Mathematics: same topics as CBT-1 at a higher difficulty level - Question Bank

1. 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?
A) 0%
B) 2%
C) 5%
D) 10%
2. Find the median of the following numbers: 2, 5, 1, 8, 3, 7, 6
A) 4
B) 5
C) 6
D) 7
3. If x = 1/2, what is the value of (4x^2 - 4x + 1)?
A) 0
B) 1
C) 2
D) 4
4. 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?
A) 12 km/hr
B) 13 km/hr
C) 14 km/hr
D) 15 km/hr
5. If the area of a circle is 154 sq cm, what is its circumference? (Use pi = 22/7)
A) 22 cm
B) 44 cm
C) 66 cm
D) 88 cm
6. What is the value of (a^2 - b^2) / (a - b) if a is not equal to b?
A) a + b
B) a - b
C) a^2 + b^2
D) a*b
7. 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?
A) 30 km
B) 40 km
C) 50 km
D) 60 km
8. If x = 3, y = 4, z = 5, what is the value of (x^2 + y^2 - z^2)?
A) 0
B) 1
C) 2
D) 3
9. The sum of the first 10 terms of an arithmetic progression is 210. If the first term is 3, what is the common difference?
A) 3
B) 4
C) 5
D) 6
10. 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?
A) 30%
B) 33.33%
C) 40%
D) 50%
11. What is the value of (0.125)^(1/3)?
A) 0.5
B) 0.25
C) 0.125
D) 0.05
12. If the speed of a car is increased by 20%, how much will its travel time be reduced for the same distance?
A) 16.67%
B) 20%
C) 25%
D) 33.33%
13. A man buys oranges at 5 for Rs. 10 and sells them at 4 for Rs. 12. What is his profit percentage?
A) 20%
B) 25%
C) 30%
D) 35%
14. If the perimeter of an equilateral triangle is 36 cm, what is its area?
A) 36*sqrt(3) sq cm
B) 72*sqrt(3) sq cm
C) 108*sqrt(3) sq cm
D) 144*sqrt(3) sq cm
15. What is the value of (x^3 - y^3) / (x - y) if x is not equal to y?
A) x^2 + y^2
B) x^2 - y^2
C) x^2 + xy + y^2
D) x^2 - xy + y^2
16. 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?
A) 1 hour
B) 2 hours
C) 3 hours
D) 4 hours
17. The sum of three consecutive integers is 63. What is the middle integer?
A) 19
B) 20
C) 21
D) 22
18. Solve for x: 2x^2 - 5x + 2 = 0
A) 1/2 and 2
B) 1 and 2
C) 1/2 and 1
D) 2 and 3
19. 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?
A) 1% decrease
B) 0% change
C) 1% increase
D) 10% decrease
20. What is the probability of drawing a spade from a standard deck of 52 cards?
A) 1/13
B) 1/4
C) 1/2
D) 3/4
21. A shopkeeper marks his goods 20% above the cost price and then offers a 10% discount. What is his net profit percentage?
A) 8%
B) 10%
C) 12%
D) 15%
22. If the mean of 5 observations x, x+2, x+4, x+6, x+8 is 10, find the value of x.
A) 6
B) 7
C) 8
D) 9
23. Find the value of sin(30) + cos(60)
A) 0
B) 1
C) 1.5
D) 2
24. If log_2(x) = 4, what is the value of x?
A) 8
B) 16
C) 32
D) 64
25. A boat travels downstream at 20 km/hr and upstream at 15 km/hr. What is the speed of the stream?
A) 2.5 km/hr
B) 5 km/hr
C) 7.5 km/hr
D) 10 km/hr
26. If the diagonal of a square is 10*sqrt(2) cm, what is its area?
A) 50 sq cm
B) 100 sq cm
C) 150 sq cm
D) 200 sq cm
27. What is the smallest number that is divisible by 3, 4, 5, and 6?
A) 30
B) 60
C) 90
D) 120
28. If 30% of a number is 150, what is 70% of that number?
A) 300
B) 350
C) 400
D) 450
29. The angles of a triangle are in the ratio 1:2:3. What is the measure of the largest angle?
A) 30 degrees
B) 60 degrees
C) 90 degrees
D) 120 degrees
30. Simplify: (a^2 - b^2) / (a + b)
A) a - b
B) a + b
C) a^2 + b^2
D) a*b
31. A sum of Rs. 8000 is invested at 5% compound interest per annum. What is the interest earned after 2 years?
A) Rs. 800
B) Rs. 820
C) Rs. 1600
D) Rs. 1640
32. If the radius of a sphere is 3 cm, what is its surface area? (Use pi = 3.14)
A) 28.26 sq cm
B) 56.52 sq cm
C) 84.78 sq cm
D) 113.04 sq cm
33. What is the volume of a cube with side length 6 cm?
A) 36 cu cm
B) 108 cu cm
C) 216 cu cm
D) 256 cu cm
34. The difference between the squares of two consecutive integers is 21. Find the integers.
A) 10 and 11
B) 11 and 12
C) 12 and 13
D) 10 and 12
35. 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?
A) 10:00 AM
B) 11:00 AM
C) 12:00 PM
D) 1:00 PM
36. Two numbers are in the ratio 5:7. If the sum of the numbers is 144, find the larger number.
A) 50
B) 60
C) 70
D) 84
37. Solve for x: sqrt(x+4) = 3
A) 1
B) 2
C) 3
D) 5
38. If a rectangle has a length of 15 cm and a perimeter of 50 cm, what is its width?
A) 8 cm
B) 10 cm
C) 12 cm
D) 15 cm
39. What is the HCF of 144, 180, and 192?
A) 6
B) 12
C) 18
D) 24
40. Find the value of (2/3)^2 * (3/4)^3 / (5/6)^2
A) 10.8
B) 12.5
C) 15.75
D) 18.9
41. A sum of money doubles itself in 5 years at simple interest. In how many years will it become 5 times itself?
A) 15 years
B) 20 years
C) 25 years
D) 30 years
42. If the circumference of a circle is 44 cm, what is its radius? (Use pi = 22/7)
A) 3.5 cm
B) 7 cm
C) 11 cm
D) 14 cm
43. What is the area of a triangle with base 12 cm and height 8 cm?
A) 48 sq cm
B) 60 sq cm
C) 96 sq cm
D) 108 sq cm
44. 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?
A) 57
B) 66
C) 75
D) 84
45. 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?
A) 5
B) 6
C) 7
D) 8
46. If x + 1/x = 5, then what is the value of x^2 + 1/x^2?
A) 23
B) 25
C) 27
D) 29
47. The ratio of two numbers is 3:5 and their LCM is 75. What is the product of the two numbers?
A) 225
B) 375
C) 525
D) 675
48. If a shopkeeper sells an item for Rs. 400 and makes a profit of 25%, what was the cost price of the item?
A) Rs. 300
B) Rs. 320
C) Rs. 340
D) Rs. 360
49. A train travels at a speed of 60 km/hr. How many seconds will it take to cover a distance of 150 meters?
A) 5
B) 10
C) 15
D) 20
50. The average of 5 consecutive odd numbers is 25. What is the largest of these numbers?
A) 27
B) 29
C) 31
D) 33
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