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# Number System Moderate

Q. An intelligence agency forms a code of two distinct digits selected from 0, 1,…, 9 such that the ﬁ rst digit of the code is non-zero. However, the code, handwritten on a slip, can potentially create confusion when read upside down, for example, code 91 may appear as 16. How many codes are there for which no such confusion can arise?

A. 80

B. 63

C. 70

D. None of these

Digits which can create confusion = 1, 6, 8, 9 (0 cannot create confusion because passwords has to be two-digit numbers). Total two-digit numbers with distinct digit = 81 Two-digit numbers created by 1, 6, 8, 9 = 12 Therefore, total numbers left = 69 However, 69 and 96 will not create confusion (it looks same upside down), and hence, total numbers = 71

Q2. N has 37 zeroes at its end. How many values of N is/ are possible?

A. 0

B. 1

C. 5

D. Infinite

N! is having 37 zeroes at its end, and therefore, N = 150 (can be arrived at by a guess). Obviously, 150 ≤ N < 155 is the answer

Q3. What is the remainder when 3450 is divided by 108?

A. 3

B. 1

C. 27

D. 81

108 = 33 × 4 = 27 × 4

Remainder obtained when 3450 is divided by 108 is same as the number obtained when 3450 is divided by 27 and 4. Remainder obtained when 3450 is divided by 33 = 0; remainder obtained when 3450 is divided by 4 = 1. Now, we are required to ﬁ nd a number that when divided by 27 gives 0 as the remainder and when divided by 4 gives 1 as the remainder = 81. Hence, option (d) is the answer.

A. 3

B. 1

C. 27

D. 81