Mathematics: same topics as CBT-1 at a higher difficulty level - One Line Questions

1. Find the value of sin(30) + cos(60) — 1
2. If x = 3, y = 4, z = 5, what is the value of (x^2 + y^2 - z^2)? — 0
3. If x = 1/2, what is the value of (4x^2 - 4x + 1)? — 0
4. What is the value of (0.125)^(1/3)? — 0.5
5. If the length of a rectangle is increased by 25% and the width is decreased by 20%, what is the net percentage change in area? — 0%
6. Solve for x: sqrt(x+4) = 3 — 1
7. A cistern can be filled by a tap in 5 hours and emptied by another tap in 4 hours. If the cistern is half full, how long will it take to empty it? — 4 hours
8. What is the probability of drawing a spade from a standard deck of 52 cards? — 1/4
9. Solve for x: 2x^2 - 5x + 2 = 0 — 1/2 and 2
10. If the length of a rectangle is increased by 10% and the width is decreased by 10%, what is the percentage change in its area? — 1% decrease
11. The difference between the squares of two consecutive integers is 21. Find the integers. — 11 and 12
12. A clock gains 5 minutes every hour. If it is set correctly at 10 AM, what time will it show at 10 AM the next day? — 12:00 PM
13. Find the value of (2/3)^2 * (3/4)^3 / (5/6)^2 — 15.75
14. A man can row upstream at 10 km/hr and downstream at 16 km/hr. What is the speed of the man in still water? — 13 km/hr
15. A sum of money doubles itself in 5 years at simple interest. In how many years will it become 5 times itself? — 20 years
16. If the speed of a car is increased by 20%, how much will its travel time be reduced for the same distance? — 16.67%
17. If the sum of the first 'n' natural numbers is 210, what is the value of 'n'? — 20
18. The sum of three consecutive integers is 63. What is the middle integer? — 21
19. A boat travels downstream at 20 km/hr and upstream at 15 km/hr. What is the speed of the stream? — 2.5 km/hr
20. A man buys oranges at 5 for Rs. 10 and sells them at 4 for Rs. 12. What is his profit percentage? — 25%
21. If the area of a circle is 154 sq cm, what is its circumference? (Use pi = 22/7) — 44 cm
22. The ratio of two numbers is 3:5 and their LCM is 75. What is the product of the two numbers? — 225
23. If x + 1/x = 5, then what is the value of x^2 + 1/x^2? — 23
24. The average of 5 consecutive odd numbers is 25. What is the largest of these numbers? — 29
25. If the radius of a sphere is 3 cm, what is its surface area? (Use pi = 3.14) — 113.04 sq cm
26. The sum of the first 10 terms of an arithmetic progression is 210. If the first term is 3, what is the common difference? — 4
27. If the circumference of a circle is 44 cm, what is its radius? (Use pi = 22/7) — 7 cm
28. What is the smallest number that is divisible by 3, 4, 5, and 6? — 60
29. The angles of a triangle are in the ratio 1:2:3. What is the measure of the largest angle? — 90 degrees
30. Two cyclists start from the same point at the same time, one going north at 10 km/hr and the other going south at 15 km/hr. How far apart will they be after 2 hours? — 50 km
31. If a shopkeeper allows a discount of 10% on the marked price, he earns a profit of 20%. By what percentage is the marked price above the cost price? — 33.33%
32. If 30% of a number is 150, what is 70% of that number? — 350
33. What is the volume of a cube with side length 6 cm? — 216 cu cm
34. If the perimeter of an equilateral triangle is 36 cm, what is its area? — 36*sqrt(3) sq cm
35. Find the median of the following numbers: 2, 5, 1, 8, 3, 7, 6 — 5
36. What is the area of a triangle with base 12 cm and height 8 cm? — 96 sq cm
37. A train travels at a speed of 60 km/hr. How many seconds will it take to cover a distance of 150 meters? — 15
38. A can do a work in 10 days and B can do the same work in 15 days. In how many days can both A and B together finish the work? — 6
39. Two numbers are in the ratio 5:7. If the sum of the numbers is 144, find the larger number. — 84
40. If the diagonal of a square is 10*sqrt(2) cm, what is its area? — 100 sq cm
41. The sum of the digits of a two-digit number is 12. If the digits are reversed, the number is increased by 18. What is the original number? — 75
42. What is the HCF of 144, 180, and 192? — 12
43. If the mean of 5 observations x, x+2, x+4, x+6, x+8 is 10, find the value of x. — 6
44. If log_2(x) = 4, what is the value of x? — 16
45. If a rectangle has a length of 15 cm and a perimeter of 50 cm, what is its width? — 8 cm
46. A shopkeeper marks his goods 20% above the cost price and then offers a 10% discount. What is his net profit percentage? — 8%
47. Simplify: (a^2 - b^2) / (a + b) — a - b
48. What is the value of (a^2 - b^2) / (a - b) if a is not equal to b? — a + b
49. If a shopkeeper sells an item for Rs. 400 and makes a profit of 25%, what was the cost price of the item? — Rs. 320
50. A sum of Rs. 8000 is invested at 5% compound interest per annum. What is the interest earned after 2 years? — Rs. 1640
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