Quadratic Equations, Data Interpretation, Percentage - Question Bank
1. If the sum of the roots of ax^2 + bx + c = 0 is equal to their product, then which of the following is true?
2. A product's price is increased by 25%. By what percentage should the new price be decreased to restore the original price?
3. If 50% of a number is 75, what is 80% of that number?
4. Given 2x^2 + 7x + 3 = 0 and y^2 + 5y + 6 = 0, what is the relationship between x and y?
5. If x^2 - 3x + 2 = 0 and y^2 - 5y + 6 = 0, what is the relationship between x and y?
6. In a pie chart showing expenditure, if the 'Rent' sector is 90 degrees, what percentage of the total expenditure is rent?
7. A number, when increased by 30%, becomes 130. What is the original number?
8. If the ratio of boys to girls in a class is 4:5, and there are 20 boys, how many girls are there?
9. If the selling price is 125% of the cost price, what is the profit percentage?
10. In a data set, if 20% of 500 items are defective, how many items are defective?
11. A number is decreased by 20% and then increased by 20%. The net result is:
12. If 15% of a salary is Rs. 4500, what is 25% of the salary?
13. A mixture contains milk and water in the ratio 3:2. If 5 liters of water are added, the ratio becomes 3:3. What was the original quantity of milk?
14. If a price is increased by 20%, and the new price is Rs. 1200, what was the original price?
15. What is 75% of 200?
16. Solve for k: k^2 - 6k + 9 = 0.
17. Given y^2 + 9y + 20 = 0, what is the sum of the squares of the roots?
18. If x^2 - 12x + 35 = 0, what is the difference between the roots?
19. What is the average of the roots of the quadratic equation 2x^2 - 10x + 12 = 0?
20. In a table, rows typically represent _______ and columns represent _______.
21. A scatter plot is used to show:
22. If a line graph shows sales of a product over five years, and the line is upward sloping, it indicates:
23. What is the primary purpose of Data Interpretation?
24. In a bar graph, the width of the bars:
25. A pie chart represents:
26. Which type of chart is best suited for showing trends over time?
27. In a Data Interpretation chart, what does the y-axis typically represent?
28. A number is first increased by 10% and then decreased by 10%. The net result is:
29. If the cost price of an item is Rs. 800 and the selling price is Rs. 1000, what is the profit percentage?
30. A survey shows that 40% of people prefer brand A, 30% prefer brand B, and the rest prefer brand C. If 1000 people were surveyed, how many prefer brand C?
31. If a town's population increased by 15% from 2020 to 2021, and the population in 2021 was 23,000, what was the population in 2020?
32. A shopkeeper marks his goods 20% above the cost price and then offers a 10% discount. What is his overall profit percentage?
33. If 30% of a number is 150, what is 50% of that number?
34. Two numbers are in the ratio 5:7. If the first number is 45, what is the second number?
35. If a price is decreased by 10%, and the new price is Rs. 900, what was the original price?
36. What percentage of 80 is 20?
37. A student scored 60% marks in an exam. If the maximum marks were 500, how many marks did the student score?
38. If a number is increased by 25%, it becomes 125. What is the number?
39. A company's profit increased by 20% in the first year and then decreased by 10% in the second year. If the initial profit was Rs. 50,000, what is the profit after two years?
40. The product of roots of ax^2 + bx + c = 0 is given by:
41. The sum of roots of ax^2 + bx + c = 0 is given by:
42. If x^2 + 6x + 9 = 0, what is the value of x?
43. Solve for m: 5m^2 - 20 = 0.
44. If x^2 - 9 = 0, find the roots.
45. What is the value of x if x^2 = 16?
46. For the equation 4q^2 + 8q + 3 = 0, what is the product of the roots?
47. If the roots of the equation k^2 - 5k + 6 = 0 are alpha and beta, what is alpha + beta?
48. Given the quadratic equation 3p^2 - 11p + 10 = 0, find the roots.
49. Solve the quadratic equation: 2y^2 + 5y - 3 = 0.
50. If x^2 - 7x + 12 = 0, what are the values of x?