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Q1. Divide 1000 base 5 by 10 base 5.
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Q2. The number 0.333... is a:
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Q3. A man travels a distance of 60 km in 6 hours. If he travels the first 30 km in 2 hours, what is his speed for the rest of the journey?
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Q4. Find the total number of divisors of 360.
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Q5. A two-digit number is 3 times the sum of its digits. If 45 is added to the number, the digits interchange their places. What is the number?
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Q6. Find the remainder when 1! + 2! + 3! + ... + 100! is divided by 10.
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Q7. Find the remainder when x³ - 2x² + 3x - 4 is divided by (x + 2).
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Q8. What is the decimal equivalent of the octal number 705?
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Q9. A, B, and C can complete a work in 10, 15, and 20 days respectively. If they work together, what is the ratio of work done by A in the first 5 days to the total work done by all three in the first 5 days?
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Q10. The product of $(21)_3$ and $(12)_3$ in base 3 is?
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Q11. When a number is divided by 3, the remainder is 2. When the quotient is divided by 5, the remainder is 1. What is the remainder when the original number is divided by 15?
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Q12. Which of the following numbers has exactly 3 prime factors (counting multiplicity)?
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Q13. Which of the following numbers is divisible by 11?
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Q14. A number that has exactly two distinct positive divisors (1 and itself) is called a:
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Q15. How many divisors does the number 75 have?
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Q16. If 25% of a number is 50, what is 12.5% of that number?
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Q17. A seller buys 50 kg of rice at Rs. 30 per kg. He sells 30 kg at a profit of 20% and the remaining 20 kg at a loss of 10%. What is his overall profit or loss percentage?
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Q18. What is the remainder when $x^3 + 1$ is divided by $(x+1)$?
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Q19. A number consists of two digits. If the number obtained by interchanging the digits is added to the original number, the result is 110. If the difference between the digits is 6, then the number is:
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Q20. If a number leaves a remainder of 2 when divided by 3, and a remainder of 3 when divided by 5, what is the smallest such positive integer?
