Number System

Ladakh Prison Department · Mathematics · 99 practice questions with answers and explanations: 45 Easy, 49 Medium, 5 Hard.

Sample questions

Sample Easy question 1

Find the number of prime numbers between 1 and 50.

  1. 13
  2. 15
  3. 16
  4. 14
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Answer: B. There are 15 primes below 50: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47.

Sample Easy question 2

Find the HCF of 48 and 60.

  1. 10
  2. 6
  3. 12
  4. 8
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Answer: C. The highest common factor of 48 and 60 is 12.

Sample Easy question 3

Find the HCF of 36 and 90.

  1. 18
  2. 15
  3. 20
  4. 12
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Answer: A. The highest common factor of 36 and 90 is 18.

Sample Medium question 4

Find the LCM of 6, 10 and 15.

  1. 20
  2. 30
  3. 35
  4. 25
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Answer: B. The least common multiple of 6, 10 and 15 is 30.

Sample Medium question 5

Find the number of trailing zeros at the end of 25!.

  1. 4
  2. 7
  3. 5
  4. 6
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Answer: D. Trailing zeros = ⌊25/5⌋ + ⌊25/25⌋ = 5 + 1 = 6.

Sample Medium question 6

Find the number of trailing zeros at the end of 50!.

  1. 12
  2. 10
  3. 13
  4. 11
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Answer: A. Trailing zeros = ⌊50/5⌋ + ⌊50/25⌋ = 10 + 2 = 12.

Sample Hard question 7

Find the number of digits in 5¹⁵ (use log₁₀5 ≈ 0.69897).

  1. 12
  2. 10
  3. 9
  4. 11
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Answer: D. 15 × 0.69897 ≈ 10.48; number of digits = ⌊10.48⌋ + 1 = 11.

Sample Hard question 8

Find the remainder when 23²³ is divided by 24.

  1. 19
  2. 1
  3. 23
  4. 11
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Answer: C. 23 ≡ -1 (mod 24); (-1)²³ = -1 ≡ 23 (mod 24).

Sample Hard question 9

Find the remainder when 3¹⁰⁰ is divided by 7.

  1. 4
  2. 6
  3. 1
  4. 2
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Answer: A. Powers of 3 mod 7 cycle as 3,2,6,4,5,1 (period 6); 100 mod 6 = 4, giving remainder 4.

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