CBSE Class 10 Mathematics Real Numbers Worksheet Set I

Choose the correct answer from the given options:

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

Question. 325 can be expressed as a product of its primes as:
(a) 52 × 7
(b) 52 × 13
(c) 5 × 132
(d) 2 × 32 × 52
Answer : B

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

Question. The decimal expansion (without actual division) and its nature (terminating or non-terminating) of 15/1600 will be
(a) Terminating after 6 places
(b) Non-terminating but repeating
(c) Non-terminating and non-repeating
(d) Terminating after 2 places
Answer : A

Question. The decimal expansion (without actual division) and its nature (terminating or non terminating) of 17/8 will be
(a) Terminating after 2 places
(b) Non-terminating but repeating
(c) Non-terminating but non-repeating
(d) Terminating after 3 places
Answer : D

Question. If a and b are co-prime, then a2 and b2 are
(a) primes
(b) composites
(c) co-primes
(d) None of these
Answer : C

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

Question. The values of x and y in the given figure respectively are

(a) x = 84, y = 21
(b) x = 21, y = 84
(c) x = 42, y = 24
(d) x = 24, y = 42
Answer : B

Question. A rational and an irrational number lying between 0.25 and 0.32 are respectively.
(a) 0.30, 0.3010203040...
(b) 0.20, 0.2010203040...
(c) 0.33, 0.3510203040...
(d) None of these
Answer : A

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

Question. The 2ⁿ5^m (where n and m are non-negative integers) from of denominator of 3/5 and its decimal expansion respectively are
(a) 2⁰ × 5¹, 0.6
(b) 2¹ × 5⁰, 0.5
(c) 2¹ × 5¹, 0.6
(d) 2² × 5⁰, 0.8
Answer : A

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

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

Question. When 156 is expressed as the product of primes, we get
(a) 22 × 3 × 13
(b) 22 × 3 × 11
(c) 2 × 32 × 13
(d) 2 × 32 × 11
Answer : C

Question. The decimal expansion (without actual division) and its nature (terminating or non-terminating) of 64/455 will be
(a) Terminating after 2 places
(b) Non-terminating but repeating
(c) Non-terminating but non-repeating
(d) Terminating after 3 places
Answer : B

Question. The 2ⁿ5^m (where n and m are non-negative integers) form of denominator of 13/80 and its decimal expansion respectively are
(a) 2³ × 5², 0.1248
(b) 2² × 5³, 0.1698
(c) 2⁴ × 5¹, 0.1625
(d) None of these
Answer : C

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

Question. A rational number can be expressed as a terminating decimal if the denominator has factors
(a) 2, 3 or 5
(b) 2 or 3
(c) 3 or 5
(d) 2 or 5
Answer : D

Question. Rational number p/q, q ≠ 0, will be terminating decimal if the prime factorisation of q is of the form (m and n are non-negative integers)
(a) 2^m × 3ⁿ
(b) 2^m × 5ⁿ
(c) 3^m × 5ⁿ
(d) 3^m × 7ⁿ
Answer : B

Question. Which of the following is the decimal expansion of an irrational number?
(a) 4.561
(b) 0.12
(c) 5.010010001…
(d) 6.03
Answer : C

Question. 2.35 is
(a) an integer
(b) a rational number
(c) an irrational number
(d) a natural number
Answer : B

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

B. Assertion-Reason Type Questions
In the following questions, a statement of assertion (A) is followed by a statement reason (R). Choose
the correct choice as:
(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.

Question. Assertion (A): The sum or difference of a rational number and an irrational number is irrational.
Reason (R): Negative of an irrational number is rational
Answer : B

Question. Assertion (A): If m and n are odd positive integers, then m² + n² is even but not divisible by 4.
Reason (R): 3 × 5 × 7 + 7 is a composite number
Answer : B

Question. Assertion (A): 5 + √3 is an irrational number.
Reason (R): The sum or difference of a rational and an irrational number is always irrational.
Answer : A

Question. Assertion (A): The number 6ⁿ, n being a natural number, ends with the digit 5.
Reason (R): The number 9ⁿ cannot end with digit 0 for any natural number n.
Answer : D

Very Short Answer Type Questions

Question. The LCM of two numbers is 182 and their HCF is 13. If one of the number is 26, find the other.
Answer : We know that HCF (a, b) × LCM (a, b) = a × b
So, 13 × 182 = 26 × b
⇒ b = 13x182/26 = 91
Thus, the other number is 91.

Question. Given that HCF (135, 225) = 45, find the LCM (135, 225).
Answer : We know that
LCM × HCF = Product of two numbers
LCM (135, 225) = Product of 135 and 225/HCF(135, 225)
= 135×225/45
= 675

Question. After how many decimal places will the decimal representation of the rational number 229/2² × 5⁷ terminate ?
Answer : Here, 
229/2²×5⁷ = 229x2⁵/2⁷x5⁷ = 229x2⁵/(10)⁷
Hence, the given rational number will terminate after 7 decimal places.

Question. Are the smallest prime and the smallest composite numbers co-prime? Justify.
Answer : No.
We know that,
Smallest prime number is 2 and smallest composite number is 4.
HCF of (2, 4) = 2
Since, there is a common factor 2.
So, they are not co-prime.

Question. The HCF of two numbers a and b is 5 and their LCM is 200. Find the product ab.
Answer : Given, HCF (a, b) = 5
LCM (a, b) = 200
HCF × LCM = Product of the numbers
⇒ a × b = 5 × 200
⇒ ab = 1000
Hence, the product of ab is 100.

Question. Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.
Answer : No.
We know that:
“The HCF of any two numbers must be a factor of the LCM of those numbers.”
So, two numbers cannot have their HCF 18 and LCM 380, as 18 does not divide 380.

Question. Find a rational number between 2 and 7 .
Answer : √2 = 1.414
and √7 = 2.6
Let the rational number be x.
∴ √2 < x < √7
or 1.4 < x < 2.6
Hence, any rational number like 1.5, 2.0, 2.5, can be the answer.

Question. Write the number of zeroes in the end of a number whose prime factorization is 22 × 53 × 32 × 17.
Answer : Given, 2² × 5² × 5 × 3² × 17
= (2 × 5)² × 5 × 3² × 17
[∵ on multiplying 2 × 5 we get 10]
= (10)² × 5 × 3² × 17
The power of 10 in the given expression is 2.
Hence, the number of zeroes in the end will be = 2.

Question. If the HCF of (336, 54) = 6, find the LCM (336, 54).
Answer : The HCF of (336, 54) = 6.
We know that:
LCM × HCF = Product of two numbers
⇒ LCM = 336 x 54/6
= 336 × 9 = 3024
Hence, the LCM of the two numbers is 3024.

Question. Find a rational number betwen 2 and 3.
Answer : Rational number between √2 (1.41 approx)  and √3 (1.73 approx) can be 1.5, 1.6, 1.63 etc.
So, a required rational number may be 1.5.

Question. Write one rational and one irrational number lying between 0.25 and 0.32.
Answer : Rational number= 0.30
Irrational number = 0.3010203040…
Or any other correct rational and irrational number.

Question. Write the exponent of 3 in the prime factorization of 144.
Answer : Prime factorization of 14⁴ = 2⁴ × 3²
So, exponent of 3 = 2.

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