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Q1. Find the smallest 5-digit number that is exactly divisible by 3, 4, 5 and 6.
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Q2. Convert the hexadecimal number 3D to its decimal representation.
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Q3. What is the positional value of the rightmost digit in any base system?
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Q4. The perimeter of a rhombus is 52 cm. What is the length of its side?
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Q5. What is the sum of 567 and 345?
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Q6. The octal number $1000_8$ is equivalent to which power of 2?
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Q7. Find the largest prime factor of 900.
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Q8. 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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Q9. The volume of a cylinder is given by V = πr²h. If the radius 'r' is increased by 10% and the height 'h' is decreased by 10%, what is the percentage change in volume?
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Q10. What is the remainder when $x^2 - 4$ is divided by $x + 2$?
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Q11. 7 years ago, the age of a father was 5 times the age of his son. 7 years from now, the father's age will be 3 times the son's age. What is the present age of the father?
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Q12. Given that $p, q, r$ are consecutive even integers such that $p < q < r$ and $p+q+r > 60$. What is the smallest possible value of $p$?
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Q13. Find the remainder when $x^3 + 2x^2 + 3x + 4$ is divided by $x + 2$.
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Q14. Which of the following is co-prime to 30?
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Q15. Divide 72 by 9.
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Q16. Subtract 45₉ from 82₉ in base 9.
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Q17. Add 27 to 35 in octal. The result is:
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Q18. What is the value of $(34)_7 \times (5)_7$ in base 7?
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Q19. What is 30% of 200?
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Q20. A number is divisible by 63 if it is divisible by both 7 and 9. Find the largest 6-digit number formed using the digits 1, 2, 3, 4, 5, 6 exactly once that is divisible by 63.
