# MCQs for Mathematics Class 10 with Answers Chapter 1 Real Numbers

Students of class 10 Mathematics should refer to MCQ Questions Class 10 Mathematics Real Numbers with answers provided here which is an important chapter in Class 10 Mathematics NCERT textbook. These MCQ for Class 10 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 10 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 10 Mathematics examination

**Chapter 1 Real Numbers MCQ with Answers Class 10 Mathematics**

MCQ Questions Class 10 Mathematics Real Numbers provided below have been prepared by expert teachers of grade 10. These objective questions with solutions are expected to come in the upcoming Standard 10 examinations. Learn the below provided MCQ questions to get better marks in examinations.

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

(a) 5

(b) 6

(c) 7

(d) none of these

**Answer**

B

**Question. 96 books of English, 240 books of hindi and 336 books of mathematics have to be packed in bundles with each bundle containing equal number of books of each of the subjects. What is the difference of the largest number of books which can be packed in each bundle and the least number of bundles which can be made? **

(a) 1

(b) 3

(c) 34

(d) 48

**Answer**

C

**Question. Choose the irrational number. **

(a) 2 – √4

(b) (√5)^{2}

(c) √9 – √4

(d) √2 – √3

**Answer**

D

**Question. The L.C.M. of 318 and 477 is expressed as 159 x p + 318.What is the value of ‘p’? **

(a) 2

(b) 4

(c) 3

(d) 0

**Answer**

B

**Question. What is the L.C.M. of 140 and 605 if their H.CF. is H? **

(a) 8000

(b) 5500

(c) 8400

(d) 7700

**Answer**

D

**Question. If 0.737373….. is expressed in the form of p/q where ‘p’ and ‘q’ are co-primes, what are the prime factors of ‘q’? **

(a) 4 and 7

(b) 3 and 11

(c) 7 and 11

(d) 4 and 3

**Answer**

B

**Question. 910 blue pens and 1001 red pens are distributed to students of class X so that each student gets the same number of pens of each kind. What is the maximum strength of the class? **

(a) 91

(b) 80

(c) 94

(d) 86

**Answer**

A

**Question. Find the respective values of H.C.F. and L.C.M. of 5474, 9775 and 11730. **

(a) 391 and 410550

(b) 319 and 401550

(c) 410550 and 319

(d) 405150 and 193

**Answer**

A

**Question. ‘p’ is the remainder obtained when a perfect square is divided by 3.What is the value of ‘p’? **

(a) 1

(b) 0

(c) Either (a) or (b).

(d) Neither (a) nor (b).

**Answer**

C

**Question. Which of the following is correct about 41/37500 **

(a) It is a non-terminating repeating decimal.

(b) It is a terminating repeating decimal.

(c) It is a terminating and not repeating decimal.

(d) It is a non-terminating and not repeating decimal.

**Answer**

A

**Question. Which of the following is a non-terminating repeating decimal? **

(a) 24/1600

(b) 171/800

(c) 123/2^{2} x 5^{3}

(d) 145/2^{3} x 5^{2} x 7^{2}

**Answer**

D

**Question. The condition to be satisfied by q, so that the rational number has a non terminating decimal expansion is: **

(a) The prime factorisation of q is of the form 2^{m} x 5^{n}

(b) The prime factorisation of q is not of the form 2^{m} x 5^{n}

(c) The prime factorisation of q is of the form m 2 x n^{5} .

(d) The prime factorisation of q is not of the form m 2 x 5^{n} .

**Answer**

B

**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. If – 2 ≤ x ≤ 2, which of the following is not true for x: **

(a) x can take only 3 values if x is a natural number.

(b) if x is an irrational number, then only one value of x is possible.

(c) if x is a non-negative integer, then only 3 values of x are possible.

(d) if x is a rational number, infinite values of x are possible.

**Answer**

D

**Question. The product of a rational and irrational number is **

(a) rational

(b) irrational

(c) both of above

(d) none of above

**Answer**

B

**Question. The largest positive integer which divides 434 and 539 leaving remainders 9 and 12 respectivelyis: **

(a) 9

(b) 108

(c) 17

(d) 539

**Answer**

C

**Question. There is a circular path around a field. Reema takes 22 minutes to complete one round while herfriend Saina takes 20 minutes to complete the same. If they both start at the same time and movein the same direction, after how many minutes will they meet again at the starting **

(a) 220

(b) 3.4

(c) 440

(d) 4.4

**Answer**

A

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

(a) Rational

(b) Irrational

(c) Both (a) and (c)

(d) Either (a) or (b)

**Answer**

B

**Question. If HCF (306, 657) = 9, then LCM of 306 and 657 is: **

(a) 1

(b) 22338

(c) 9

(d) 12

**Answer**

B

**Question. √7 is **

(a) An integer

(b) An irrational number

(c) A rational number

(d) None of these

**Answer**

B

**Question. Euclid’s Lemma states that, for given positive integers a and b, there exist unique integers q and r,such that a = bq + r, where : **

(a) 0 < r < b

(b) 0 ≤ r < b

(c) 0 < r ≤ b

(d) 0 ≤ r ≤ b

**Answer**

B

**Question. A number which can be expressed in the form where q ≠ 0 is a rational number is: **

(a) p and q are co-prime numbers

(b) p and q are real numbers

(c) p and q are numbers

(d) p and q are integers

**Answer**

D

**Question. In decimal expansion and representation, which of the following is not a rational numbers: **

(a) terminating decimal

(b) terminates after 17 digits

(c) non-terminating repeating

(d) non-terminating non-repeating

**Answer**

D

**Question. In a seminar, the number of participants in English, German and Sanskrit are 45,75 and 135. Findthe number of rooms required to house them, if in each room, the same number of participants areto be accommodated and they should be of the same language. **

(a) 45

(b) 17

(c) 75

(d) 135

**Answer**

B

**Question. A number , when expressed in decimal form, terminates after 7 digits, then factors of q are ofthe form x m x y n ; the value of x + y should be : **

(a) 7

(b) 14

(c) 9

(d) 26

**Answer**

A

**Question. Write an irrational number between 2 and 3. **

(a) 2.5

(b) 2.001

(c) 2.1333333456…

(d) 2.13

**Answer**

C

**Question. Which of the following are irrational whose sum and product are both rationals : **

(a) √2 + 3,√2 – 3

(b) √2 + √3,√2 – √3

(c) 3 + √2, 3 – √2

(d) √2 + 1,√2 – 1

**Answer**

C

**Question. Find the value of x from the following such that x ^{2} is irrational but x^{ 4} is rational: **

(a) √2

(b) 3√2

(c) 4√2

(d) 2

**Answer**

C

**Question 20. A rational number between 72 and 73 is: **

(a) √ 2 + √ 3/2

(b) √ 2 – √ 3/2

(c) 1.5

(d) 1.8

**Answer**

C

**Question. The rational number that corresponds to 0.6+0. +0.4 is : **

(a) 83/90

(b) 7/9

(c) 43/90

(d) 167/90

**Answer**

D

**Question. HCF and LCM of two positive integers a and b satisfy a relationship, that: **

(a) (HCF)(LCM) =

(b) (HCF) (LCM) = 1

(c) (HCF)(LCM) = ab

(d) No defined relation

**Answer**

C

**Question. If we write 0.9 as a rational number, we get: **

(a) 9/10

(b) 1

(c) 1/2

(d) 1/10

**Answer**

B

**Question. If a positive integer ‘a’ is divided by 2, what can be the remainder ? **

(a) 0 or 1

(b) 0,1 or 2

(c) 1 or 2

(d) Any positive number

**Answer**

A

**Question. The least number that is divisible by all the numbers from 1 to 8 (both inclusive) is **

(a) 840

(b) 2520

(c) 8

(d) 420

**Answer**

A

**Question. If a non-zero rational number is multiplied to an irrational number, we always get: **

(a) an irrational number

(b) a rational number

(c) zero

(d) one

**Answer**

A

**Question. The greatest number which divides 87 and 97, leaving 7 as remainder is : **

(a) 10

(b) 1

(c) 87 x 97

(d) 6300

**Answer**

A

**Question. A number when divided by 61 gives 27 as quotient and 32 as remainder. find the number **

(a) 1967

(b) 1796

(c) 1679

(d) 1569

**Answer**

C

**Question. The least number, which when divided by 10,14 and 18, leaves remainder 4, is : **

(a) 630

(b) 634

(c) 252

(d) 496

**Answer**

B

**Question. Which of the following is a rational number ? **

**Answer**

B

**Question. The greatest number which divides 17, 28 and 34 leaving remainders 2, 3 and 4 respectively is: **

(a) 5

(b) 24

(c) 1

(d) 17

**Answer**

A

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

(a) q

(b) q + 1

(c)2q

(d)2q + l

**Answer**

C

**Question. 72 litres of liquid A and 108 litres of liquid B are to be packed in containers of the same size. Theminimum number of containers required are: **

a) 36

(b) 18

(c) 5

(d) 10

**Answer**

C

**Question. An army contingent of 616 members is to march behind an army band of 32 members in a parade.The two groups have to march in the same number of columns. Find the maximum number ofcolumns in which they can march ? **

(a) 32

(b) 60

(c) 40

(d) 8

**Answer**

D

**Question. The factor tree of a number has some unknowns, find the values of a, b, c, d, e,f and g. **

**Answer**

A

**Question. 91/625 ,when written in decimal form 625 terminates; as factors of denominator are in the form m 2 xn 5 . This number will terminate after how many digits ? **

(a) 3

(b) 2

(c) 1

(d) 4

**Answer**

D

**Question. 91/625 ,when written in decimal form 625 terminates; as factors of denominator are in the form m 2 xn 5 . This number will terminate after how many digits ? ****(a) 3****(b) 2****(c) 1****(d) 4**

**Answer**

D

**Question. If P= √n -1+ √n+1 where n is a positive integer then the value of P is **

(a) a rational number

(b) not a rational number

(c) an integer

(d) a natural number

(e) None of these

**Answer**

B

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

(a) 17

(b) 11

(c) 13

(d) 31

(e) None of these

**Answer**

D

**Question. The smallest three digit number which leaves remainders 8 and 12 when divided by 28 and 32 respectively, is _________ **

(a) 102

(b) 222

(c) 202

(d) 204

(e) None of these

**Answer**

D

**Question. he HCF of two consecutive rational numbers x and x +1 is : **

(a) x

(b) x + 1

(c) 1

(d) 0

**Answer**

C

**Question. Select the incorrect answer,(2 + √5)(2-√5) is: **

(a) a natural number

(b) a rational number

(c) a whole number

(d) an irrational number

**Answer**

D

**Question. The least positive integer divisible by 20 and 24 is **

(a) 360

(b) 120

(c) 480

(d) 240

**Answer**

B

**Question. The HCF and LCM of two numbers is 9 and 459 respectively. If one of the numbers is 27, then theother number is **

(a) 459

(b) 153

(c) 135

(d) 150

**Answer**

B

**Question. The HCF of a number which is neither prime nor composite and any other number x is: **

(a) x

(b) x + 1

(c) 1

(d) Any number

**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. Select the incorrect answer, (2 + √5)(2-√5) is: **

(a) a natural number

(b) a rational number

(c) a whole number

(d) an irrational number

**Answer**

D

**Question. Find q and r, if 12560 = 215 q + r. **

(a) q = 58, r = 0

(b) q = 58, r = 10

(c) q = 58, r = 4

(d) q = 58, r = 90

**Answer**

D

**Question. Using Euclid’s Lemma, if d is the HCF of 1155 and 506, find ‘d’ **

(a) 11

(b) 143

(c) 77

(d) 66

**Answer**

A

**Question. The smallest composite number is: **

(a) 1

(b) 2

(c) 3

(d) 4

**Answer**

C

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

(a) 2p + 1

(b) 2p

(c) p + 1

(d) p

**Answer**

A

**Question. The smallest composite number is: **

(a) 1

(b) 2

(c) 3

(d) 4

**Answer**

C

**Question. A lemma is an axiom used for proving **

(a) other statement

(b) no statement

(c) contradictory statement

(d) none of these

**Answer**

A

**Question. Which of the following rational numbers, in decimal form, terminates ? **

(a) 64/ 455

(b) 77/210

(c) 31/200

(d) 29/343

**Answer**

C

**Question. HCF of 8, 9, 25 is **

(a) 8

(b) 9

(c) 25

(d) 1

**Answer**

D

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

(a) Always irrational

(b) Always rational

(c) Rational or irrational

(d) One

**Answer**

A

**Question. Every positive even integer is of the form ____ for some integer ‘q’. **

(a) 2q

(b) 2q – 1

(c) 2q + 1

(d) none of these

**Answer**

A

**Question. 1/√3 is – **

(a) A rational number

(b) An irrational number

(c) A whole number

(d) None of these

**Answer**

B

**Question. The largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is **

(a) 260

(b) 75

(c) 65

(d) 13

**Answer**

D

**Question. p is **

(a) a rational number

(b) an irrational number

(c) both (a) & (b)

(d) neither rational nor irrational

**Answer**

B

**Question. For any two positive integers a and b, there exist (unique) whole numbers q and r such that **

(a) q = ar + b , 0 = r < b.

(b) a = bq + r , 0 = r < b.

(c) b = aq + r , 0 = r < b.

(d) none of these

**Answer**

B

**Question. The largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectivelyis **

(a) 17

(b) 11

(c) 34

(d) 45

**Answer**

A

**Question. Which number is divisible by 11? **

(a) 1516

(b) 1452

(c) 1011

(d) 1121

**Answer**

B

**Question. For positive integers a and 3, there exist unique integers q and r such that a = 3q + r, where r mustsatisfy: **

(a) 0 < r < 3

(b) 1 < r < 3

(c) 0 < r < 3

(d) 0 < r < 3

**Answer**

A

**Question. If p is a single digit natural number and the unit digits of p ^{4} 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. If LCM and HCF of two numbers are 3003 and 21 respectively, then how many such numbers are possible? **

(a) 0

(b) 1

(c) 2

(d) 3

(e) None of these

**Answer**

C

**Question. If HCF of the numbers (3600, x) = 20 then how many values are possible for x? (where it is assumed that x is a product of a power of 2 and a power of 5 only) **

(a) One

(b) Two

(c) Three

(d) Four

(e) None of these

**Answer**

B

**Question. A mason has to fit two bathrooms with square marble tiles of the largest possible size. The dimensions of each such bathroom are 12 fts and 10 fts. If the size of the tiles in inches has to be taken then number of such tiles required is ____ **

(a) 15

(b) 30

(c) 60

(d) 80

(e) None of these

**Answer**

C

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

(a) 0

(b) 1

(c) 2

(d) 3

(e) None of these

**Answer**

B

**Question. Two natural numbers whose difference is 66 and the least common multiple is 360, are: **

(a) 120 and 54

(b) 90 and 24

(c) 180 and 114

(d) 130 and 64

**Answer**

B

**One Word Questions :**

**Question. What is the value of x? **

**Answer**

42

**Question. What is the H.C.F. of 152 and 171?**

**Answer**

19

**Question. Division of 133 by 19 gives remainders = 0. What is the H.C.F. (133,9)?**

**Answer**

19

**Question. Which smallest irrational number should be added to (3+ √5) to get a rational number?**

**Answer**

(– √5)

**Question. What will be the units digit of 7 ^{5}?**

**Answer**

7

**Question. Simplify :– (3+ √5)²(3 – √5)²**

**Answer**

16

**Question. Find the digit at units place of 4 ^{5}.**

**Answer**

4

**Question. What is the sum of 0.¯3 and 0.¯4 .**

**Answer**

0.¯7

**Question. H.C.F. and L.C.M. of two numbers are 19 and 380 respectively. If one of the numbers is 95, what is the other number?**

**Answer**

76

**Question. When 176 is divided by a number it gives the remainder 5 and quotient 9. What is the number?**

**Answer**

19

**Question. What will be the unit’s digit of (7×3 ) ^{21} ?**

**Answer**

1

**Question. 1000 2x 5y . What is the value of x and y.**

**Answer**

x=3, y=3

**Question. What is the value of x and y? **

**Answer**

x=72, y=24

**Question. Which prime numbers will be repeatedly multiplied in prime factorization of 3200.**

**Answer**

2 and 5

**Question. Which digit you will get at units place of 618?**

**Answer**

6

**Question. Give the decimal representation of 13/11 .**

**Answer**

1.¯18

**Question. Express as a rational number :– (4 – √3) (4 + √3)/(√5–2)(√5 + 2) .**

**Answer**

13

**Question. Find the digit at units place of 8n if n is 9.**

**Answer**

8

**Question. If L.C.M. of two numbers 16 & 28 is 112, then what is the H.C.F. of these numbers.**

**Answer**

4

**Question. Simplify :– (2+ √3)+(5 – √3)+(6+ √3)+(7 – √3)**

**Answer**

20

We hope the above multiple choice questions for Class 10 Mathematics for Chapter 1 Real Numbers provided above with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Real Numbers is an important chapter in Class 10 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefit of class 10 students. Please go through these and let us know if you have any feedback in the comments section.