Question 1 of 20 · CSAT 2026, Q42
The digit in the unit place of the number 6¹²⁹ × 7³⁰⁷ is
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CSAT · Number system · Set 6 of 7
Number system: practice set 6
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 6; 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.
- 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 | 4 | 0 | 3 | 1 |
| 2024 | 2 | 2 | 0 | 0 |
| 2023 | 3 | 1 | 2 | 0 |
| 2022 | 2 | 0 | 2 | 0 |
| 2021 | 1 | 1 | 0 | 0 |
| 2020 | 3 | 2 | 1 | 0 |
| 2019 | 2 | 2 | 0 | 0 |
| 2017 | 1 | 0 | 0 | 1 |
| 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 6 · Set 6 of 7
0 of 20 answered
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Question 2 of 20 · CSAT 2025, Q5
A natural number N is such that it can be expressed as N = p + q + r, where p, q and r are distinct factors of N. How many numbers below 50 have this property?
Question 3 of 20 · CSAT 2025, Q27
Let both p and k be prime numbers such that (p² + k) is also a prime number less than 30. What is the number of possible values of k?
Question 4 of 20 · CSAT 2025, Q48
What is the 489th digit in the number 123456789101112...?
Question 5 of 20 · CSAT 2025, Q80
The difference between any two natural numbers is 10. What can be said about the natural numbers which are divisible by 5 and lie between these two numbers?
Question 6 of 20 · CSAT 2024, Q20
Consider the following statements in respect of the sum S = x + y + z, where x, y and z are distinct prime numbers each less than 10:
- 1.The unit digit of S can be 0.
- 2.The unit digit of S can be 9.
- 3.The unit digit of S can be 5.
Which of the statements given above are correct?
Question 7 of 20 · CSAT 2024, Q55
Let p and q be positive integers satisfying p < q and p + q = k. What is the smallest value of k that does not determine p and q uniquely?
Question 8 of 20 · CSAT 2023, Q15
Consider the following in respect of prime number p and composite number c.
- 1.(p + c)/(p − c) can be even.
- 2.2p + c can be odd.
- 3.pc can be odd.
Which of the statements given above are correct?
Question 9 of 20 · CSAT 2023, Q29
What is the sum of all digits which appear in all the integers from 10 to 100?
Question 10 of 20 · CSAT 2023, Q74
What is the remainder if 2¹⁹² is divided by 6?
Question 11 of 20 · CSAT 2022, Q54
Let A, B and C represent distinct non-zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition.
Consider the following statements:
- 1.The 4-digit least value of x is 1332.
- 2.The 3-digit greatest value of x is 888.
Which of the above statements is/are correct?
Question 12 of 20 · CSAT 2022, Q78
The sum of three consecutive integers is equal to their product. How many such possibilities are there?
Question 13 of 20 · CSAT 2021, Q67
Consider the following statements:
- 1.The sum of 5 consecutive integers can be 100.
- 2.The product of three consecutive natural numbers can be equal to their sum.
Which of the above statements is/are correct?
Question 14 of 20 · CSAT 2020, Q10
How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without repetition of digits?
Question 15 of 20 · CSAT 2020, Q50
What is the largest number among the following?
Question 16 of 20 · CSAT 2020, Q76
Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6?
Question 17 of 20 · CSAT 2019, Q48
What is X in the sequence 132, 129, 124, 117, 106, 93, X?
Question 18 of 20 · CSAT 2019, Q75
An 8-digit number 4252746B leaves remainder 0 when divided by 3. How many values of B are possible?
Question 19 of 20 · CSAT 2017, Q49
Certain 3-digit numbers have the following characteristics:
- 1.All the three digits are different.
- 2.The number is divisible by 7.
- 3.The number on reversing the digits is also divisible by 7.
How many such 3-digit numbers are there?
Question 20 of 20 · CSAT 2016, Q29
In aid of charity, every student in a class contributes as many rupees as the number of students in that class. With the additional contribution of Rs. 2 by one student only, the total collection is Rs. 443. Then how many students are there in the class?
Your result · Number system · Set 6
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Next: Number system · Set 7
Keep the momentum — set 7 of 7 has different questions on Number system.