Question 1 of 20 · CSAT 2026, Q45
How many three-digit numbers can be expressed as an integral power of 2?
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CSAT · Number system · Set 7 of 7
Number system: practice set 7
20 questions UPSC asked between 2016 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 7.
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- 1Answer in any order: skip, mark for review and come back from the question palette.
- 2Submit when you're done, or the 30 min timer submits for you. Close the page and come back any time — your answers are saved in this browser.
- 3See your score straight away. Sign up free (or log in) for the full report and every question with UPSC's answer and a step-by-step solution.
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 | 1 | 1 | 0 | 0 |
| 2025 | 3 | 0 | 3 | 0 |
| 2024 | 3 | 1 | 2 | 0 |
| 2023 | 3 | 1 | 1 | 1 |
| 2022 | 1 | 1 | 0 | 0 |
| 2021 | 2 | 2 | 0 | 0 |
| 2020 | 3 | 2 | 1 | 0 |
| 2019 | 1 | 1 | 0 | 0 |
| 2018 | 1 | 1 | 0 | 0 |
| 2017 | 1 | 1 | 0 | 0 |
| 2016 | 1 | 1 | 0 | 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.
Prefer to read? Every Number system question with solutions →
Number system · Set 7 · Set 7 of 7
0 of 20 answered
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Question 2 of 20 · CSAT 2025, Q6
Three prime numbers p, q and r, each less than 20, are such that p − q = q − r. How many distinct possible values can we get for (p + q + r)?
Question 3 of 20 · CSAT 2025, Q28
There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is the value of n?
Question 4 of 20 · CSAT 2025, Q58
The 5-digit number PQRST (all distinct digits) is such that T ≠ 0. P is thrice T. S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible?
Question 5 of 20 · CSAT 2024, Q9
How many consecutive zeros are there at the end of the integer obtained in the product 1² × 2⁴ × 3⁶ × 4⁸ × ⋯ × 25⁵⁰?
Question 6 of 20 · CSAT 2024, Q35
Let X be a two-digit number and Y be another two-digit number formed by interchanging the digits of X. If (X + Y) is the greatest two-digit number, then what is the number of possible values of X?
Question 7 of 20 · CSAT 2024, Q79
What will come in place of in the sequence 3, 14, 39, 84, , 258?
Question 8 of 20 · CSAT 2023, Q16
A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A + B + C?
Question 9 of 20 · CSAT 2023, Q40
Choose the group which is different from the others:
Question 10 of 20 · CSAT 2023, Q76
AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 8, then what is A + B + C equal to?
Question 11 of 20 · CSAT 2022, Q58
What is the remainder when 91 × 92 × 93 × 94 × 95 × 96 × 97 × 98 × 99 is divided by 1261?
Question 12 of 20 · CSAT 2021, Q5
If 3²⁰¹⁹ is divided by 10, then what is the remainder?
Question 13 of 20 · CSAT 2021, Q75
Joseph visits the club on every 5th day, Harsh visits on every 24th day, while Sumit visits on every 9th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?
Question 14 of 20 · CSAT 2020, Q11
In the sum
⊗ + 1⊗ + 5⊗ + ⊗⊗ + ⊗1 = 1⊗⊗
for which digit does the symbol ⊗ stand?
Question 15 of 20 · CSAT 2020, Q51
What is the greatest length x such that 3½ m and 8¾ m are integral multiples of x?
Question 16 of 20 · CSAT 2020, Q77
A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4?
Question 17 of 20 · CSAT 2019, Q50
If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is
Question 18 of 20 · CSAT 2018, Q2
Consider the following sum:
• + 1• + 2• + •3 + •1 = 21•
In the above sum, • stands for
Question 19 of 20 · CSAT 2017, Q51
How many numbers are there between 99 and 1000 such that the digit 8 occupies the units place?
Question 20 of 20 · CSAT 2016, Q62
If R and S are different integers both divisible by 5, then which of the following is not necessarily true?
Your result · Number system · Set 7
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