The Mathematics section is a high-scoring, core component of Computer-Based Tests (CBTs) across major Railway Recruitment Board (RRB) examinations, including RRB NTPC, Group D, ALP, and Junior Engineer. Covering both arithmetic foundations and advanced quantitative fields such as Number Systems, Simplification, Profit & Loss, Time & Work, Time, Speed & Distance, Algebra, Geometry, and Mensuration the section tests both accuracy and time-management under strict examination constraints. Practicing targeted multiple-choice questions helps candidates master essential shortcuts, avoid common pitfalls, and secure top percentile scores required to clear railway cutoffs.
1. What is the face value of 8 in the number 45892?
Correct Answer: a) 8
Explanation:
The face value of any digit in a number is the digit itself, regardless of its position.
2. What is the sum of the first 20 natural numbers?
Correct Answer: a) 210
Explanation:
The sum of the first n natural numbers is given by the formula n(n+1)/2. For n = 20, sum = 20(21)/2 = 210.
3. Which of the following is a prime number?
Correct Answer: c) 97
Explanation:
97 is divisible only by 1 and itself, making it a prime number. 33, 81, and 93 are divisible by 3.
4. Find the Least Common Multiple (LCM) of 12, 15, and 20.
Correct Answer: b) 60
Explanation:
The prime factorizations are: 12 = 2^2 * 3, 15 = 3 * 5, 20 = 2^2 * 5. LCM = 2^2 * 3 * 5 = 60.
5. The Highest Common Factor (HCF) of 36 and 84 is:
Correct Answer: c) 12
Explanation:
36 = 12 * 3 and 84 = 12 * 7. Since 3 and 7 are co-prime, the HCF is 12.
6. Simplify: 25 + 5 * 2 - 10 / 2
Correct Answer: a) 30
Explanation:
According to BODMAS: Division first (10/2 = 5), then Multiplication (5*2 = 10). Equation becomes 25 + 10 - 5 = 30.
7. If 15% of x is 45, what is the value of x?
Correct Answer: c) 300
Explanation:
(15/100) * x = 45 => x = (45 * 100) / 15 = 300.
8. A number is increased by 20% and then decreased by 20%. The net change in the number is:
Correct Answer: c) 4% decrease
Explanation:
If a value is increased by x% and then decreased by x%, there is always a net decrease of (x^2/100)%. Here, (20^2)/100 = 4% decrease.
9. Convert 0.75 into a fraction.
Correct Answer: c) 3/4
Explanation:
0.75 can be written as 75/100. Simplifying by dividing the numerator and denominator by 25 gives 3/4.
10. If A:B = 2:3 and B:C = 4:5, what is A:B:C?
Correct Answer: a) 8:12:15
Explanation:
To equate B, multiply A:B by 4 (getting 8:12) and B:C by 3 (getting 12:15). Thus, A:B:C = 8:12:15.
11. The fourth proportional to 5, 8, 15 is:
Correct Answer: b) 24
Explanation:
Let the fourth proportional be x. Then 5/8 = 15/x. => 5x = 120 => x = 24.
12. The average of 5 consecutive odd numbers is 27. What is the largest number?
Correct Answer: b) 31
Explanation:
The middle number is the average, which is 27. The numbers are 23, 25, 27, 29, 31. The largest is 31.
13. Find the average of first 10 multiples of 3.
Correct Answer: b) 16.5
Explanation:
First 10 multiples of 3 are 3, 6, 9... 30. Average = (First term + Last term)/2 = (3 + 30)/2 = 33/2 = 16.5.
14. A person bought an article for Rs. 500 and sold it for Rs. 600. What is the profit percentage?
Correct Answer: c) 20%
Explanation:
Profit = 600 - 500 = 100. Profit % = (Profit/CP) * 100 = (100/500) * 100 = 20%.
15. By selling a watch for Rs. 1440, a man loses 10%. To gain 10%, at what price should he sell it?
Correct Answer: b) Rs. 1760
Explanation:
SP = 1440 at 10% loss. CP = (1440 * 100) / 90 = 1600. For 10% gain, SP = 1600 * 110/100 = 1760.
16. A shopkeeper offers a discount of 20% on the marked price. If the marked price is Rs. 400, the selling price is:
Correct Answer: a) Rs. 320
Explanation:
Discount = 20% of 400 = 80. Selling Price = Marked Price - Discount = 400 - 80 = Rs. 320.
17. Find the Simple Interest on Rs. 2000 at 5% per annum for 3 years.
Correct Answer: c) Rs. 300
Explanation:
Simple Interest (SI) = (P * R * T) / 100 = (2000 * 5 * 3) / 100 = 300.
18. At what rate per annum will a sum double itself in 8 years at simple interest?
Correct Answer: b) 12.5%
Explanation:
If a sum doubles, SI = P. Formula: R = (100 * SI) / (P * T) = (100 * P) / (P * 8) = 100 / 8 = 12.5%.
19. A can do a piece of work in 10 days and B in 15 days. If they work together, in how many days will they finish the work?
Correct Answer: b) 6 days
Explanation:
Work done by A in 1 day = 1/10. Work by B = 1/15. Together in 1 day = 1/10 + 1/15 = 5/30 = 1/6. Total days = 6.
20. Pipe A can fill a tank in 4 hours and Pipe B can fill it in 6 hours. If both are opened together, the tank will be filled in:
Correct Answer: b) 2.4 hours
Explanation:
Work done per hour = 1/4 + 1/6 = 5/12. Time taken = 12/5 = 2.4 hours.
21. A train covers 180 km in 4 hours. What is its speed in m/s?
Correct Answer: b) 12.5 m/s
Explanation:
Speed = Distance/Time = 180/4 = 45 km/hr. To convert to m/s, multiply by 5/18. 45 * (5/18) = 12.5 m/s.
22. A train 100 meters long is running at 36 km/hr. How long will it take to cross a telegraph pole?
Correct Answer: b) 10 seconds
Explanation:
Speed = 36 * (5/18) = 10 m/s. Time = Distance / Speed = 100 / 10 = 10 seconds.
23. A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
Correct Answer: c) 4 hours
Explanation:
Downstream speed = Speed of boat + Speed of stream = 13 + 4 = 17 km/hr. Time = Distance / Speed = 68 / 17 = 4 hours.
24. What is the area of a circle with a radius of 7 cm? (Use pi = 22/7)
Correct Answer: b) 154 sq cm
Explanation:
Area of circle = pi * r^2 = (22/7) * 7 * 7 = 154 sq cm.
25. Find the perimeter of a rectangle whose length is 15 m and breadth is 10 m.
Correct Answer: b) 50 m
Explanation:
Perimeter of rectangle = 2(l + b) = 2(15 + 10) = 2(25) = 50 m.
26. The volume of a cube whose side is 5 cm is:
Correct Answer: c) 125 cubic cm
Explanation:
Volume of a cube = a^3 = 5^3 = 5 * 5 * 5 = 125 cubic cm.
27. If x + y = 10 and x - y = 4, find the value of x.
Correct Answer: c) 7
Explanation:
Adding both equations: (x + y) + (x - y) = 10 + 4 => 2x = 14 => x = 7.
28. The square root of 1024 is:
Correct Answer: a) 32
Explanation:
32 * 32 = 1024. Therefore, the square root of 1024 is 32.
29. What is the value of 5^3 - 3^3?
Correct Answer: a) 98
Explanation:
5^3 = 125 and 3^3 = 27. 125 - 27 = 98.
30. A sum of Rs. 800 amounts to Rs. 920 in 3 years at simple interest. If the interest rate is increased by 3%, it would amount to how much?
Correct Answer: c) Rs. 992
Explanation:
Extra SI for 3% over 3 years = (800 * 3 * 3)/100 = Rs. 72. New amount = 920 + 72 = Rs. 992.
31. Find the compound interest on Rs. 1000 at 10% per annum for 2 years.
Correct Answer: b) Rs. 210
Explanation:
Amount = P(1+R/100)^T = 1000(1.1)^2 = 1000 * 1.21 = 1210. CI = Amount - Principal = 1210 - 1000 = Rs. 210.
32. The ages of A and B are in the ratio 3:4. Five years ago, the ratio was 2:3. What is A's present age?
Correct Answer: b) 15 years
Explanation:
Let present ages be 3x and 4x. (3x - 5)/(4x - 5) = 2/3 => 9x - 15 = 8x - 10 => x = 5. A's age = 3x = 15 years.
33. A man crosses a 600m long street in 5 minutes. What is his speed in km/hr?
Correct Answer: b) 7.2
Explanation:
Speed = Distance / Time = 600m / 300s = 2 m/s. Convert to km/hr: 2 * (18/5) = 36/5 = 7.2 km/hr.
34. If the price of sugar is increased by 25%, by how much percent must a householder reduce his consumption so as not to increase his expenditure?
Correct Answer: a) 20%
Explanation:
Reduction % = [R / (100 + R)] * 100. [25 / (100 + 25)] * 100 = (25 / 125) * 100 = 20%.
35. What is the HCF of two co-prime numbers?
Correct Answer: b) 1
Explanation:
By definition, co-prime numbers share no common factors other than 1, so their HCF is 1.
36. In a triangle, the angles are in the ratio 1:2:3. What is the value of the largest angle?
Correct Answer: b) 90 degrees
Explanation:
Sum of angles is 180. 1x + 2x + 3x = 180 => 6x = 180 => x = 30. Largest angle = 3x = 90 degrees.
37. Simplify: (a + b)^2 - (a - b)^2
Correct Answer: b) 4ab
Explanation:
Expansion gives: (a^2 + 2ab + b^2) - (a^2 - 2ab + b^2) = 4ab.
38. A train passes a platform 150m long in 15s and a man standing on the platform in 9s. Find the speed of the train.
Correct Answer: b) 25 m/s
Explanation:
Let train length be L and speed V. L = 9V. (L + 150) = 15V. Substituting L: 9V + 150 = 15V => 6V = 150 => V = 25 m/s.
39. If sin X = 3/5, find the value of cos X.
Correct Answer: b) 4/5
Explanation:
In a right triangle, if perpendicular is 3 and hypotenuse is 5, the base is 4 (Pythagorean triplet). cos X = Base / Hypotenuse = 4/5.
40. A right circular cone has base radius 3 cm and height 4 cm. What is its slant height?
Correct Answer: a) 5 cm
Explanation:
Slant height l = sqrt(r^2 + h^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5 cm.
41. The median of the data set: 12, 15, 11, 19, 21, 14, 10 is:
Correct Answer: b) 14
Explanation:
Ordering the numbers: 10, 11, 12, 14, 15, 19, 21. The middle value (4th term) is 14.
42. Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new ratio is 12:23. The smaller number is:
Correct Answer: b) 33
Explanation:
Let numbers be 3x and 5x. (3x - 9)/(5x - 9) = 12/23. 23(3x - 9) = 12(5x - 9) => 69x - 207 = 60x - 108 => 9x = 99 => x = 11. Smaller number = 3(11) = 33.
43. What is the unit digit in the product (2467)^153 * (341)^72?
Correct Answer: c) 7
Explanation:
Unit digit of 341^72 is 1. For 2467^153, cyclicity of 7 is 4. 153/4 leaves remainder 1. 7^1 = 7. 7 * 1 = 7.
44. Find the simple interest on Rs 3000 at 6.25% per annum for the period from 4th Feb 2005 to 18th April 2005.
Correct Answer: b) Rs. 37.5
Explanation:
Days = 24 (Feb) + 31 (Mar) + 18 (Apr) = 73 days. T = 73/365 = 1/5 year. SI = (3000 * 6.25 * 1) / (100 * 5) = 37.5.
45. Which fraction is the largest: 7/8, 13/16, 31/40, or 63/80?
Correct Answer: a) 7/8
Explanation:
Make denominators equal (80). 7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80. 70/80 is the largest, hence 7/8.
46. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest is:
Correct Answer: c) 12%
Explanation:
SI for 3 years = 12005 - 9800 = 2205. SI for 1 year = 735. SI for 5 years = 3675. Principal = 9800 - 3675 = 6125. R = (735 * 100) / 6125 = 12%.
47. The difference between simple and compound interest compounded annually on a certain sum of money for 2 years at 4% per annum is Re 1. The sum is:
Correct Answer: a) Rs. 625
Explanation:
Difference = P(R/100)^2. 1 = P(4/100)^2 = P(1/25)^2 => 1 = P/625 => P = 625.
48. X and Y invest in a business in the ratio 3:2. If 5% of the total profit goes to charity and X's share is Rs. 855, the total profit is:
Correct Answer: b) Rs. 1500
Explanation:
Remaining profit = 95%. X's share = (3/5) of 95% = 57%. So, 57% = 855 => 1% = 15 => Total profit (100%) = Rs. 1500.
49. A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both taps are opened, in how much time will it be filled?
Correct Answer: b) 7.2 hours
Explanation:
Net work per hour = 1/4 - 1/9 = 5/36. Time = 36/5 = 7.2 hours.
50. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:
Correct Answer: d) 3.6 km
Explanation:
Downstream speed = 15 + 3 = 18 km/hr. Distance = Speed * Time = 18 * (12/60) = 18 * 0.2 = 3.6 km.
51. An article is sold at a profit of 20%. If it had been sold at a profit of 25%, it would have fetched Rs. 35 more. The cost price of the article is:
Correct Answer: b) Rs. 700
Explanation:
Difference in profit % = 25% - 20% = 5%. 5% of CP = 35 => CP = (35/5) * 100 = 700.
52. In how many years will Rs. 2000 amount to Rs. 2420 at 10% per annum compound interest?
Correct Answer: a) 2 years
Explanation:
Amount = P(1+R/100)^N. 2420 = 2000(1+10/100)^N => 1.21 = (1.1)^N. Since 1.1^2 = 1.21, N = 2 years.
53. Find the length of the longest pole that can be placed in a room 12m long, 9m broad, and 8m high.
Correct Answer: c) 17 m
Explanation:
Length of longest pole = Diagonal of cuboid = sqrt(l^2 + b^2 + h^2) = sqrt(144 + 81 + 64) = sqrt(289) = 17 m.
54. The ratio of the radii of two cylinders is 2:3 and the ratio of their heights is 5:3. The ratio of their volumes is:
Correct Answer: b) 20:27
Explanation:
Volume ratio = (r1/r2)^2 * (h1/h2) = (2/3)^2 * (5/3) = (4/9) * (5/3) = 20/27 or 20:27.
55. 12 men can complete a work in 8 days. 16 men can complete the same work in:
Correct Answer: c) 6 days
Explanation:
M1D1 = M2D2. 12 * 8 = 16 * D2 => 96 = 16 * D2 => D2 = 6 days.
56. The average of 20 numbers is 15. If each number is multiplied by 3, what will be the new average?
Correct Answer: c) 45
Explanation:
If each number in a data set is multiplied by a constant k, the new average is the old average multiplied by k. 15 * 3 = 45.
57. 30% of a number when subtracted from 91, gives the number itself. Find the number.
Correct Answer: c) 70
Explanation:
Let number be x. 91 - 0.30x = x => 91 = 1.30x => x = 91 / 1.30 = 70.
58. A number whose one-fifth part is increased by 4 is equal to its one-fourth part diminished by 10. The number is:
Correct Answer: c) 280
Explanation:
Let the number be x. (x/5) + 4 = (x/4) - 10 => 14 = (x/4) - (x/5) => 14 = x/20 => x = 280.
59. Solve for x: 3^(x+2) = 243
Correct Answer: c) 3
Explanation:
243 is 3^5. So, 3^(x+2) = 3^5 => x+2 = 5 => x = 3.
60. What least number must be added to 1056 so that the sum is completely divisible by 23?
Correct Answer: a) 2
Explanation:
1056 / 23 gives a quotient of 45 and a remainder of 21. Number to be added = Divisor - Remainder = 23 - 21 = 2.
61. If x^2 + 1/x^2 = 34, find the value of x + 1/x (assume x > 0).
Correct Answer: c) 6
Explanation:
(x + 1/x)^2 = x^2 + 1/x^2 + 2 = 34 + 2 = 36. Therefore, x + 1/x = 6.
62. If log 2 = 0.3010, the value of log 16 is:
Correct Answer: c) 1.2040
Explanation:
log 16 = log (2^4) = 4 * log 2 = 4 * 0.3010 = 1.2040.
63. The difference between two numbers is 1365. On dividing the larger number by the smaller, the quotient is 6 and the remainder is 15. The smaller number is:
Correct Answer: b) 270
Explanation:
Let smaller = x. Larger = x + 1365. x + 1365 = 6x + 15 => 5x = 1350 => x = 270.
64. What is the HCF of 2/3, 8/9, 16/81 and 10/27?
Correct Answer: a) 2/81
Explanation:
HCF of fractions = (HCF of numerators) / (LCM of denominators). HCF(2,8,16,10) = 2. LCM(3,9,81,27) = 81. Answer: 2/81.
65. Which of the following is equivalent to 5.6 bar (bar on 6)?
Correct Answer: b) 51/9
Explanation:
5.6 bar = 5 + 6/9 = 5 + 2/3 = 17/3. Equivalently, (56-5)/9 = 51/9 = 17/3.
66. Two natural numbers are in the ratio 3:5 and their product is 2160. The smaller number is:
Correct Answer: d) 36
Explanation:
Let numbers be 3x and 5x. 3x * 5x = 15x^2 = 2160 => x^2 = 144 => x = 12. Smaller number = 3 * 12 = 36.
67. The mean proportional between 9 and 16 is:
Correct Answer: a) 12
Explanation:
Mean proportional between a and b = sqrt(a * b) = sqrt(9 * 16) = sqrt(144) = 12.
68. If 12 carpenters working 6 hours a day can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, working 8 hours a day?
Correct Answer: b) 1380
Explanation:
(M1*D1*H1)/W1 = (M2*D2*H2)/W2. (12*24*6)/460 = (18*36*8)/W2 => W2 = (18*36*8*460)/(12*24*6) = 1380.
69. To paint a sphere of radius 14 cm, what is the surface area to be painted?
Correct Answer: c) 2464 sq cm
Explanation:
Surface area of a sphere = 4 * pi * r^2 = 4 * (22/7) * 14 * 14 = 2464 sq cm.
70. A sum was put at simple interest at a certain rate for 3 years. Had it been put at 2% higher rate, it would have fetched Rs. 360 more. Find the sum.
Correct Answer: b) Rs. 6000
Explanation:
Extra interest = 2% per year for 3 years = 6% total. 6% of sum = 360 => Sum = (360/6) * 100 = 6000.
71. The mode of the following data: 2, 3, 4, 3, 5, 3, 6, 4 is:
Correct Answer: b) 3
Explanation:
The mode is the number that appears most frequently in a data set. Here, 3 appears three times.
72. A polygon has 54 diagonals. Find the number of sides.
Correct Answer: c) 12
Explanation:
Diagonals = n(n-3)/2 => 54 = n(n-3)/2 => 108 = n(n-3). Solving the quadratic equation n^2 - 3n - 108 = 0, n=12.
73. If sin X + cos X = 1, then sin X * cos X equals:
Correct Answer: a) 0
Explanation:
Squaring both sides: (sin X + cos X)^2 = 1 => sin^2 X + cos^2 X + 2sin X cos X = 1 => 1 + 2sin X cos X = 1 => 2sin X cos X = 0 => sin X cos X = 0.
74. Find the value of tan 45 + cot 45.
Correct Answer: c) 2
Explanation:
tan 45 = 1 and cot 45 = 1. So, 1 + 1 = 2.
75. The volume of a hemisphere of radius 21 cm is:
Correct Answer: a) 19404 cubic cm
Explanation:
Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * (22/7) * 21 * 21 * 21 = 44 * 441 = 19404 cubic cm.
76. Two circles touch externally. The sum of their areas is 130 pi sq. cm and the distance between their centers is 14 cm. Find the radius of the larger circle.
Correct Answer: d) 11 cm
Explanation:
Let radii be r1 and r2. r1 + r2 = 14. pi(r1^2 + r2^2) = 130 pi => r1^2 + r2^2 = 130. Solving gives r1=11, r2=3.
77. If x% of y is 100 and y% of z is 200, then find a relation between x and z.
Correct Answer: a) z = 2x
Explanation:
(x*y)/100 = 100 => xy = 10000. (y*z)/100 = 200 => yz = 20000. Dividing the two equations: (yz)/(xy) = 20000/10000 => z/x = 2 => z = 2x.
78. The population of a town is 10,000. It increases by 10% during the first year and decreases by 10% during the second year. The population after 2 years is:
Correct Answer: a) 9900
Explanation:
10000 * (110/100) * (90/100) = 10000 * 1.1 * 0.9 = 9900.
79. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
Correct Answer: b) 3 hours 45 mins
Explanation:
Half tank takes 3 hours. Remaining half takes 3 hours for 1 tap. With 4 taps, it takes 3/4 hour = 45 mins. Total time = 3 hrs 45 mins.
80. Walking at 3/4 of his usual speed, a man reaches his office 20 minutes late. His usual time to reach the office is:
Correct Answer: b) 60 minutes
Explanation:
Let usual time be t. New time is (4/3)t because speed is 3/4. (4/3)t - t = 20 => (1/3)t = 20 => t = 60 minutes.
81. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is:
Correct Answer: d) 10.8 seconds
Explanation:
Total distance = 140 + 160 = 300 m. Relative speed = 60 + 40 = 100 km/hr = 100 * (5/18) m/s. Time = Distance / Speed = 300 / (500/18) = 10.8 s.
82. A sum of money placed at compound interest doubles itself in 5 years. It will amount to 8 times itself in:
Correct Answer: c) 15 years
Explanation:
In 5 years it becomes 2 times. 8 is 2^3. Time required = 5 * 3 = 15 years.
83. The side of a square is increased by 10%. By what percentage does its area increase?
Correct Answer: c) 21%
Explanation:
Net effect = x + y + (xy/100) = 10 + 10 + (100/100) = 21%.
84. In an election between two candidates, one got 55% of the total valid votes and 20% of the votes were invalid. If total votes were 7500, the number of valid votes that the other candidate got was:
Correct Answer: a) 2700
Explanation:
Valid votes = 80% of 7500 = 6000. Other candidate gets 45% of valid votes = 0.45 * 6000 = 2700.
85. The value of (256)^(0.16) * (256)^(0.09) is:
Correct Answer: a) 4
Explanation:
Base is same, add exponents: 0.16 + 0.09 = 0.25. (256)^0.25 = 256^(1/4) = 4.
86. Find the odd one out: 3, 5, 11, 14, 17, 21
Correct Answer: b) 14
Explanation:
All numbers except 14 are odd numbers. 14 is an even number.
87. Find the next term in the series: 2, 5, 10, 17, 26, ?
Correct Answer: c) 37
Explanation:
The differences are 3, 5, 7, 9. The next difference is 11. 26 + 11 = 37. (Alternatively, n^2 + 1).
88. If 80% of A = 50% of B and B = x% of A, then the value of x is:
Correct Answer: c) 160
Explanation:
0.8A = 0.5B => B = (8/5)A = 1.6A. Since B = x% of A => x/100 = 1.6 => x = 160.
89. The L.C.M. of two numbers is 48. The numbers are in the ratio 2:3. The sum of the numbers is:
Correct Answer: c) 40
Explanation:
Let numbers be 2x and 3x. LCM of 2x and 3x is 6x. 6x = 48 => x = 8. Sum = 2x + 3x = 5x = 5(8) = 40.
90. Calculate the value of (1/2) + (1/4) + (1/8) + (1/16).
Correct Answer: a) 15/16
Explanation:
LCM is 16. (8/16) + (4/16) + (2/16) + (1/16) = 15/16.
91. Find the remainder when 4^96 is divided by 6.
Correct Answer: d) 4
Explanation:
Any power of 4, when divided by 6, always leaves a remainder of 4. (e.g., 4^1=4, 4^2=16 (rem 4)).
92. Which of the following numbers is completely divisible by 99?
Correct Answer: d) 114345
Explanation:
Divisible by 99 means divisible by 9 and 11. Sum of digits of 114345 is 18 (divisible by 9). Alt digits: (1+4+4) - (1+3+5) = 9 - 9 = 0 (divisible by 11).
93. If the radius of a circle is decreased by 50%, find the percentage decrease in its area.
Correct Answer: c) 75%
Explanation:
New radius = 0.5r. New area = pi*(0.5r)^2 = 0.25*pi*r^2. Area is 25% of original, so it decreased by 75%.
94. Find the probability of getting a sum of 9 when two dice are thrown simultaneously.
Correct Answer: a) 1/9
Explanation:
Favorable outcomes for sum 9 are (3,6), (4,5), (5,4), (6,3) = 4. Total outcomes = 36. Probability = 4/36 = 1/9.
95. Evaluate: cos 60 * cos 30 - sin 60 * sin 30
Correct Answer: a) 0
Explanation:
Using formula cos(A+B) = cos A cos B - sin A sin B. So, cos(60+30) = cos 90 = 0.
96. The diagonal of a rectangle is sqrt(41) cm and its area is 20 sq.cm. The perimeter of the rectangle must be:
Correct Answer: b) 18 cm
Explanation:
l^2 + b^2 = 41 and lb = 20. (l+b)^2 = l^2 + b^2 + 2lb = 41 + 40 = 81 => l+b = 9. Perimeter = 2(l+b) = 18 cm.
97. If the sum of interior angles of a regular polygon is 1080 degrees, the number of sides is:
Correct Answer: b) 8
Explanation:
(n-2) * 180 = 1080 => n-2 = 6 => n = 8.
98. The roots of the quadratic equation x^2 - 5x + 6 = 0 are:
Correct Answer: b) 2, 3
Explanation:
Factorizing x^2 - 5x + 6 = 0 gives (x-2)(x-3) = 0. Therefore, roots are 2 and 3.
99. What is the degree of the polynomial 4x^3 + 3x^2 - 7x + 9?
Correct Answer: c) 3
Explanation:
The degree of a polynomial is the highest power of the variable present in it, which is 3 here.
100. Which among the following is equivalent to a discount series of 10%, 20%, and 25%?
Correct Answer: b) 46%
Explanation:
Let MP = 100. Price after discounts = 100 * 0.9 * 0.8 * 0.75 = 54. Total discount = 100 - 54 = 46%.
101. The ratio of present ages of P and Q is 5:8. Three years later their ages will be in ratio 8:11. What is the present age of Q?
Correct Answer: b) 8
Explanation:
(5x + 3)/(8x + 3) = 8/11 => 55x + 33 = 64x + 24 => 9x = 9 => x = 1. Present age of Q = 8(1) = 8 years.
102. In a 100m race, A beats B by 20m or 5 seconds. Find A's speed.
Correct Answer: b) 5 m/s
Explanation:
B runs 20m in 5s. Speed of B = 4 m/s. B takes 100/4 = 25s for the full race. A takes 25 - 5 = 20s. Speed of A = 100/20 = 5 m/s.
103. Find the third proportional to 9 and 12.
Correct Answer: b) 16
Explanation:
Let third proportional be x. 9/12 = 12/x => 9x = 144 => x = 16.
104. A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
Correct Answer: d) 700 apples
Explanation:
Remaining = 60%. So, 60% of total = 420 => (60/100) * T = 420 => T = 700.
105. Calculate the surface area of a cube whose volume is 343 cubic cm.
Correct Answer: b) 294 sq cm
Explanation:
a^3 = 343 => a = 7 cm. Surface area = 6a^2 = 6 * 49 = 294 sq cm.
106. Find the sum of all two-digit numbers divisible by 5.
Correct Answer: a) 945
Explanation:
Sequence: 10, 15, ... 95. Number of terms, n = (95-10)/5 + 1 = 18. Sum = (n/2)*(a+l) = (18/2)*(10+95) = 9 * 105 = 945.
107. Solve: 2/3 of 1/4 of 4/5 of a number is 15. Find the number.
Correct Answer: b) 112.5
Explanation:
(2/3) * (1/4) * (4/5) = 8/60 = 2/15. (2/15) * N = 15 => N = (15 * 15) / 2 = 225 / 2 = 112.5.
108. What is the HCF of x^2 - y^2 and (x - y)^2?
Correct Answer: b) x - y
Explanation:
Factors of x^2 - y^2 are (x-y)(x+y). Factors of (x-y)^2 are (x-y)(x-y). Common factor is (x-y).
109. At what time between 4 and 5 o'clock will the hands of a clock be right angles?
Correct Answer: d) Both a and b
Explanation:
Formula: Angle = |30H - 5.5M|. 90 = |120 - 5.5M|. Gives M = 5 5/11 and M = 38 2/11.
110. A cylindrical wire of radius 0.5 mm is drawn from a piece of copper of radius 5 cm and length 2 cm. Find the length of the wire.
Correct Answer: a) 200 m
Explanation:
Volume remains constant. pi*(5)^2*2 = pi*(0.05)^2*L. 50 = 0.0025 * L => L = 20000 cm = 200 m.
111. In a class of 40 students, 20 play cricket, 15 play football and 5 play both. How many students play neither?
Correct Answer: b) 10
Explanation:
Total playing = n(C U F) = n(C) + n(F) - n(C intersect F) = 20 + 15 - 5 = 30. Playing neither = 40 - 30 = 10.
112. What is the simple interest on Rs. 4000 for 18 months at 12% per annum?
Correct Answer: b) Rs. 720
Explanation:
Time = 18 months = 1.5 years. SI = (4000 * 12 * 1.5) / 100 = 720.
113. If 15 pens cost Rs. 60, how much will 12 pens cost?
Correct Answer: c) Rs. 48
Explanation:
Cost of 1 pen = 60 / 15 = Rs. 4. Cost of 12 pens = 12 * 4 = Rs. 48.
114. The perimeter of a square is 48 cm. The area of a rectangle is 4 sq cm less than the area of the square. If the length of the rectangle is 14 cm, what is its breadth?
Correct Answer: b) 10 cm
Explanation:
Side of square = 48/4 = 12 cm. Area of square = 144 sq cm. Area of rect = 144 - 4 = 140. l*b = 140 => 14*b = 140 => b = 10.
115. Find the value of sqrt(12 + sqrt(12 + sqrt(12 + ...))) to infinity.
Correct Answer: b) 4
Explanation:
Let x = sqrt(12 + x). Then x^2 - x - 12 = 0. Solving gives x = 4 or -3. Since it's positive, x = 4.
116. By selling 33 meters of cloth, a person gains the selling price of 11 meters. Find his gain percent.
Correct Answer: c) 50%
Explanation:
Profit = SP of 33 - CP of 33 = SP of 11. => CP of 33 = SP of 22. Profit % = (11 / 22) * 100 = 50%.
117. A dishonest dealer claims to sell his goods at CP but uses a weight of 900g for 1 kg. His gain percentage is:
Correct Answer: b) 11.11%
Explanation:
Gain % = (Error / True Weight - Error) * 100. Gain % = (100 / 900) * 100 = 100/9 = 11.11%.
118. Find the missing number: 7, 26, 63, 124, 215, 342, ?
Correct Answer: d) 511
Explanation:
Pattern is n^3 - 1. 2^3-1=7, 3^3-1=26, 4^3-1=63... 8^3 - 1 = 512 - 1 = 511.
119. Evaluate 1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(99*100)
Correct Answer: b) 99/100
Explanation:
This is a telescoping series: (1/1 - 1/2) + (1/2 - 1/3) ... + (1/99 - 1/100) = 1 - 1/100 = 99/100.
120. If the length of a rectangle is increased by 30% and its breadth decreased by 20%, the area changes by:
Correct Answer: a) 4% increase
Explanation:
Effective change = x + y + (xy/100) = 30 - 20 + (30 * -20)/100 = 10 - 6 = +4%. Increase is 4%.
