### Multiple Choice Questions (MCQ) On Mathematics

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### Maths MCQ Ch -1 Class 10 | Real Numbers

Mathematics*
Multiple Choice Questions (MCQ)
Class 10 | Chapter 1 | Real Numbers

MCQ Based on Fundamental of Arithmetic's (FTA)
MCQ  Based on the LCM and HCF of Numbers.
MCQ Based on the Rational and Irrational Numbers.
MCQ Based on the Terminating and Non-Terminating But repeating Decimals.
MCQ Based from the CBSE Sample Questions

In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. Solution Hints are also given to some difficult problems. Each MCQ contains four options from which one option is correct. On the right hand side column of the pdf Answer option is given.

Action Plan
First of all students should Learn and write all basic points and Formulas related to the real numbers.
Start solving  the NCERT Problems with examples.
Solve the important assignments on the number system.
Then start solving the following MCQ.

# 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) Euclid’s division lemma states that for two positive integers a and b, there exist unique integer q and r such that a = bq + r, where r must satisfy
(a) a < r < b
(b) 0 < r ≤ b
(c) 1 < r < b
(d) 0 ≤ r < b
Ans d

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 b = 3, then any integer can be expressed as a =
(a) 3q, 3q+ 1, 3q + 2
(b) 3q
(c) 3q+ 1
(d) None of These
Ans a

Q7) The product of three consecutive positive integers is divisible by
(a) 4
(b) only 1
(c) No Common Factor
(d) 6
Ans d

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) 23 × 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) For some integer p, every even integer is of the form
(a) 2p + 1
(b) 2p
(c) p + 1
(d) p
Ans b

Q17) For some integer p, every odd integer is of the form
(a) 2p + 1
(b) 2p
(c) p + 1
(d) p
Ans a

Q18) m² – 1 is divisible by 8, if m is
(a) an even integer
(b) a whole number
(c) a natural number
(d) an odd integer
Ans d

Q19) If two positive integers A and B can be ex-pressed as A = xy3 and B = x4y2z ; x, y being prime numbers, the LCM (A, B) is
(a) xy²
(b) x4y²z
(c) x4y3
(d) x4y3z

Ans d
Q20) If two positive integers A and B can be expressed as A = xy3 and B = x4y2z ; x, y being prime numbers then HCF (A, B) is
(a) xy²
(b) x4y²z
(c) x4y3
(d) x4y3z
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) 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
Ans c

Q25) 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
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 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
Ans d

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 45)

Ans d
Hint:

Q 46) Find HCF of

Ans: c
Hint: Required Number

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 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

Q 53) 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

Q 54) LCM of 3a2b3c2 and 5a3b2c3
a) a2b2c2
b) 3a3b3c2
c) 5a3b2c3
d) 15a3b3c3
Ans: d

Questions From CBSE Sample Paper 2021-22

Q 55) The decimal representation of will be
(a) Terminating
(b) Non-terminating
(c) Non-terminating and repeating
(d) Non-terminating and non-repeating
Ans: a

Q 56) The prime factorization of 3825 is
(a) 3 x 52 x 21
(b) 32 x 52 x 35
(c) 32 x 52 x 17
(d) 32 x 25 x 17
Ans: c

Q 57) 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 58) 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 59) The LCM of 23 x 32 and 22 x 33 is

a) 23
b) 33
c) 23 x 33
d) 22 x 33

Ans: c

Q 60) 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 61) The decimal expansion of     will terminate after how many places of decimals?
(a) 1
(b) 2
(c) 3
(d) 4
Ans: c

Q 62) 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

Q 63) 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

Q 64) If a2 = 23/25, then a is
(a) rational
(b) irrational
(c) whole number
(d) integer
Ans: b

Q 65) If LCM (x, 18) = 36 and HCF (x, 18) = 2, then x is
(a) 2
(b) 3
(c) 4
(d) 5
Ans: c

Q 66) 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

Q 67) The smallest number by which 1/13 should be multiplied so that its decimal expansion terminates after two decimal places is
(a) 13/100
(b) 13/10
(c) 10/13
(d) 100/13
Ans: a

Q 68) 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

Questions from CBSE Final Question Paper 2021-22 (Basic)

Q 69) If xy = 180 and HCF (x, y) = 3, then LCM (x, y) is
a) 177
b) 183
c) 60
d) 63
Ans: c

Q 70) Prime factorization of 156 is
a) 22 x 3 x 13
b) 22 x 32 x 13
c) 62 x 22
d) 23 x 3 x 13
Ans: a

Q 71) The decimal expansion of rational number    will terminate after how many places of decimals ?
a) 1
b) 2
c) 3
d) 5
Ans: b

Q 72) The HCF of 30, 72, 432 is
a) 2
b) 3
c) 6
d) 4
Ans: c

Q 73) What condition is to be satisfied by q so that a rational number     has a terminating decimal expansion ?
a) q = 2m3n, m, n are non-negative integers
b) q = 2m + 3n, m, n are non-negative integers
c) q = 2m x 5n, m, n are non-negative integers
d) q = 2m + 5n, m, n are non-negative integers
Ans: c

Q 74) The smallest number by which   should be multiplied so that its decimal expansion terminate after two decimal places is:

a)

b)

c)
d)
Ans: c

Q 75) 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

Questions from CBSE Final Question Paper 2021-22 (Standard)

Q 76) If HCF (39, 91) = 13, then LCM (39, 91) is:
a) 91
b) 273
c) 39
d) 3549
Ans: b

Q 77)    is a/an
a) Integer
b) Rational number
c) Natural Number
d) Irrational Number
Ans: b

Q 78) 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 =   = 44

44 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 79) The decimal expansion of the rational number      will terminate after
a) One Decimal Place
b) Two Decimal Place
c) Three Decimal Place
d) Four Decimal Place
Ans: c

Q 80) 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 81) 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

Q 82) The decimal expansion of     is :
a) Terminating
b) Non- Terminating and non-Recurring
c) Non-terminating and Recurring
d) Does not exist
Ans: c

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