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Real Number MCQs

Real Number
Xth Mathematics

 MULTIPLE CHOICE QUESTIONS

  1   Euclid’s division algorithm can be applied to :
       (a) only positive integers
       (b) only negative integers
       (c) all integers
       (d) all integers except 0.

   2.   For some integer m, every even integer is of the form :
      (a)
      (b) m + 1
      (c) 2
      (d) 2m + 1
  3.   If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is :
      (a) 1 
      (b) 2
      (c) 3 
      (d) 4
  4.  If two positive integers p and q can be expressed as p = ab2 and q = a3b, a; b being prime numbers, then LCM (p, q) is :
      (a) ab 
      (b) a2b2 
      (c) a3b2 
      (d) a3b3
  5. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is :
     (a) 10 
     (b) 100 
     (c) 504 
     (d) 2520
  6.  7 × 11 × 13 × 15 + 15 is :
     (a) composite number
     (b) prime number
     (c) neither composite nor prime
     (d) none of these
  7. 1.2348 is :
    (a) an integer 
    (b) an irrational number 
    (c) a rational number 
    (d) none of these
  8. 2.35 is :
    (a) a terminating decimal
    (b) a rational number
    (c) an irrational number
    (d) both (a) and (c)
  9. 3.24636363... is :
    (a) a terminating decimal number
    (b) a non-terminating repeating decimal number
    (c) a rational number
    (d) both (b) and (c)
  10. For some integer q, every odd integer is of the form :
    (a) 2
    (b) 2q +
    (c)
    (d) q + 1
  11. If the HCF of 85 and 153 is expressible in the form 85m – 153, then the value of m is :
    (a) 1 
    (b) 4 
     (c) 3 
     (d) 2
  12. The decimal expansion of the rational number 47 / 22.5. will terminate after :
     (a) one decimal place 
     (b) three decimal places
     (c) two decimal places
     (d) more than 3 decimal places

13. If two positive integers p and q can be expressed as p = ab2 and q = a2b; a, b being prime numbers, then LCM (p, q) is :
 (a) ab 
(b) a2b2 
(c) a3b2 
(b) a3b3
14. 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 :
(a) 0 < r
(b) 1 < r < b 
(c) 0 < r < b 
(d) 0 ≤ r < b
15. Following are the steps in finding the GCD of 21 and 333 :
      333 = 21 × m + 18
      21 = 18 × 1 + 3
      n = 3 × 6 + 0
     The integers m and n are :
(a) m = 15, n = 15 
(b) m = 15, n = 18 
(c) m = 15, n = 16 
(d) m = 18, n = 15
16. HCF and LCM of a and b are 19 and 152 respectively. If a = 38, then b is equal to :
      (a) 152 
      (b) 19 
      (c) 38 
      (d) 76
17. (n + 1)2 – 1 is divisible by 8, if n is :
      (a) an odd integer 
      (b) an even integer
      (c) a natural number 
      (d) an integer
18. The largest number which divides 71 and 126, leaving remainders 6 and 9 respectively is :
(a) 1750 
(b) 13 
(c) 65 
(d) 875
19. If two integers a and b are written as a = x3y2 and b = xy4; x, y are prime numbers, then H.C.F. (a, b) is :
(a) x3y3 
(b) x2y2 
(c) xy 
(d) xy2
20. The decimal expansion of the rational number 145171250 will terminate after :
(a) 4 decimal places
(b) 3 decimal places
(c) 2 decimal places
(d) 1 decimal place

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