**Mathematics***

**Multiple Choice Questions (MCQ)**

**Class 10 | Chapter 1 | Real Numbers**

# MCQ | CHAPTER 1 | REAL NUMBERS

**CHAPTER 1 CLASS – 10**

**(MCQ WORKSHEET) **

**Real Numbers**

Q1) HCF of 8, 9, 25 is

a) 8

b) 9

c) 25

d) 1

Ans : d

Q2) Which of the following is not irrational

Ans c

Q3) The product of a rational and irrational number is

(a) rational

b) irrational

(c) both of above

d) none of these

Ans : b

Q4) The LCM of two prime numbers p and q (p > q) is 221. Find the value of 3p – q.

(a) 4

(b) 28

(c) 38

(d) 48

Ans: c

Solution Hint

LCM of two prime numbers = product of the numbers

221 = 13 x 17.

So p = 17 & q = 13

⸫ 3p – q = 51 - 13 = 38

Q5) The sum of a rational and irrational number is

(a) rational

(b) irrational

(c) both of above

(d) none of above

Ans b

Q6) If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs of such numbers are

(a) 2

(b) 3

(c) 4

(d) 5

Ans: c

Solution Hint

Since HCF = 81, two numbers can be taken as 81x and 81y,

ATQ 81x + 81y = 1215 Or x + y = 15

which gives four co prime pairs-

1,14 2,13 4,11 7, 8

Q7) If LCM (x, 18) = 36 and HCF (x, 18) = 2, then x is

(a) 2

(b) 3

(c) 4

(d) 5

Ans: c

Q8) The set A = {0,1, 2, 3, 4, …} represents the set of

(a) whole numbers

(b) integers

(c) natural numbers

(d) even numbers

Ans a

Q9) Which number is divisible by 11?

(a) 1516

(b) 1452

(c) 1011

(d) 1121

Ans b

Q10) LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by

(a) x

(b) y

(c) xy

(d) x / y

Ans b

Q11) The largest number that will divide 398,436 and 542 leaving remainders 7,11 and 15 respectively is

(a) 17

(b) 11

(c) 34

(d) 45

Ans a

Q12) There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students

(a) 48

(b) 56

(c) 52

(d) 63

Ans c

Q13) There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet ?

(a) 36 minutes

(b) 18 minutes

(c) 6 minutes

(d) They will not meet

Ans a

Q14) Express 98 as a product of its primes

(a) 2² × 7

(b) 2² × 7²

(c) 2 × 7²

(d) 2^{3} × 7

Ans c

Q 15) Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.

(a) 350 kg

(b) 290 kg

(c) 200 kg

(d) 98 kg

Ans d

Q16) The ratio of LCM and HCF of the least composite and the least prime numbers is

(a) 1:2

(b) 2:1

(c) 1:1

(d) 1:3

Ans: b

Solution Hint

Least composite number is 4 and the least prime number is 2. LCM(4, 2) : HCF(4, 2) = 4 : 2 = 2 : 1

Q17) If a^{2} = 23/25, then a is

(a) rational

(b) irrational

(c) whole number

(d) integer

Ans: b

Q18) Prime factors of the denominator of a rational number with the decimal expansion 44.123 are

(a) 2, 3

(b) 2, 3, 5

(c) 2, 5

(d) 3, 5

Ans: c

Solution Hint

Since it has a terminating decimal expansion, so prime factors of the denominator will be 2,5

Q19) If two positive integers A and B can be ex-pressed as A = xy^{3}
and B = x^{4}y^{2}z ; x, y being prime numbers, the LCM (A, B)
is
(a) xy²

(b) x

^{4}y²z

(c) x

^{4}y

^{3}
(d) x

^{4}y

^{3}z

Ans d

Q20) If two positive integers A and B can be
expressed as A = xy

^{3} and B = x

^{4}y

^{2}z ; x, y
being prime numbers then HCF (A, B) is

(a) xy²

(b) x

^{4}y²z

(c) x

^{4}y

^{3}
(d) x

^{4}y

^{3}z

Ans a

Q21) The largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is

(a) 260

(b) 75

(c) 65

(d) 13

Ans d

Q22) The least number that is divisible by all the numbers from 1 to 5 (both inclusive) is

(a) 5

(b) 20

(c) 60

(d) 100

Ans c

Hint. LCM of 1, 2, 3, 4, 5 = 60

Q 23) 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

Ans a

Hint. LCM of 1, 2, 3, 4, 5,6,7,8 = 840

Q 24) LCM of two coprime numbers is 91. If one number is 13 then find the other.

a) 3

b) 13

c) 7

d) 11

Ans: c

Q25) LCM of 3a^{2}b^{3}c^{2} and 5a^{3}b^{2}c^{3}

a) a^{2}b^{2}c^{2}

b) 3a^{3}b^{3}c^{2}

c) 5a^{3}b^{2}c^{3}

d) 15a^{3}b^{3}c^{3}

Ans: d

Q26) The product of two consecutive natural numbers is always:

(a) prime number

(b) even number

(c) odd number

(d) even or odd

Ans b

Q27) When a number is divided by 7, its remainder is always:

(a) greater than 7

(b) at least 7

(c) less than 7

(d) at most 7

Ans c

Q28) If HCF (16, y) = 8 and LCM (16, y) = 48, then the value of y is

(a) 24

(b) 16

(c) 8

(d) 48

Ans a

Q29) If LCM (77, 99) = 693, then HCF (77, 99) is

(a) 22

(b) 7

(c) 9

(d) 11

Ans d

Q30) Find the greatest number of 5 digits, that will give us remainder of 5 when divided by 8 and 9 respectively.

(a) 99921

(b) 99931

(c) 99941

(d) 99951

Ans c

Hint: The greatest number will be multiple of LCM (8, 9)

LCM of 8 and 9 = 72

Now divide the greatest 5 digit number by 72.

Required no. = Greatest 5 digit number – Remainder + 5

Q31) The ratio between the LCM and HCF of 5, 15, 20 is

(a) 9 : 1

(b) 4:3

(c) 11:1

(d) 12:1

Ans: d

Hint : LCM(5, 15, 20) = 5 × 3 × 2 × 2 = 60

HCF(5, 15, 20) = 5

Q 32) The HCF and LCM of two numbers are 9 and 360 respectively. If one number is 45, then find the other.

a) 78

b) 84

c) 72

d) 96

Ans: c

Q33) LCM of two co-prime numbers x and y is

a) x + y

b) 1

c) xy

d) x – y

Ans c

Q34) Two numbers are in the ratio 3 : 5 and their HCF = 8. Find their LCM

a) 960

b) 120

c) 480

d) 240

Ans b

Hint: Let numbers are 3x and 5x. Common factor is x.

HCF is the product of common factors. So HCF of 3x and 5x = x = 8

So Numbers are 3 x 8 = 24 and 5 X 8 = 40

Now LCM X HCF = Product of numbers LCM X 8 = 24 X 40 LCM = (24 X 40) / 8 = 120

Q35) Product of two numbers is 1600. If their HCF is 20, find their LCM

a) 40

b) 800

c) 8

d) 80

Ans d

Q36) Two numbers are in the ratio 2 : 7 and their LCM is 70. Find their HCF

a) 25

b) 10

c) 4

d) 5

Ans d

Hint: Let two numbers are 2x and 7x. LCM is the product of common and non-common factors

So LCM of 2x and 7x = 14x = 70 x = 5 As x is the common factor of 2x and 7x. Therefore HCF (2x and 7x ) = x = 5

Q37) LCM of two numbers be 72, then which of the following cannot be their HCF

a) 12

b) 18

c) 16

d) 24

Ans c

Hint: LCM of two numbers is always factor of their HCF

Q38) Which of the following is not a terminating decimal ?

a) 21 / 12

b) 15/ 200

c) 21/45

d) 6/15

Ans c

Q39) LCM of two co-prime numbers is 187. If one number is 17 then find the other number ?

a) 13

b) 11

c) 19

d) 15

Ans b

Q40) What is the LCM of smallest prime number and smallest composite number

a) 4

b) 8

c) 2

d) 12

Ans a

Q41) Find the greatest number which divides 120 and 144 exactly

a) 12

b) 36

c) 24

d) 48

Ans c

Q 42) Find 4 digit largest number which is divisible by 12, 15 and 24

a) 9960

b) 9999

c) 9980

d) 9940

Ans a

Hint: Find LCM of 12,15 and 24 = 120

Divide largest 4 digit number (9999) by 120 and find remainder = 39 Required largest number is 9999 – 39 = 9960

Q 43) Find the greatest number which on dividing 205 and 238 leaving remainder 7 and 4 respectively

a) 9

b) 27

c) 36

d) 18

Ans d

Hint: Subtract 7 and 4 from 205 and 238 respectively we get 198 and 234 Requires number id the HCF (198 and 234) = 18

Q 44) Find the smallest 5 digit number which is divisible by 8, 10 and 12

a) 10040

b) 10080

c) 10020

d) 10060

Ans b

Hint: Find LCM of 8,10,12 = 120

Divide smallest 5 digit number (10000) by 120 and find the remainder = 40

Divisor – Remainder = 120 – 40 = 80 Required number = 10000 + 80 = 10080

Q 47) Find the smallest number which when divided by 6, 8 and 12 leaves same remainder 2 in each case.

a) 24

b) 26

c) 22

d) 28

Ans: b

Hint: Required number = LCM (6, 8, 12) + 2

Q 48) Find the least number which leaves remainder 5 after dividing by 16, 24, 30

a) 255

b) 240

c) 235

d) 245

Ans: d

Q 49) If two numbers are in 3 : 4 and their LCM is 60 then find the smallest number

a) 15

b) 25

c) 18

d) 20

Ans: a

Q 50) If two numbers are in 5 : 3 and their LCM is 90 then find their HCF

a) 3

b) 9

c) 6

d) 12

Ans: c

Q 51) If HCF (135,285) = 15 then LCM (135, 285) is

a) 2565

b) 2655

c) 2555

d) 2465

Ans: a

Q 52) The prime factorization of 3825 is

(a)
3 x 5^{2} x 21

(b) 3^{2} x 5^{2} x 3^{5}

(c) 3^{2} x 5^{2} x 17

(d) 3^{2} x 2^{5} x 17

Ans: c

Q 53) The least number that is divisible by all the numbers from 1 to 10 (both inclusive)

(a) 100

(b) 1000

(c) 2520

(d) 5040

Ans: c

Solution Hint

1 = 1, 2 = 2 × 1, 3 = 3 × 1, 4 = 2 × 2

5 = 5 × 1, 6 = 2 × 3, 7 = 7 × 1, 8 = 2 × 2 × 2

9 = 3 × 3, 10 = 2 × 5

So, LCM of these numbers = 1 × 2 × 2 × 2 × 3 × 3 × 5 × 7 = 2520 Hence, least number divisible by all the numbers from 1 to 10 is 2520

Q 54) Three bells ring at intervals of 4, 7 and 14 minutes. All three rang at 6 AM. When will they

ring together again?

(a) 6:07 AM

(b) 6:14 AM

(c) 6:28 AM

(d) 6:25 AM

Ans: c

Solution Hint

LCM 0f 4,7,14 = 28 Bells will they ring together again at 6 : 28 AM

Q 55) The LCM of 2^{3}
x 3^{2} and 2^{2} x 3^{3} is

a) 2^{3}

b) 3^{3}

c) 2^{3} x 3^{3}

d) 2^{2} x 3^{3}

Ans: c

Q 56) The HCF of two numbers is 18 and their product is 12960. Their LCM will be

(a) 420

(b) 600

(c) 720

(d) 800

Ans: c

Q 57) If xy = 180 and HCF (x, y) = 3, then LCM (x, y) is

a) 177

b) 183

c) 60

d) 63

Ans: c

Q 58) Prime factorization of 156 is

a) 2^{2} x 3 x 13

b) 2^{2} x 3^{2} x 13

c) 6^{2} x 2^{2}

d) 2^{3} x 3 x 13

Ans: a

Q 59) The HCF of 30, 72, 432 is

a) 2

b) 3

c) 6

d) 4

Ans: c

Q 60) Three bells ring at intervals of 4, 7 and 14 minutes. If all three ring at 6 a.m., when will they ring after that together again ?

a) 6:04 a.m.

b) 6:07 a.m.

c) 6:14 a.m.

d) 6:28 a.m.

Ans: d

Q 61) If HCF (39, 91) = 13, then LCM (39, 91) is:

a) 91

b) 273

c) 39

d) 3549

Ans: b

Q 62)

is a/an

a) Integer

b) Rational number

c) Natural Number

d) Irrational Number

Ans: b

Q 63) Two positive numbers have their HCF as 12 and their product as 6336. The number of pairs possible for the numbers is :

a) 2

b) 3

c) 4

d) 1

Ans: a

Solution Hint

Let two numbers be 12x and 12y where x and y are coprime numbers.

ATQ 12x X 12y = 6336 ⇒ 144 xy = 6336 ⇒ xy = = 4444 can be written as : (1 x 44), (2 x 22) and (4 x 11)

But x and y are co-primes so 2, 22 cannot be possible Hence required numbers are 1, 44 or 4, 11 ⇒ Two pair of numbers are possible.

Q 64) If n is any natural number, then (12)^{n} cannot end with the digit

a) 2

b) 4

c) 8

d) 0

Ans: d

Q 65) The number 385 can be expressed as the product of prime factors as

a) 5 x 11 x 13

b) 5 x 7 x 11

c) 5 x 7 x 13

d) 5 x 11 x 17

Ans: b

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