Class 10 Maths – RD Sharma Chapter 1: Real Numbers Multiple Choice Question : MCQs (Step-by-Step Guide)

RD Sharma Chapter 1: Real Numbers Multiple Choice Question : MCQs

1. The exponent of 2 in the prime factorisation of 144, is (a) 4 (b) 5 (c) 6 (d) 3 Watch Solution
2. The LCM of two numbers is 1200. Which of the following cannot be their HCF? (a) 600 (b) 500 (c) 400 (d) 200 Watch Solution
3. If n = 2^3 ✕ 3^4 ✕ 5^4 ✕ 7, then the number of consecutive zeros in n, where n is a natural number, is (a) 2 (b) 3 (c) 4 (d) 7 Watch Solution
4. The sum of the exponents of the prime factors in the prime factorisation of 196, is (a) 1 (b) 2 (c) 4 (d) 6 Watch Solution
5. The number of decimal place after which the decimal expansion of the rational number 23/2^2×5 will terminate, is (a) 1 (b) 2 (c) 3 (d) 4 Watch Solution
6. If two positive integers a and b are expressible in the form a = pq^2 and b = p^3 q; p, q being prime number, then LCM (a, b) is Watch Solution
7. If two positive integers a and b are expressible in the form a = pq^2 and b = p^3 q; p, q being prime number, then HCF (a, b) is Watch Solution
8. If two positive integers m and n are expressible in the form m = pq^3 and n = p^3 q^2, where p, q are prime numbers, then HCF (m, n) = Watch Solution
9. 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 Watch Solution
10. The HCF of 95 and 152, is (a) 57 (b) 1 (c) 19 (d) 38 Watch Solution
11. If HCF (26, 169) = 13, then LCM (26, 169) = (a) 26 (b) 52 (c) 338 (d) 13 Watch Solution
12. If a = 2^3 ✕ 3, b = 2 ✕ 3 ✕ 5, c = 3^n ✕ 5 and LCM (a, b, c) = 2^3 ✕ 3^2 ✕ 5, then n = Watch Solution
13. The decimal expansion of the rational number 14587/1250 will terminate after (a) one decimal place (b) two decimal place (c) three decimal place (d) four decimal place Watch Solution
14. If p and q are co-prime numbers , then p^2 and q^2 are (a) coprime (b) not coprime (c) even (d) odd Watch Solution
15. Which of the following rational numbers have terminating decimal?(i) 16/25(ii) 5/18(iii) 2/21(iv) 7/250 Watch Solution
16. If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a+b is (a) 2 (b) 3 (c) 5 (d) 10 Watch Solution
17. 3.27 bar is (a) an integer (b) a rational number (c) a natural number (d) an irrational number Watch Solution
18. The smallest number by which √27 should be multiplied so as to get a rational number is (a) √27 (b) 3√3 (c) √3 (d) 3 Watch Solution
19. The smallest rational number by which 1/3 should be multiplied so that its decimal expansion terminates after one place of decimal, is Watch Solution
20. If n is a natural number, then 9^2n − 4^2n is always divisible by (a) 5 (b) 13 (c) both 5 and 13 (d) None of these Watch Solution
21. If n is any natural number, then 6^n − 5^n always ends with (a) 1 (b) 3 (c) 5 (d) 7 Watch Solution
22. The LCM and HCF of two rational numbers are equal, then the numbers must be (a) prime (b) co-prime (c) composite (d) equal Watch Solution
23. If the sum of LCM and HCF of wo numbers is 1260 and their LCM is 900 more than their HCF, then the product of two numbers is (a) 203400 (b) 194400 (c) 198400 (d) 205400 Watch Solution
24. The remainder when the square of any prime number greater than 3 is divided by 6, is (a) 1 (b) 3 (c) 2 (d) 4 Watch Solution
25. For some integer m, every even integer is of the form (a) m (b) m + 1 (c) 2m (d) 2m+1 Watch Solution
26. For some integer q, every odd integer is of the form (a) q (b) q+1 (c) 2q (d) 2q+ 1 Watch Solution
27. n^2 – 1 is divisible by 8, if n is (a) an integer (b) a natural number (c) an odd integer (d) an even integer Watch Solution
28. The decimal expansion of the rational number 33/2^2✕ 5 will terminate after (a) one decimal place (b) two decimal places (c) three decimal places (d) more than 3 decimal places Watch Solution
29. If p1 and p2 are two odd prime numbers such that P1 greater than P2, then p1^2 – p2^2 is (a) an even number (c) an odd prime number (b) an odd number (d) a prime number Watch Solution
30. If two positive integers a and b are written as a = x^3 y^2 and b = xy^3 ; x, y are prime numbers, then HCF (a, b) is (a) xy (b) xy^2 (c) x^3 y^3 (d) x^2 y^2 Watch Solution
31. The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is (a) 13 (b) 65 (c) 875 (d) 1750 Watch Solution
32. The product of a non-zero rational number and an irrational number is (a) always irrational (b) always rational (c) rational or irrational (d) one Watch Solution
33. The HCF and LCM of 12, 21, 15 respectively are (a) 3,140 (b) 12,420 (c) 3,420 (d) 420,3 Watch Solution
34. Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq+r, where r must satisfy Watch Solution

1. Real Numbers – R.D. Sharma Class 10th Math

1. Real Numbers Exercise 1.1 Video Solution

2. Real Numbers Exercise 1.2 Video Solution

3. Real Numbers Exercise 1.3 Video Solution

4. Real Numbers Exercise 1.4 Video Solution

5. Real Numbers Exercise 1.5 Video Solution

6. Real Numbers Exercise 1.6 Video Solution

7. Real Numbers Multiple Choice Questions (MCQs) Video Solution Video Solution

8. Real Numbers Fill in the Blanks (FBQs) Video Solution

9. Real Numbers Very Short Answer Questions (VSAQs) Video Solution Video Solution