CBSE Class 10 Real Numbers Sure Shot Questions Set K

Question. [HCF × LCM] for the numbers 100 and 190 is
(a) 190
(b) 1900
(c) 19000
(d) None of the options
Answer: (c) 19000

Question. The HCF of the smallest composite number and the smallest prime number is
(a) 1
(b) 2
(c) 3
(d) 5
Answer: (b) 2

Question. On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. The minimum distance each should walk so that each can cover the same distance in complete steps is
(a) 1260 cm
(b) 1920 cm
(c) 2242 cm
(d) 2520 cm
Answer: (d) 2520 cm

Question. The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then the other number is
(a) 20
(b) 28
(c) 60
(d) 80
Answer: (d) 80

Question. Four bells toll at an interval of 8, 12, 15 and 18 seconds respectively. All the four begin to toll together. The number of times they toll together in one hour excluding the one at the start will be
(a) 5
(b) 8
(c) 10
(d) 12
Answer: (c) 10

Exercise 

Question. The LCM of smallest two-digit composite number and smallest composite number is:
(a) 12
(b) 4
(c) 20
(d) 44
Answer: (c) 20

Question. 325 can be expressed as a product of its primes as:
(a) \( 5^2 \times 7 \)
(b) \( 5^2 \times 13 \)
(c) \( 5 \times 13^2 \)
(d) \( 2 \times 3^2 \times 5^2 \)
Answer: (b) \( 5^2 \times 13 \)

Question. HCF (a, b) × LCM (a, b) is equal to
(a) a + b
(b) a – b
(c) a × b
(d) a ÷ b
Answer: (c) a × b

Question. If a and b are co-prime, then \( a^2 \) and \( b^2 \) are
(a) primes
(b) composites
(c) co-primes
(d) None of the options
Answer: (c) co-primes

Question. When 429 is expressed as a product of its prime factors, we get
(a) 2 × 5 × 29
(b) 33 × 13 × 1
(c) 3 × 11 × 9
(d) 3 × 11 × 13
Answer: (d) 3 × 11 × 13

Question. The LCM of two numbers is 182 and their HCF is 13. If one of the numbers is 26, the other number is
(a) 31
(b) 71
(c) 61
(d) 91
Answer: (d) 91

Question. When 156 is expressed as the product of primes, we get
(a) \( 2^2 \times 3 \times 13 \)
(b) \( 2^2 \times 3 \times 11 \)
(c) \( 2 \times 3^2 \times 13 \)
(d) \( 2 \times 3^2 \times 11 \)
Answer: (a) \( 2^2 \times 3 \times 13 \)

Question. The HCF and LCM of 404 and 96 respectively are
(a) 2, 9696
(b) 4, 9696
(c) 8, 3636
(d) 10, 2020
Answer: (b) 4, 9696

Question. The LCM of 150 and 200 is
(a) 320
(b) 400
(c) 550
(d) 600
Answer: (d) 600

Question. 3 bells ring at an interval of 4, 7 and 14 minutes. All three bells rang at 6 am. When the three bells will ring together next?
(a) 6:20 am
(b) 6:24 am
(c) 6:28 am
(d) 6:30 am
Answer: (c) 6:28 am

Question. The LCM and the HCF of 15, 18, 45 respectively are
(a) 3, 30
(b) 4, 40
(c) 5, 50
(d) 90, 3
Answer: (d) 90, 3

Question. Assertion (A): The number \( 6^n \), n being a natural number, ends with the digit 5.
Reason (R): The number \( 9^n \) cannot end with digit 0 for any natural number n.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer: (d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): If m and n are odd positive integers, then \( m^2 + n^2 \) is even but not divisible by 4.
Reason (R): \( 3 \times 5 \times 7 + 7 \) is a composite number.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer: (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

2. Decimal Representation of Rational Numbers

Question. The decimal expansions (without actual division) and its nature (terminating or non-terminating) of \( \frac{987}{10500} \) will be
(a) 0.094, non-terminating
(b) 0.094, terminating
(c) 0.094, non-terminating
(d) 0.049, terminating
Answer: (b) 0.094, terminating

Question. The decimal expansion of the rational number \( \frac{43}{2^4 5^3} \) will terminate after how many places of decimals?
(a) 2 places
(b) 3 places
(c) 4 places
(d) 5 places
Answer: (c) 4 places

Question. Rational number between \( \sqrt{2} \) and \( \sqrt{3} \) is
(a) 1.5
(b) 1.6
(c) 1.7
(d) All of the options
Answer: (d) All of the options

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 be distributed equally among students of Section A or Section B?
(a) 144
(b) 128
(c) 288
(d) 272
Answer: (c) 288

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

Question. 36 can be expressed as a product of its primes as
(a) \( 2^2 \times 3^2 \)
(b) \( 2^1 \times 3^3 \)
(c) \( 2^3 \times 3^1 \)
(d) \( 2^0 \times 3^0 \)
Answer: (a) \( 2^2 \times 3^2 \)

Question. \( 7 \times 11 \times 13 \times 15 + 15 \) is a
(a) Prime number
(b) Composite number
(c) Neither prime nor composite
(d) None of the options
Answer: (b) Composite number

Question. If p and q are positive integers such that \( p = ab^2 \) and \( q = a^2b \), where \( a \) and \( b \) are prime numbers, then the LCM(\( p, q \)) is
(a) ab
(b) \( a^2b^2 \)
(c) \( a^3b^2 \)
(d) \( a^3b^3 \)
Answer: (b) \( a^2b^2 \)

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) 12

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

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

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

Question. 108 can be expressed as a product of its primes as
(a) \( 2^3 \times 3^2 \)
(b) \( 2^3 \times 3^3 \)
(c) \( 2^2 \times 3^2 \)
(d) \( 2^2 \times 3^3 \)
Answer: (d) \( 2^2 \times 3^3 \)

A Mathematics 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: (b) 13915

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

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

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: (a) Composite number

Question. The prime factorisation of 13915 is
(a) \( 5 \times 11^3 \times 13^2 \)
(b) \( 5 \times 11^3 \times 23^2 \)
(c) \( 5 \times 11^2 \times 23 \)
(d) \( 5 \times 11^2 \times 13^2 \)
Answer: (c) \( 5 \times 11^2 \times 23 \)