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1- 186 x 186 + 159 x 159 - 2 x 186 x 159 =?
A.329 B.700 C.729 D.848 E.None of these
View Answer (-)
Answer & Explanation
Answer  -  C (729)
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
2- The number of prime factors of (3 x 5)12 (2 x 7)10 (10)25 is:
A.69 B.84 C.93 D.94 E.None of these
View Answer (-)
Answer & Explanation
Answer  -  D (94)
Explanation  -  (3 x 5)12 x (2 x 7)10 x (10)25 = (3 x 5)12 x (2 x 7)10 x (2 x 5)25
                                                             
                                            = 312 x 512 x 210 x 710 x 225 x 525
                                                             
                                            = 235 x 312 x 537 x 710

Total number of prime factors = (35 + 12 + 37 + 10) = 94
3- If (64)2 - (36)2 = 20z, the value of z is:
A.140 B.142 C.684 D.670 E.None of these
View Answer (-)
Answer & Explanation
Answer  -  A (140)
Explanation  -  20z = (64)2 - (36)2

20z = (64 + 36) (64 - 36)

20z - 100 x 28

z = (100 x 28) / 20

  = 140
4- Which of the following numbers is divisible by 3, 7, 9 and 11?
A.639 B.2079 C.3791 D.37911 E.None of these
View Answer (-)
Answer & Explanation
Answer  -  B (2079)
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
5- 39798 + 3798 + 378 =?
A.43576 B.43974 C.43984 D.49532 E.None of these
View Answer (-)
Answer & Explanation
Answer  -  B (43974)
Explanation  -  39798 + 3798 + 378 = 43974
6- A six-digit number is formed by repeating a three-digit number; for example, 256256 or 678678 etc. Any number of this form is always exactly divisible by:
A.7 only B.13 only C.11 only D.1001 E.None of these
View Answer (-)
Answer & Explanation
Answer  -  D (1001)
Explanation  -  256256 = 256 x 1001; 678678 = 678 x 1001, etc.

So, any number of this form is divisible by 1001
7- The unit's digit in the product (3127)173 is:
A.1 B.3 C.7 D.9 E.None of these
View Answer (-)
Answer & Explanation
Answer  -  C (7)
Explanation  -  Unit digit in (3127)173 - Unit digit in (7)173. Now, 74 gives unit digit 1

(7)173 = (74)43 x 71. Thus, (7)173 gives unit digit 7
8- The number of digits of the smallest number, which when multiplied by 7 gives the result consisting entirely of nines, is:
A.3 B.5 C.6 D.8 E.None of these
View Answer (-)
Answer & Explanation
Answer  -  C (6)
Explanation  -    By hit and trial, we find that a number exactly divisible by 7 and consisting entirely of nines is 999999.

  Number of digits in it = 6
9- Which of the following numbers is exactly divisible by 99?
A.114345 B.913464 C.135792 D.3572404 E.None of these
View Answer (-)
Answer & Explanation
Answer  -  A (114345)
Explanation  -  The required number should be divisible by both 9 and 11.

Clearly, 114345 is divisible by both 9 and 11. So, it is divisible by 99
10- On dividing a number by 999, the quotient is 366 and the remainder is 103. The number is:
A.364724 B.365387 C.365737 D.366757 E.None of these
View Answer (-)
Answer & Explanation
Answer  -  C (365737)
Explanation  -  Required number = 999 x 366 + 103 = (1000 - 1) x 366 + 103 = 366000 - 366 + 103
                             
                             = 365737