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Q1. Which of the following is the largest prime number less than 100 that can be expressed as the sum of two squares?
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Q2. P can do a piece of work in 20 days and Q can do it in 30 days. They work together for 5 days. Then R joins them and they complete the remaining work in 3 days. If R's daily wages are ₹ 15 more than P's daily wages, and Q's daily wages are ₹ 10 less than P's, what is the total wage earned by R?
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Q3. A merchant buys 20 kg of rice at Rs. 10 per kg. He sells 15 kg at Rs. 12 per kg and the remaining 5 kg at Rs. 8 per kg. What is his overall profit/loss percentage?
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Q4. The average of the first 8 natural numbers is:
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Q5. The prime factorization of 40 is:
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Q6. A father is now three times as old as his son. 10 years ago, the father was five times as old as his son. What is the present age of the son?
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Q7. Find the number of ways to arrange the digits 1, 2, 3, 4, 5, 6 such that the digit 1 is followed by the digit 2, and the digit 3 is followed by the digit 4.
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Q8. The HCF of two numbers is 12. Their LCM is 720. If one of the numbers is 180, find the other number.
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Q9. Which of the following numbers is divisible by 7? (1428)
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Q10. Which of the following numbers has the most divisors?
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Q11. Find the sum of the first 7 terms of the arithmetic progression: 2, 7, 12, 17, ...
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Q12. When a polynomial p(x) is divided by x - 1, the remainder is 5. When divided by x - 3, the remainder is 9. What is the remainder when p(x) is divided by (x - 1)(x - 3)?
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Q13. What is the largest power of 3 that divides 50! * 75! ?
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Q14. Which of the following numbers is divisible by 9?
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Q15. Which of these numbers is part of the amicable pair (5020, 5564)?
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Q16. A number is divisible by 81 if the sum of its digits is divisible by 81. Find the smallest 7-digit number divisible by 81.
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Q17. If a number is decreased by 15%, the result is 34. The number is:
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Q18. A number is divisible by 7 if the difference between twice the last digit and the number formed by the remaining digits is divisible by:
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Q19. A number is divisible by 5 and 6. What is the smallest possible remainder when that number is divided by 30?
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Q20. The present age of a father is three times the sum of the ages of his three children. If the ages of the children are in the ratio 1:2:3, and the sum of the father's age and the eldest child's age is 64 years, what is the father's present age?
