# CBSE NCERT Class 10 Real Numbers Worksheet

- REAL NUMBERS

Following Are The Questions :

**Q1. **HCF X LCM for the numbers 50 and 20 is

(a) 10 (b) 100 (c) 1000 (d) 50

Q2. If HCF ( 72 , 120 ) = 24 , then LCM ( 72 , 120 ) is

(a) 240 (b) 360 (c) 1728 (d) 2880

Q3. Given that LCM(91,26 ) = 182 , HCF ( 91, 126 ) is

(a) 13 (b) 26 (c) 17 (d) 9

Q4. If the HCF and LCM of two numbers 12 and 180 , and one of the numbers is 36 then the other number is

(a) 540 (b) 180 (c) 60 (d) 12

Q5. If HCF ( a, 8 ) = 4 and LCM (a, 8 ) = 24 , then a is

(a) 8 (b) 10 (c) 12 (d) 14

Q6. Given that HCF ( 2520 , 6600 ) = 120 and LCM (2520, 6600 ) = 252k , then the value of k is

(a) 165 (b) 550 (c) 990 (d) 1650

Q7. If the HCF of 65 and 117 is in the form of 65m-117 , then the value of m is

(a) 1 (b) 2 (c) 3 (d) 4

Q8. The product of the HCF and LCM of the smallest prime number and the smallest composite number is

(a) 2 (b) 4 (c) 6 (d) 8

Q9. If two positive integers a and b are written as a = x^{3}y^{2} and b = xy^{3} where x, y are prime numbers , HCF of a and b is

(a) xy (b) xy^{2} (c) x^{3}y^{3 } (d) x^{2}y^{2}

Q10. If two positive integers p and q are written as p = ab^{2} and q = a^{3}b , where a and b are prime numbers , then LCM of p and q is

(a) ab (b) a^{2}b^{2} (c) a^{3}b^{2} (d) a^{3}b^{3}

Q11. The largest number which divides 70 and 125 , leaving remainders 5 and 8 respectively , is

(a) 13 (b) 65 (c) 875 (d) 1750

Q12. For some integer m , every even integer is of the form

(a) m (b) m+1 (c) 2m (d) 2m+1

Q13. For some integer m , every odd integer is of the form

(a) m (b) m+1 (c) 2m (d) 2m+1

Q14. 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

Q15. The LCM of the smallest two digit number and the smallest composite number is

(a) 12 (b) 4 (c) 20 (d) 40

Q16. If n is any natural number , then which of the following numbers end with 0 :

(a) (3×2)^{n} (b)(5X2)^{n} (c)(6X2)^{n} (d) (4X2)^{n}

Q17. If n is a natural number , then 8^{n} ends with an even digit except

(a) 0 (b) 2 (c) 4 (d) 6

Q18. If n is a natural number , then 12^{n} will always end with an even digit except

(a) 4 (b) 6 (c) 8 (d) 0

Q19. (√3 + √2 )^{2} is

(a) not a rea number (b) a rational number

(c) an irrational number (d) an integer

Q20. The number (√5 +2) / (√5 – 2 ) is

(a) a rational number (b) an irrational number

(c) an integer (d) a natural number

Q21. If x is a positive rational number which is not a perfect square , then –5√x is

(a) a negative integer (b) an integer

(c) a rational number (d) an irrational number

Q22. A rational number p/q , p and q are co-prime , has a terminating decimal expansion if the prime factorization of q is of the form

(a) 2^{m}X3^{n }(b) 2^{m} X 5^{n } (c) 3^{m} X^{ }5^{n } (d) 3^{m} X 7^{n }

Q23. Which of the following numbers has a non- terminating repeating decimal expansion ?

(a) 6/15 (b) 21/280 (c) 117 / 6^{2}X5^{3} (d) 77/210

Q24. The decimal expansion of the rational number 11/ 2^{3}X5^{2} will terminate after decimal places of

(a) one (b) two (c) three (d) four

Q25. If a = 2^{3} X3, b = 2 X3X5 , c= 3^{n}X5 and LCM (a, b, c ) = 2^{3}X3^{2}x5 , then n =

(a) 1 (b) 2 (c) 3 (d) 4

Q26. If 3 is the least prime factor of a and 7 is the least prime factor of b , then the least prime factor of a and b , is

(a) 2 (b) 3 (c) 5 (d) 10

Q27. 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

Q28. The least number is divisible by all the numbers from 1 to 10 , is

(a) 10 (b) 100 (c) 504 (d) 2520

Q29. The largest number which divides 70 and 125 , leaving remainders 5 and 8 respectively , is

(a) 13 (b) 65 (c) 875 (d) 1750

Q30. Two numbers are in the ratio 3:4 and their LCM is 120 . The sum of the numbers is ;

(a)70 (b) 60 (c) 10 (d) none