CBSE Class 10 Mathematics Real Numbers MCQs Set H

Question. If m = pq³ and n = p3q,then HCF (m, n) =
a) pq
b) pq³
c) p³q³
d) p²q³

Answer: A

Question. HCF of co-primes a and b is
a) ab
b) 1
c) a
d) b

Answer: B

Question. The LCM of smallest composite number and the smallest prime number is
a) 2
b) 1
c) 4
d) 3

Answer: C

Question. Which of the following rational numbers have terminating decimal?
i) 16/125 ii) 5/18 iii) 2/21 iv) 7/250
a) i and ii
b) ii and iii
c) i and iii
d) i and iv

Answer: D

Question. After how many places the decimal expansion of 13/23 × 52 terminates?
a) 3
b) 2
c) 4
d) 1

Answer: A

Question. The LCM and HCF of two rational numbers are equal, then the numbers must be
a) prime
b) co-prime
c) composite
d) equal

Answer: D

Question. 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) 5

Answer: A

Question. If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then a = …
a) 2
b) 3
c) 4
d) 1

Answer: C

Question. The least number that is divisible by all the numbers between 1 and 10 (both inclusive) is
a) 2520
b) 2450
c) 2420
d) 2250

Answer: A

Question. The smallest number which gives remainders 8 and 12 when divided by 28 and 32 respectively is..
a) 180
b) 240
c) 204
d) 210

Answer: C

Question. The smallest 4 digit number divisible by 24,15 and 36 is
a) 1000
b) 1208
c) 1800
d)1080

Answer: D

Question. The largest number which exactly divides 280 and 1245 leaving remainders 4 and 3respectively
is…
a) 36
b) 54
c) 138
d) 72

Answer: C

Question. 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

Answer: B

Question. If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairsof such numbers are
a) 2
b) 3
c) 4
d) 5

Answer: C

Question. The sum of the exponents of the prime factors in the prime factorisation of 196,is
a) 1
b) 2
c) 4
d) 6

Answer: C

Question. The LCM of two numbers is 1200,Which of the following cannot be their HCF?
a) 600
b) 500
c) 400
d) 200

Answer: B

SECTION B

(CASE STUDY BASED QUESTIONS)

1. Three sets of English, Hindi and Mathematics books have to be stacked in such a way that all the books are stored topic-wise and the height of each stack is same. The number of English books is 96,the number of Hindi books is 240 and the number of Mathematics books is 336. Assuming that the books are of the same thickness. Using this data answer the following questions

Question. The maximum number of books in each stack is
a) 12
b) 24
c) 48
d) 36

Answer: C

Question. Number of stacks of English books is
a) 2
b) 7
c) 5
d) 12

Answer: A

Question. Number of stacks of Mathematics books is
a) 2
b) 7
c) 5
d) 12

Answer: B

Question. Number of stacks of Hindi books is
a) 2
b) 7
c) 5
d) 12

Answer: C

Question. Which Mathematical concept was used in finding the maximum number of books in each stack?
a) LCM
b) HCF
c) Neither HCF nor LCM
d) Fundamental theorem of Arithmetic

Answer: B

2. 105 goats,140 donkeys and 175 cows have to be taken across a river. There is only one boat which will have to make many trips in order to do so. The lazy boatman has his own conditions for transporting them. He insists that he will take the same number of animals in every trip and they have to be of same kind. He will naturally like to take the largest possible number each time.

Question. How many animals have been taken in each trip?
a) 12
b) 35
c) 70
d) 24

Answer: B

Question. How many trips to be done so that all animals crossed the river?
a) 12
b) 35
c) 70
d) 24

Answer: A

Question. When the animals were doubled,how many animals could be taken in each trip?
a) 12
b) 35
c) 70
d) 24

Answer: C

Question. The LCM of all animals is
a) 2400
b) 2300
c) 2100
d) 2000

Answer: C

3. To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections –Section A and Section B of grade X. There are 32 students in section A and 36 students in section B

Question. What is the minimum number of books you will acquire for the class library, so that they can bedistributed equally among students of Section A or Section B?
a) 144
b) 128
c) 288
d) 272

Answer: C

Question. If the product of two positive integers is equal to the product of their HCF and LCM is true, thenthe HCF(32,36)is..
a) 2
b) 4
c) 6
d) 8

Answer: B

Question. 36 can be expressed as a product of its primes as
a) 22 x 32
b) 21 x 33
c) 23 x 31
d) 20 x 30

Answer: A

Question. 7 x 11 x 13 x 15 + 15 is a
a) Prime number
b) composite number
c) neither prime or composite
d) None of the above

Answer: B

Question. If p and q are positive integers such that p = ab2 and q = a2b,where a and b are prime numbers, then the LCM (p, q) is…
a) ab
b) a²b²
c) _a3b²
d) a³b³

Answer: B

4. A seminar is being conducted by an Educational Organisation,where the participants will be educators of different subjects. The number of participants in Hindi,English and Mathematics are 60, 84 and 108 respectively.

Question. In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are
a) 14
b) 12
c) 16
d) 18

Answer: B

Question. What is the minimum number of rooms required during the event?
a) 11
b) 31
c) 41
d) 21

Answer: D

Question. The LCM of HCF and LCM of 60, 84 and 108 is
a) 3780
b) 3680
c) 4780
d) 4680

Answer: A

Question. The product of HCF and LCM 60,84 and 108 is…
a) 55360
b) 35360
c) 45500
d) 45360

Answer: D

Question. 108 can be expressed as a product of its primes as
a) 22 x 32
b) 23 x 33
c) 22 x 32
d) 22 x 33

Answer: D

5. A mathematical Exhibition is being conducted in your school and one of your friends is making a model of a factor tree. He has some difficulty and ask for your help in completing a quiz for the audience. Observe the following factor tree and answer the following.

Question. What will be the value of x?
a) 15005
b) 13915
c) 56920
d) 17429

Answer: a

Question. What will be the value of y?
a) 23
b) 22
c) 11
d) 19

Answer: D

Question. What will be the value of z?
a) 22
b) 23
c) 17
d) 19

Answer: a

Question. According to Fundamental Theorem of Arithmetic, 13915 is a.
a) Composite number
b) Prime number
c) Neither prime nor composite
d) Even number

Answer: D

Question. The prime factorisation of 13915 is
a) 5 x 113 x 132
b) 5 x 113 x 232
c) 5 x 112 x 23
d) 5 x 112 x 132

Answer: D

6. Klick has a camera that takes film that allows 24 exposures,whereas Snapp has a camera that takes film that allows 36 exposures.Both of them want to be able to to take the same number of photographs and complete their rolls of film.

Question. Minimum number of exposures that should be taken by each
a) 24
b) 36
c) 72
d) 12

Answer: C

Question. Number of rolls Klick should buy
a) 6
b) 3
c) 2
d) 12

Answer: B

Question. Number of rolls Snapp should buy
a) 6
b) 3
c) 2
d) 12

Answer: C

Question. Which Mathematical concept was used in finding minimum number of exposures taken by each
a) HCF
b) LCM
c) Neither HCF nor LCM
d) Fundamental theorem of Arithmetic

Answer: B