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71.
The number of prime factors of (3 x 5)12 (2 x 7)10 (10)25 is:
  • A.
    47
  • C.
    72
  • B.
    60
  • D.
    None of these
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Answer : [D]
Explanation :
 
(3 x 5)12 x (2 x 7)10 x (10)25 = (3 x 5)22 x (2 x 7)10 x (2 x 5)25
 
  = 312 x 512 x 210 x 710 x 235 x 525  
 
  = 235 x 312 x 537 x 710  
 
Total number of prime factors = (35 + 12 + 37 + 10) = 94.
 
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72.
39798 + 3798 + 378 =?
  • A.
    43576
  • C.
    43984
  • B.
    43974
  • D.
    49532
  • Answer & Explanation
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Answer : [B]
Explanation :
 
39798 + 3798 + 378 = 43974
 
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73.
If (64)2 - (36)2 = 20z, the value of z is :
  • A.
    70
  • C.
    180
  • B.
    120
  • D.
    None of these
  • Answer & Explanation
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Answer : [D]
Explanation :
 
20z = (64)2 - (36)2      20z = (64 + 36) (64 - 36)    
 
       20z - 100 x 28    
 
 
 
  z =
100 x 28
20
 = 140.  
 
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74.
Which of the following numbers is divisible by 3, 7, 9 and 11?
  • A.
    639
  • C.
    3791
  • B.
    2079
  • D.
    37911
  • Answer & Explanation
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Answer : [B]
Explanation :
 
(a) 639 is not divisible by 7.
 
(b) 2079 is divisible by 3, 7, 9 and 11
 
(c) 3791 is not divisible by 3
 
(d) 37911 is not divisible by 9.
 
    Correct answer is (b).    
 
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75.
186 x 186 + 159 x 159 - 2 x 186 x 159 = ?
  • A.
    729
  • C.
    2019
  • B.
    1039
  • D.
    7029
  • Answer & Explanation
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Answer : [A]
Explanation :
 
Given Exp.  = a2 + b2 - 2ab, where a = 186 and b = 159      
 
  = (a - b)2 = (186 - 159)2 = (27)2    
 
  = (20 + 7)2 = (20)2 + 7 + 2 x 20 x 7 = 400 + 49 + 280 = 729    
 
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