Class 10 Maths Chapter 1: Real Numbers MCQs with answers
10 multiple-choice questions on Real Numbers, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.
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Answer: (d) 100
Common primes are 2 and 5. Smallest powers: 22 and 52. HCF = 4 × 25 = 100. 7 and 11 are not common, so they do not enter.
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Answer: (a) a3b3
LCM takes the greatest power of each prime involved: a3 and b3. a2b is the HCF; a5b4 is the product.
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Answer: (a) 240
HCF × LCM = product of the two numbers, so LCM = 2880 ÷ 12 = 240. (For example 48 and 60.)
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Answer: (c) 22 × 32 × 5
180 = 2 × 90 = 2 × 2 × 45 = 2 × 2 × 3 × 15 = 2 × 2 × 3 × 3 × 5 = 22 × 32 × 5. 4 × 9 × 5 and 22 × 3 × 15 multiply to 180 but contain non-primes (4, 9, 15); 23 × 32 × 5 is 360.
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Answer: (c) √50
√196 = 14 and 2.5 = 5/2 are rational, and 22/7 is a ratio of integers. √50 = 5√2, and 5√2 cannot be written as p/q, so it is irrational.
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Answer: (c) √(2.25)
√(2.25) = 1.5 = 3/2, a ratio of integers. 0.101101110… neither terminates nor repeats, π is irrational, and √3 + 1 is a rational plus an irrational.
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Answer: (b) 1
The only factors of p are 1 and p, and of q are 1 and q. With no common prime, the HCF is 1. pq is the LCM.
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Answer: (a) 2717
No two of 11, 13, 19 share a prime, so the LCM is the product 11 × 13 × 19 = 2717. 1 is their HCF.
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Answer: (c) 2
1764 = 2 × 882 = 2 × 2 × 441 = 22 × 32 × 49 = 22 × 32 × 72. The power of 7 is 2.
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Answer: (b) (4, 3)
432 = 2 × 216 = 2 × 23 × 27 = 24 × 33. The factorisation is unique, so a = 4 and b = 3.