Question 1 of 20 · CSAT 2026, Q19
If 10ᵐ × 1000 × n = 75²⁵ × 25³² × 32⁷⁵, where n is not divisible by 10, then the value of m is
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CSAT · Number system · Set 2 of 7
Number system: practice set 2
20 questions UPSC asked between 2017 and 2026, 30 minutes, negative marking — your score as soon as you submit.
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Number system has 7 sets of about 20 questions — together, every question UPSC has asked on it since 2016. This is set 2; when you finish, the next one is a tap away.
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- 1Answer in any order: skip, mark for review and come back from the question palette.
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Marking, as in the exam: +2.5 for a correct answer, −0.83 for a wrong one, 0 if you leave it. CSAT is qualifying: 33%.
Questions from the latest paper are scored against UPSC's provisional answer key (the final key comes out after the final result).
What's in this test
| Year | Questions | Easy | Medium | Hard |
|---|---|---|---|---|
| 2026 | 2 | 1 | 1 | 0 |
| 2025 | 3 | 3 | 0 | 0 |
| 2024 | 2 | 2 | 0 | 0 |
| 2023 | 3 | 2 | 0 | 1 |
| 2022 | 2 | 1 | 0 | 1 |
| 2021 | 2 | 2 | 0 | 0 |
| 2020 | 2 | 2 | 0 | 0 |
| 2019 | 2 | 2 | 0 | 0 |
| 2018 | 1 | 1 | 0 | 0 |
| 2017 | 1 | 0 | 1 | 0 |
Difficulty is the Vault's own rating of each question; subjects and topics follow the official syllabus.
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About this test
- How is this test marked?
- As in UPSC's CSAT (GS Paper II): 2.5 marks for each correct answer and a third of that (0.83) deducted for each wrong one. A question you leave scores nothing. The maximum here is 50.
- How long do I get?
- 30 minutes — the exam's pace (80 questions in 2 hours) for 20 questions. When the time runs out, your answers are submitted as they stand.
- How are the sets made?
- Every question UPSC has asked on Number system since 2016 is in one of the 7 sets of about 20, each mixing years (a passage always comes with all its questions). Questions UPSC dropped from evaluation are left out. Take them in any order; the sets page shows which you've done.
- Is it free?
- Yes. Anyone can take the test and see their score straight away. A free sign-up shows the full report and every question with UPSC's answer and a step-by-step solution.
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Number system · Set 2 · Set 2 of 7
0 of 20 answered
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Question 2 of 20 · CSAT 2026, Q59
If the product of the HCF and LCM of two distinct numbers is the cube of one of the numbers, then which of the following statements is/are correct?
- I.The difference of the numbers is an even number.
- II.One of the numbers is a perfect square.
Select the answer using the code given below.
Question 3 of 20 · CSAT 2025, Q18
A 4-digit number N is such that when divided by 3, 5, 6, 9 leaves a remainder 1, 3, 4, 7 respectively. What is the smallest value of N?
Question 4 of 20 · CSAT 2025, Q35
What is the maximum value of n such that 7 × 343 × 385 × 1000 × 2401 × 77777 is divisible by 35ⁿ?
Question 5 of 20 · CSAT 2025, Q67
What is the remainder when 9³ + 9⁴ + 9⁵ + 9⁶ + ... + 9¹⁰⁰ is divided by 6?
Question 6 of 20 · CSAT 2024, Q15
222³³³ + 333²²² is divisible by which of the following numbers?
Question 7 of 20 · CSAT 2024, Q45
What is the number of fives used in numbering a 260-page book?
Question 8 of 20 · CSAT 2023, Q8
What is the unit digit in the expansion of (57242)^(9×7×5×3×1)?
Question 9 of 20 · CSAT 2023, Q25
Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible?
Question 10 of 20 · CSAT 2023, Q46
Let pp, qq and rr be 2-digit numbers where p < q < r. If pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero, consider the following statements:
- 1.The number of possible values of p is 5.
- 2.The number of possible values of q is 6.
Which of the above statements is/are correct?
Question 11 of 20 · CSAT 2022, Q5
An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number?
Question 12 of 20 · CSAT 2022, Q66
Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p × q = 2430, then what is the difference between p and q?
Question 13 of 20 · CSAT 2021, Q19
Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10?
Question 14 of 20 · CSAT 2021, Q79
When a certain number is multiplied by 7, the product entirely comprises ones only (1111...). What is the smallest such number?
Question 15 of 20 · CSAT 2020, Q13
A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, ... results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence?
Question 16 of 20 · CSAT 2020, Q54
What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?
Question 17 of 20 · CSAT 2019, Q15
In a school every student is assigned a unique identification number. A student is a football player if and only if the identification number is divisible by 4, whereas a student is a cricketer if and only if the identification number is divisible by 6. If every number from 1 to 100 is assigned to a student, then how many of them play cricket as well as football?
Question 18 of 20 · CSAT 2019, Q53
A printer numbers the pages of a book starting with 1 and uses 3089 digits in all. How many pages does the book have?
Question 19 of 20 · CSAT 2018, Q24
X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number?
Question 20 of 20 · CSAT 2017, Q73
A 2-digit number is reversed. The larger of the two numbers is divided by the smaller one. What is the largest possible remainder?
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Keep the momentum — set 3 of 7 has different questions on Number system.