CBSE NCERT Class 10 Real Numbers Worksheet
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 = x3y2 and b = xy3 where x, y are prime numbers , HCF of a and b is
(a) xy (b) xy2 (c) x3y3 (d) x2y2
Q10. If two positive integers p and q are written as p = ab2 and q = a3b , where a and b are prime numbers , then LCM of p and q is
(a) ab (b) a2b2 (c) a3b2 (d) a3b3
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) (3x2)n (b)(5X2)n (c)(6X2)n (d) (4X2)n
Q17. If n is a natural number , then 8n ends with an even digit except
(a) 0 (b) 2 (c) 4 (d) 6
Q18. If n is a natural number , then 12n 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) 2mX3n (b) 2m X 5n (c) 3m X 5n (d) 3m X 7n
Q23. Which of the following numbers has a non- terminating repeating decimal expansion ?
(a) 6/15 (b) 21/280 (c) 117 / 62X53 (d) 77/210
Q24. The decimal expansion of the rational number 11/ 23X52 will terminate after decimal places of
(a) one (b) two (c) three (d) four
Q25. If a = 23 X3, b = 2 X3X5 , c= 3nX5 and LCM (a, b, c ) = 23X32x5 , 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
