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UP Police Constable Number System Questions with Answers & Explanations

20 Number System questions from the Numerical & Mental Ability section of UP Police Constable, each with the correct answer and a worked explanation. Try each question first, then tap Show answer to check. When you're ready, take the timed chapter-wise test to see your all-India rank.

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Question 1

What is the square root of 7744?

  1. A89
  2. B87
  3. C90
  4. D88
Show answer
Answer: (D) 88 88 × 88 = 7744.
Question 2

What is the unit digit of 4^74?

  1. A6
  2. B1
  3. C7
  4. D3
Show answer
Answer: (A) 6 Unit digits of powers of 4 repeat in a cycle of 4; 74 mod 4 = 2, so the unit digit is 6.
Question 3

What is the sum of the first 97 natural numbers?

  1. A4753
  2. B9409
  3. C4850
  4. D4656
Show answer
Answer: (A) 4753 Sum = n(n + 1)/2 = 97 × 98/2 = 4753.
Question 4

What is the remainder when 33923 is divided by 13?

  1. A5
  2. B6
  3. C0
  4. D7
Show answer
Answer: (B) 6 33923 = 13 × 2609 + 6.
Question 5

What is the unit digit of 23^40?

  1. A5
  2. B1
  3. C9
  4. D8
Show answer
Answer: (B) 1 Unit digits of powers of 3 repeat in a cycle of 4; 40 mod 4 = 0, so the unit digit is 1.
Question 6

What is the value of 63² − 46²?

  1. A289
  2. B1953
  3. C1870
  4. D1853
Show answer
Answer: (D) 1853 a² − b² = (a + b)(a − b) = 109 × 17 = 1853.
Question 7

What is the LCM of 27 and 45?

  1. A144
  2. B1215
  3. C67.5
  4. D135
Show answer
Answer: (D) 135 LCM = HCF × 3 × 5 = 135.
Question 8

What is the square root of 6889?

  1. A85
  2. B83
  3. C80
  4. D82
Show answer
Answer: (B) 83 83 × 83 = 6889.
Question 9

What is the remainder when 96840 is divided by 13?

  1. A3
  2. B12
  3. C6
  4. D4
Show answer
Answer: (A) 3 96840 = 13 × 7449 + 3.
Question 10

What is the HCF of 42 and 98?

  1. A28
  2. B14
  3. C7
  4. D42
Show answer
Answer: (B) 14 42 = 14 × 3 and 98 = 14 × 7, so HCF = 14.

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Question 11

What is the value of 85² − 33²?

  1. A6036
  2. B6236
  3. C6188
  4. D6136
Show answer
Answer: (D) 6136 a² − b² = (a + b)(a − b) = 118 × 52 = 6136.
Question 12

What is the unit digit of 27^52?

  1. A5
  2. B1
  3. C6
  4. D7
Show answer
Answer: (B) 1 Unit digits of powers of 7 repeat in a cycle of 4; 52 mod 4 = 0, so the unit digit is 1.
Question 13

What is the sum of the first 36 natural numbers?

  1. A630
  2. B1296
  3. C666
  4. D702
Show answer
Answer: (C) 666 Sum = n(n + 1)/2 = 36 × 37/2 = 666.
Question 14

What is the square root of 5329?

  1. A75
  2. B72
  3. C70
  4. D73
Show answer
Answer: (D) 73 73 × 73 = 5329.
Question 15

What is the remainder when 11581 is divided by 7?

  1. A5
  2. B0
  3. C3
  4. D6
Show answer
Answer: (C) 3 11581 = 7 × 1654 + 3.
Question 16

What is the LCM of 60 and 75?

  1. A150
  2. B4500
  3. C300
  4. D600
Show answer
Answer: (C) 300 LCM = HCF × 4 × 5 = 300.
Question 17

What is the value of 59² − 49²?

  1. A1090
  2. B1080
  3. C100
  4. D1180
Show answer
Answer: (B) 1080 a² − b² = (a + b)(a − b) = 108 × 10 = 1080.
Question 18

What is the unit digit of 7^84?

  1. A0
  2. B1
  3. C4
  4. D9
Show answer
Answer: (B) 1 Unit digits of powers of 7 repeat in a cycle of 4; 84 mod 4 = 0, so the unit digit is 1.
Question 19

What is the sum of the first 71 natural numbers?

  1. A2556
  2. B5041
  3. C2627
  4. D2485
Show answer
Answer: (A) 2556 Sum = n(n + 1)/2 = 71 × 72/2 = 2556.
Question 20

What is the square root of 2304?

  1. A48
  2. B49
  3. C47
  4. D45
Show answer
Answer: (A) 48 48 × 48 = 2304.

These are RankerClub practice questions written in the UP Police Constable pattern. They are not official SSC/IBPS/RRB papers.

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