# 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 = 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) (3×2)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

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