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For your ATM debit card, you have a $4$-decimal-digit personal secret code. In the absence of any clue, a brute-force attack takes time-$'t'$ to crack the code on an ATM terminal. Therefore $'t'$ is the secure-time for a customer to report in case the card is misplaced. Your Bank has decided to facilitate an increased secure-time. Out of the following, which option should provide the largest rise in the value of $'t'$?

  1. Instead of 4-decimal-digits, maintain the personal secret code in 4-hexadecimal-digits.
  2. Instead of 4-decimal digits, maintain a 5-decimal-digit personal secret code.
  3. Reduce the processing speed of the ATM terminals to the half of their current speed.
  4. None of the above provides any improvement.
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With 4 digit pin where each digit is Hexadecimal there will be total of ${16}^4 = 65536$ combinations

with 5 digit pin where each digit is decimal there will be total of ${10}^5 = 100000$ combinations

Therefore 5 digit pin will take more time to brute force.
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Ans. B

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You have to provide justification !
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