) 5

**Answer**

A

**Question. Find the H.C.F. of 6930 and 8085. **

(a) 1155

(b) 2205

(c) 1515

(d) 2025

**Answer**

A

**Question. Choose the terminating decimal. **

(a) 141/1000

(b) 17/30

(c) 271/90

(d) 53/343

**Answer**

A

**Question. Find the L.C.M. of 3465 and 5460. **

(a) 181080

(b) 180180

(c) 108108

(d) 108801

**Answer**

B

**Question. A book seller purchased 117 books out of which 45 books are of mathematics and the remaining 72 books are of physics. Each book has the same size. Mathematics and physics books are to be packed in separate bundles and each bundle must contain the same number of books. Find the least number of bundles which can be made of these 117 books. **

(a) 8

(b) 11

(c) 13

(d) 9

**Answer**

C

**Question. The circumferences of the front wheel and the rear wheels of a tricycle are 120 cm and 90 cm respectively. Before beginning to ride the tricycle, Ruth marks the points where the tyres touch the ground as A and B respectively on the front and the rear wheels. How many revolutions do the front and rear wheel make when both A and B touch the ground again simultaneously? **

(a) 6, 8

(b) 3, 4

(c) 9, 12

(d) 1, 4

**Answer**

B

**Question. Which of the following is an incorrect statement? **

(a) If √ + √b is an irrational number, then ab is also an irrational number.

(b) The reciprocal of an irrational number is always an irrational number.

(c) There are infinitely many rational numbers between any two irrational numbers.

(d) 7 x 13 +13 is a prime number.

**Answer**

D

**Question. I. The L.C.M. of x and 18 is 36. II. The H.C.F. of x and 18 is 2. What is the number x ? **

(a) 1

(b) 2

(c) 3

(d) 4

**Answer**

D

**Question. Which of the following statement(s) is/are not correct? **

(a) Every integer is a rational number.

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

(c) Every real number is rational.

(d) Every point on a number line is associated with a real number.

**Answer**

C

**Question. The largest non-negative integer k such that 24k divides 13! is **

(a) 2

(b) 3

(c) 4

(d) 5

**Answer**

B

**Question. Which of the following statement(s) is/are not correct? **

(a) There are infinitely many even primes.

(b) Let ‘a’ be a positive integer and p be a prime number such that a^{2} is divisible by p, then a is divisible by p.

(c) Every positive integer different from 1 can be expressed as a product of non-negative power of 2 and an odd number.

(d) If ‘p’ is a positive prime, then √p is an irrational number.

**Answer**

A

**Question. If a = 2 ^{3} × 3, b = 2 × 3 × 5, c = 3^{n} × 5 and L.C.M. (a, b, c) = 2^{3} × 3^{2} × 5, then n = **

(a) 1

(b) 2

(c) 3

(d) 4

**Answer**

B

**Question. A number lies between 300 and 400. If the number is added to the number formed by reversing the digits, the sum is 888 and if the unit’s digit and the ten’s digit change places, the new number exceeds the original number by 9. Then, the number is **

(a) 339

(b) 341

(c) 378

(d) 345

**Answer**

D

**Question. If p _{1} and p_{2} are two odd prime numbers such that p_{1} > p_{2}, then p_{1}^{ 2} – p_{2}^{2} is **

(a) an even number

(b) an odd number

(c) an odd prime number

(d) a prime number

**Answer**

A

**Question. When a natural number x is divided by 5, the remainder is 2. When a natural number y is divided by 5, the remainder is 4. The remainder is z when x + y is divided by 5. The value of 2z −5/3 is **

(a) –1

(b) 1

(c) –2

(d) 2

**Answer**

A

**Question. Given that L.C.M. (91, 26) = 182, then H.C.F. (91, 26) is **

(a) 13

(b) 26

(c) 17

(d) 9

**Answer**

A

**Question. The value of ^{—}0.235 is : **

(a) 233/ 900

(b) 233/ 990

(c) 235/ 999

(d) 235/ 990

**Answer**

C

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

(a) 15

(b) 16

(c) 9

(d) 5

**Answer**

B

**Question. Given that 1/7= 0.142857 7 , which is a repeating decimal having six different digits. If x is the sum of such first three positive integers n such that 1/n= 0. ^{—}abcdef n, where a, b, c, d, e and f are different digits, then the value of x is **

(a) 20

(b) 21

(c) 41

(d) 42

**Answer**

C

**Question. If m = n ^{2} – n, where n is an integer, then m^{2} – 2m is divisible by **

(a) 20

(b) 24

(c) 30

(d) 16

**Answer**

B

**Question. The unit digit in the expression 55 ^{725} + 73^{5810} + 22^{853} is **

(a) 0

(b) 4

(c) 5

(d) 6

**Answer**

D

**Question. A class of 20 boys and 15 girls is divided into n groups so that each group has x boys and y girls. Values of x, y and n respectively are **

(a) 3, 4 and 8

(b) 4, 3 and 6

(c) 4, 3 and 7

(d) 7, 4 and 3

**Answer**

C

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

(a) m

(b) m + 1

(c) 2m

(d) 2m + 1

**Answer**

C

**Question. On dividing a natural number by 13, the remainder is 3 and on dividing the same number by 21, the remainder is 11. If the number lies between 500 and 600, then the remainder on dividing the number by 19 is **

(a) 4

(b) 6

(c) 9

(d) 13

**Answer**

A

**Question. Product of two co-prime numbers is 117. Their L.C.M. should be **

(a) 1

(b) 117

(c) equal to their H.C.F.

(d) Lies between 1 to 117

**Answer**

B

**Question. Which of the following statement(s) is/are always true? **

(a) The sum of two distinct irrational numbers is rational.

(b) The rationalising factor of a number is unique.

(c) Every irrational number is a surd.

(d) None of these

**Answer**

D

**Question. The product of unit digit in (7 ^{95} – 3^{58}) and (7^{95} + 3^{58}) is **

(a) 8

(b) lies between 3 and 7

(c) 6

(d) lies between 3 and 6

**Answer**

A

**Question. If p, q are two consecutive natural numbers, then H.C.F. (p, q) is **

(a) p

(b) q

(c) 1

(d) pq

**Answer**

C

**Fill in the Blanks :**

**Question. 35/50 is a ………………… decimal expansion. **

**Answer**

** terminating**

**Question. The exponent of 2 in the prime factorisation of 144, is …………… **

**Answer**

**4**

**Question. √5 is a/ an …………… number. **

**Answer**

**irrational **

** Question. An ………….. is a series of well defined steps which gives a procedure for solving a type of problem. **

**Answer**

**algorithm**

**Question. An……….. is a proven statement used for proving another statement. **

**Answer**

** lemma**

**Question. L.C.M. of 96 and 404 is ……………… **

**Answer**

** 9696**

**Question. 6 +√ 2 is a/ an …………… number. **

**Answer**

** irrational**

**Question. H.C.F. of 6, 72 and 120 is ………….. **

**Answer**

**6**

**Question. 1/√2 is a/ an …………… number. **

**Answer**

** irrational**

**Question. 156 as a product of its prime factors …………. **

**Answer**

** 2 ^{2} × 3 × 13**

**Question. 7 √5 is a/ an …………… number. **

**Answer**

** irrational**

**True or False :**

**Question. Every fraction is a rational number. **

**Answer**

** True**

**Question. √2 and √3 are irrational numbers. **

**Answer**

**True **

**Question. The number of irrational numbers between 15 and 18 is infinite. **

**Answer**

**True**

**Question. Every composite number can be expressed (factorised) as a product of primes and this factorisation is unique, apart from the order in which the prime factors occur. **

**Answer**

**True**

**Question. The quotient of two integers is always a rational number. **

**Answer**

** False**

**Question. Given positive integers a and b, there exist whole numbers q and r satisfying a = bq + r, 0 ≤ r < b. **

**Answer**

**True**

**Question. If x = p/q be 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 x has a decimal expansion which is terminating. **

**Answer**

**True**

**Question. 1/0 is not rational. **

**Answer**

**True**

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

**Answer**

** True**

**Match the Following : ** ** Question. **

Column-I | Column-II |

(A) H.C.F of the smallest composite number and the smallest prime number | (p) 6 |

(B) H.C.F of 336 and 54 | (q) 5 |

(C) H.C.F of 475 and 495 | (r) 2 |

**Answer**

**(A) → (r); (B) → (p); (C) → (q)**

** Question. **

Column-I | Column-II |

(A) 551/2^{3} × 5^{6} × 7^{9} | (p) a prime number |

(B) Product of ( √5 – √3) and (√ 5 + √3) is | (q) is an irrational number |

(C) √5 – 4 | (r) is a terminating decimal representation |

(D) 422/2^{3} × 5^{4} | (s) is a non-terminating but repeating decimal representation |

**Answer**

**(A) → (s); (B) → (p); (C) → (q); (D) → (r)**

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