RRB NTPC Maths Mock Test 2026: Topic-Wise Questions With Timer
Practise Mathematics with a 100-question bank covering the main RRB NTPC topics. Choose CBT-1 practice, CBT-2 practice, the complete bank, or one weak topic and check your score with negative marking.
Maths in RRB NTPC is not only about learning formulas. You also need to recognise the right method quickly and avoid small calculation mistakes. A chapter may feel easy during revision, but the real check comes when you solve it with a timer and negative marking.
This free RRB NTPC Maths Mock Test 2026 gives you both mixed and topic-wise practice. Start with one weak chapter if your basics are not clear. Once your accuracy becomes stable, move to the 30-question CBT-1 practice or the 35-question CBT-2 practice.
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100 RRB NTPC Maths Topic-Wise Questions
All questions and options are displayed directly on this page. First solve a question yourself, then open Show Answer and Solution to check the correct option, explanation and useful formula.
Number System and Divisibility
What is the least number that must be added to 7,643 to make it exactly divisible by 9?
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Correct Answer: A. 7
Explanation: The sum of the digits is 7 + 6 + 4 + 3 = 20. The next multiple of 9 after 20 is 27, so 27 - 20 = 7 must be added.
Formula or Shortcut: For divisibility by 9, the digit sum must be a multiple of 9.
What is the greatest four-digit number exactly divisible by 27?
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Correct Answer: D. 9,990
Explanation: 9,999 / 27 gives quotient 370 with a remainder. Therefore, the greatest four-digit multiple is 27 * 370 = 9,990.
Formula or Shortcut: Greatest required multiple = divisor * floor(largest limit / divisor).
What is the remainder when 2^50 is divided by 7?
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Correct Answer: A. 4
Explanation: Powers of 2 modulo 7 repeat as 2, 4, 1. Since 50 leaves remainder 2 when divided by 3, the required remainder is the second value in the cycle, which is 4.
Formula or Shortcut: Use the repeating remainder cycle: 2^1, 2^2, 2^3 = 2, 4, 1 (mod 7).
If the five-digit number 50x72 is divisible by 9, what is the value of x?
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Correct Answer: A. 4
Explanation: The known digits add to 5 + 0 + 7 + 2 = 14. For divisibility by 9, 14 + x must be 18, so x = 4.
Formula or Shortcut: Digit sum must be divisible by 9.
Two co-prime numbers have a product of 117. If one number is 9, what is the other number?
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Correct Answer: A. 13
Explanation: The other number is 117 / 9 = 13. Also, HCF(9, 13) = 1, so the numbers are co-prime.
Formula or Shortcut: For two numbers, product = first number * second number.
How many positive factors does 360 have?
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Correct Answer: A. 24
Explanation: 360 = 2^3 * 3^2 * 5^1. The number of factors is (3 + 1)(2 + 1)(1 + 1) = 4 * 3 * 2 = 24.
Formula or Shortcut: If N = p^a * q^b * r^c, number of factors = (a + 1)(b + 1)(c + 1).
What is the unit digit of 7^45?
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Correct Answer: A. 7
Explanation: The unit digits of powers of 7 repeat as 7, 9, 3, 1. Since 45 leaves remainder 1 when divided by 4, the unit digit is 7.
Formula or Shortcut: Use the four-term unit-digit cycle of 7.
What is the least three-digit number exactly divisible by 8, 12 and 15?
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Correct Answer: A. 120
Explanation: LCM(8, 12, 15) = 120. Since 120 is already a three-digit number, it is the least required number.
Formula or Shortcut: A number divisible by all given numbers must be a multiple of their LCM.
Simplification, BODMAS, Surds and Square Roots
Simplify: 48 / 6 * (5 + 3) - 7
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Correct Answer: A. 57
Explanation: First solve the bracket: 5 + 3 = 8. Then 48 / 6 = 8, 8 * 8 = 64, and 64 - 7 = 57.
Formula or Shortcut: Follow BODMAS; multiplication and division are solved from left to right.
Find sqrt(1,764).
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Correct Answer: A. 42
Explanation: 42 * 42 = 1,764, so sqrt(1,764) = 42.
Formula or Shortcut: Recognise nearby perfect squares: 40^2 = 1,600 and 42^2 = 1,764.
Find three-fourths of 64 plus two-fifths of 50.
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Correct Answer: A. 68
Explanation: (3/4) * 64 = 48 and (2/5) * 50 = 20. Their sum is 48 + 20 = 68.
Formula or Shortcut: 'Of' means multiplication.
Find sqrt(2,025) + cbrt(1,728).
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Correct Answer: C. 57
Explanation: sqrt(2,025) = 45 and cbrt(1,728) = 12. Therefore, the required sum is 45 + 12 = 57.
Formula or Shortcut: 45^2 = 2,025 and 12^3 = 1,728.
Simplify: 25% of 480 - three-eighths of 160
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Correct Answer: A. 60
Explanation: 25% of 480 = 120. Three-eighths of 160 = 60. Therefore, 120 - 60 = 60.
Formula or Shortcut: 25% = 1/4.
Simplify: (18^2 - 12^2) / (18 - 12)
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Correct Answer: A. 30
Explanation: Using a^2 - b^2 = (a - b)(a + b), the expression becomes 18 + 12 = 30.
Formula or Shortcut: (a^2 - b^2) / (a - b) = a + b.
Find sqrt(0.0081).
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Correct Answer: C. 0.09
Explanation: 0.09 * 0.09 = 0.0081. Therefore, sqrt(0.0081) = 0.09.
Formula or Shortcut: 81 has square root 9; place the decimal after counting pairs of decimal places.
Simplify: 2*sqrt(50) - sqrt(8)
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Correct Answer: A. 8*sqrt(2)
Explanation: sqrt(50) = 5*sqrt(2) and sqrt(8) = 2*sqrt(2). Therefore, 2*sqrt(50) - sqrt(8) = 10*sqrt(2) - 2*sqrt(2) = 8*sqrt(2).
Formula or Shortcut: Take perfect-square factors outside the radical.
Decimals, Fractions, LCM and HCF
Express 0.375 in its simplest fractional form.
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Correct Answer: C. 3/8
Explanation: 0.375 = 375/1,000. Dividing numerator and denominator by 125 gives 3/8.
Formula or Shortcut: Write the decimal over a power of 10, then reduce.
Find the HCF of 72, 120 and 168.
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Correct Answer: A. 24
Explanation: 72 = 2^3 * 3^2, 120 = 2^3 * 3 * 5 and 168 = 2^3 * 3 * 7. The common part is 2^3 * 3 = 24.
Formula or Shortcut: For HCF, take common prime factors with the smallest powers.
Find the LCM of 18, 24 and 30.
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Correct Answer: A. 360
Explanation: 18 = 2 * 3^2, 24 = 2^3 * 3 and 30 = 2 * 3 * 5. LCM = 2^3 * 3^2 * 5 = 360.
Formula or Shortcut: For LCM, take every prime factor with its highest power.
Which of the following fractions is the greatest?
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Correct Answer: D. 13/20
Explanation: Their decimal values are 0.625, about 0.583, about 0.611 and 0.65 respectively. Therefore, 13/20 is the greatest.
Formula or Shortcut: Compare fractions by cross multiplication or by converting them to decimals.
Simplify: 2.75 + 0.625 - 1.4
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Correct Answer: A. 1.975
Explanation: 2.75 + 0.625 = 3.375. Then 3.375 - 1.4 = 1.975.
Formula or Shortcut: Align decimal points before addition or subtraction.
Three bells ring at intervals of 18 seconds, 24 seconds and 30 seconds. If they ring together now, after how much time will they next ring together?
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Correct Answer: D. 6 minutes
Explanation: LCM(18, 24, 30) = 360 seconds. Since 360 seconds = 6 minutes, they will next ring together after 6 minutes.
Formula or Shortcut: Simultaneous repetition time = LCM of the intervals.
What is the smallest number greater than 20 that leaves remainder 7 when divided by 12, 15 and 20?
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Correct Answer: A. 67
Explanation: LCM(12, 15, 20) = 60. A number leaving remainder 7 is 60k + 7. The smallest such number greater than 20 is 60 + 7 = 67.
Formula or Shortcut: Required number = LCM * k + common remainder.
The HCF and LCM of two numbers are 12 and 720 respectively. If one number is 144, find the other number.
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Correct Answer: C. 60
Explanation: Product of the two numbers = HCF * LCM = 12 * 720. The other number is (12 * 720) / 144 = 60.
Formula or Shortcut: For two positive integers: first * second = HCF * LCM.
Ratio, Proportion and Partnership
The ratio of boys to girls in a class is 7:5. If the total number of students is 144, how many boys are there?
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Correct Answer: A. 84
Explanation: Total ratio parts = 7 + 5 = 12. Boys = (7/12) * 144 = 84.
Formula or Shortcut: Required share = required ratio part / total ratio parts * total.
Divide Rs. 840 in the ratio 3:4:5. What is the largest share?
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Correct Answer: D. Rs. 350
Explanation: Total parts = 3 + 4 + 5 = 12. The largest share is (5/12) * Rs. 840 = Rs. 350.
Formula or Shortcut: Largest share corresponds to the largest ratio part.
If A:B = 4:7 and B:C = 14:15, find A:B:C.
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Correct Answer: C. 8:14:15
Explanation: Make the B terms equal. Multiply 4:7 by 2 to get 8:14. Combining this with 14:15 gives A:B:C = 8:14:15.
Formula or Shortcut: Equalise the common term before combining two ratios.
The incomes of A and B are in the ratio 5:4 and their expenditures are in the ratio 3:2. If each saves Rs. 2,000 per month, what is A's monthly income?
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Correct Answer: C. Rs. 5,000
Explanation: Let incomes be 5x and 4x, and expenditures be 3y and 2y. Then 5x - 3y = 2,000 and 4x - 2y = 2,000. Subtracting gives x = y. Hence 2x = 2,000, so x = 1,000 and A's income is 5x = Rs. 5,000.
Formula or Shortcut: Form one saving equation for each person and solve simultaneously.
A invests Rs. 40,000 for 12 months and B invests Rs. 60,000 for 8 months. In what ratio should they divide the profit?
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Correct Answer: A. 1:1
Explanation: A's capital-time product is 40,000 * 12 = 4,80,000. B's is 60,000 * 8 = 4,80,000. Therefore, the profit ratio is 1:1.
Formula or Shortcut: Profit ratio = capital * time ratio.
On a map with scale 1:50,000, two stations are 3.6 cm apart. What is the actual distance?
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Correct Answer: A. 1.8 km
Explanation: Actual distance = 3.6 * 50,000 = 1,80,000 cm. Since 1,00,000 cm = 1 km, the distance is 1.8 km.
Formula or Shortcut: Actual distance = map distance * scale factor.
Find the fourth proportional to 6, 9 and 15.
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Correct Answer: A. 22.5
Explanation: Let the fourth proportional be x. Then 6:9 = 15:x, so 6x = 9 * 15 and x = 22.5.
Formula or Shortcut: If a:b = c:x, then x = bc/a.
Percentage
35% of a number is 154. What is the number?
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Correct Answer: C. 440
Explanation: Number = 154 * 100 / 35 = 440.
Formula or Shortcut: Whole = given part * 100 / percentage.
A salary is increased by 20% and then reduced by 10%. What is the net percentage change?
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Correct Answer: A. 8% increase
Explanation: Take the original salary as 100. After a 20% rise it becomes 120, and after a 10% reduction it becomes 108. The net change is an 8% increase.
Formula or Shortcut: Net change for +a% and -b% = a - b - ab/100.
A student scores 220 marks and fails by 20 marks. If the pass percentage is 40%, what are the maximum marks?
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Correct Answer: A. 600
Explanation: Pass marks = 220 + 20 = 240. If 240 is 40% of the maximum, maximum marks = 240 * 100 / 40 = 600.
Formula or Shortcut: Maximum marks = pass marks * 100 / pass percentage.
A town has a population of 50,000. It rises by 10% in one year and falls by 10% in the next. What is the final population?
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Correct Answer: C. 49,500
Explanation: After a 10% rise, population = 55,000. A 10% fall on 55,000 is 5,500, so the final population is 49,500.
Formula or Shortcut: Equal percentage rise and fall result in a net loss of a^2/100 percent.
A is 25% more than B. By what percentage is B less than A?
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Correct Answer: C. 20%
Explanation: Let B = 100, then A = 125. B is 25 less than A, so the percentage decrease with A as base is 25/125 * 100 = 20%.
Formula or Shortcut: If A is x% more than B, B is [x/(100 + x)] * 100% less than A.
The price of an item falls by 20%. By what percentage can its consumption be increased so that total expenditure remains unchanged?
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Correct Answer: A. 25%
Explanation: New price is 80% of the old price. Required consumption factor = 100/80 = 1.25, which means a 25% increase.
Formula or Shortcut: Required increase = reduction / (100 - reduction) * 100.
72% of a number is equal to 54% of 240. Find the number.
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Correct Answer: D. 180
Explanation: Let the number be x. Then 0.72x = 0.54 * 240 = 129.6. Hence x = 129.6 / 0.72 = 180.
Formula or Shortcut: Equate the two percentage expressions and isolate the unknown.
Profit, Loss and Discount
An article is bought for Rs. 800 and sold at a profit of 15%. Find its selling price.
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Correct Answer: C. Rs. 920
Explanation: Profit = 15% of Rs. 800 = Rs. 120. Selling price = Rs. 800 + Rs. 120 = Rs. 920.
Formula or Shortcut: SP = CP * (100 + profit%)/100.
The marked price of a bag is Rs. 1,500. If a discount of 12% is offered, what is its selling price?
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Correct Answer: D. Rs. 1,320
Explanation: Discount = 12% of Rs. 1,500 = Rs. 180. Selling price = Rs. 1,500 - Rs. 180 = Rs. 1,320.
Formula or Shortcut: SP = MP * (100 - discount%)/100.
An article is sold for Rs. 540 at a loss of 10%. Find its cost price.
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Correct Answer: D. Rs. 600
Explanation: Rs. 540 represents 90% of the cost price. Therefore, CP = 540 * 100 / 90 = Rs. 600.
Formula or Shortcut: CP = SP * 100/(100 - loss%).
Two articles are sold for Rs. 1,000 each. One is sold at a 20% gain and the other at a 20% loss. What is the overall result?
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Correct Answer: B. 4% loss
Explanation: First CP = 1,000/1.20 = Rs. 833.33; second CP = 1,000/0.80 = Rs. 1,250. Total CP = Rs. 2,083.33 and total SP = Rs. 2,000. The loss is Rs. 83.33, which is 4% of total CP.
Formula or Shortcut: For equal selling prices with equal gain and loss x%, overall loss = x^2/100%.
What single discount is equivalent to successive discounts of 10% and 20%?
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Correct Answer: B. 28%
Explanation: Equivalent discount = 10 + 20 - (10 * 20)/100 = 28%.
Formula or Shortcut: Successive discount = a + b - ab/100.
A shopkeeper charges the cost price of 1 kg but gives only 900 g. What is his profit percentage?
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Correct Answer: B. 11.11%
Explanation: Assume the cost of 1 kg is Rs. 100. The cost of 900 g is Rs. 90, but he charges Rs. 100. Profit = Rs. 10, so profit percentage = 10/90 * 100 = 11.11%.
Formula or Shortcut: With x% less weight, gain% = shortage / actual weight given * 100.
A trader marks an article 25% above its cost price and allows a 10% discount. What is the profit percentage?
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Correct Answer: D. 12.5%
Explanation: Let CP = Rs. 100. MP = Rs. 125. After a 10% discount, SP = Rs. 112.50. Profit = Rs. 12.50, so profit percentage = 12.5%.
Formula or Shortcut: SP factor = markup factor * discount factor.
Simple and Compound Interest
Find the simple interest on Rs. 5,000 at 8% per annum for 3 years.
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Correct Answer: D. Rs. 1,200
Explanation: SI = 5,000 * 8 * 3 / 100 = Rs. 1,200.
Formula or Shortcut: SI = PRT/100.
Find the amount on Rs. 10,000 at 10% compound interest per annum for 2 years.
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Correct Answer: D. Rs. 12,100
Explanation: Amount = 10,000 * (1.10)^2 = Rs. 12,100.
Formula or Shortcut: A = P(1 + r/100)^n.
Find the difference between compound interest and simple interest on Rs. 8,000 at 5% per annum for 2 years.
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Correct Answer: B. Rs. 20
Explanation: For 2 years, difference = P(r/100)^2 = 8,000 * (5/100)^2 = Rs. 20.
Formula or Shortcut: For 2 years, CI - SI = P(r/100)^2.
A sum earns Rs. 900 as simple interest at 7.5% per annum in 2 years. Find the principal.
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Correct Answer: D. Rs. 6,000
Explanation: P = SI * 100 / (R * T) = 900 * 100 / (7.5 * 2) = Rs. 6,000.
Formula or Shortcut: P = SI * 100/(R * T).
In how many years will a sum double at 12.5% per annum simple interest?
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Correct Answer: B. 8 years
Explanation: To double, the simple interest must equal the principal. Time = 100/R = 100/12.5 = 8 years.
Formula or Shortcut: At simple interest, doubling time = 100/rate.
A sum amounts to Rs. 13,310 in 3 years at 10% compound interest per annum. Find the principal.
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Correct Answer: D. Rs. 10,000
Explanation: P = 13,310 / (1.10)^3 = 13,310 / 1.331 = Rs. 10,000.
Formula or Shortcut: P = A/(1 + r/100)^n.
Average and Ages
The average of 8 numbers is 24. If the number 40 is added, what is the new average?
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Correct Answer: D. 25 7/9
Explanation: Sum of 8 numbers = 8 * 24 = 192. New sum = 192 + 40 = 232. New average = 232/9 = 25 7/9.
Formula or Shortcut: Average = total sum / number of observations.
The average age of 5 people is 32 years. A 44-year-old person is replaced by a 29-year-old person. What is the new average age?
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Correct Answer: B. 29 years
Explanation: The total age falls by 44 - 29 = 15 years. Average falls by 15/5 = 3 years. New average = 32 - 3 = 29 years.
Formula or Shortcut: Change in average = change in total / number of observations.
What is the average of the first 10 natural numbers?
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Correct Answer: B. 5.5
Explanation: The first 10 natural numbers run from 1 to 10. Their average is (1 + 10)/2 = 5.5.
Formula or Shortcut: Average of consecutive equally spaced numbers = (first + last)/2.
A batsman has an average of 48 runs after 12 innings. How many runs must he score in the 13th innings to raise the average to 50?
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Correct Answer: D. 74
Explanation: Current runs = 12 * 48 = 576. Required total after 13 innings = 13 * 50 = 650. Required score = 650 - 576 = 74.
Formula or Shortcut: Required next value = new required total - current total.
The present ages of a father and son are in the ratio 5:2. After 8 years, their ages will be in the ratio 2:1. What is the sum of their present ages?
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Correct Answer: D. 56 years
Explanation: Let present ages be 5x and 2x. Then (5x + 8)/(2x + 8) = 2. So 5x + 8 = 4x + 16, giving x = 8. Sum = 7x = 56 years.
Formula or Shortcut: Add the same number of years to both present ages before forming the future ratio.
The average of 20 observations was calculated as 35. Later, 48 was found to have been entered as 84. What is the correct average?
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Correct Answer: D. 33.2
Explanation: Wrong total = 20 * 35 = 700. Correct total = 700 - 84 + 48 = 664. Correct average = 664/20 = 33.2.
Formula or Shortcut: Correct total = wrong total - wrong entry + correct entry.
Time and Work, Pipes and Cisterns
A can finish a job in 12 days and B in 18 days. In how many days can they finish it together?
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Correct Answer: B. 7 1/5 days
Explanation: Combined rate = 1/12 + 1/18 = 5/36 job per day. Time = 36/5 = 7 1/5 days.
Formula or Shortcut: Together time = ab/(a + b) when both work positively.
A can complete a job in 15 days. After A works alone for 5 days, B completes the remaining work in 8 days. In how many days can B alone complete the full job?
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Correct Answer: B. 12 days
Explanation: A completes 5/15 = 1/3 of the job. Remaining work = 2/3. If B completes 2/3 in 8 days, B's daily work is 1/12. Therefore, B alone needs 12 days.
Formula or Shortcut: Individual rate = work completed / time taken.
Twelve men can complete a job in 18 days. How many days will 27 men take, if all work at the same rate?
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Correct Answer: B. 8 days
Explanation: Total work = 12 * 18 = 216 man-days. Required days = 216/27 = 8.
Formula or Shortcut: For fixed work, men * days remains constant.
A is twice as efficient as B. Working together, they finish a job in 18 days. In how many days can A alone finish it?
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Correct Answer: B. 27 days
Explanation: Let B's rate be x and A's rate be 2x. Then 3x = 1/18, so x = 1/54. A's rate is 1/27, so A alone takes 27 days.
Formula or Shortcut: Efficiency is directly proportional to work rate and inversely proportional to time.
A pipe fills a tank in 20 minutes, while an outlet empties it in 30 minutes. If both are opened together, how long will the empty tank take to fill?
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Correct Answer: D. 60 minutes
Explanation: Net rate = 1/20 - 1/30 = 1/60 tank per minute. Hence the tank fills in 60 minutes.
Formula or Shortcut: Net rate = inlet rate - outlet rate.
Two pipes can fill a tank in 12 hours and 15 hours. If both run for 3 hours, what fraction of the tank remains empty?
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Correct Answer: B. 11/20
Explanation: Combined hourly rate = 1/12 + 1/15 = 3/20. In 3 hours they fill 9/20. Therefore, the empty fraction is 1 - 9/20 = 11/20.
Formula or Shortcut: Remaining fraction = 1 - combined rate * time.
Eight workers working 6 hours per day complete a job in 15 days. How many days will 12 workers working 5 hours per day take?
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Correct Answer: D. 12 days
Explanation: Total work units = 8 * 6 * 15 = 720. Required days = 720 / (12 * 5) = 12.
Formula or Shortcut: Workers * hours per day * days = constant for the same work.
Time, Speed and Distance, Trains and Boats
How much time will a car take to cover 180 km at 60 km/h?
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Correct Answer: D. 3 hours
Explanation: Time = distance / speed = 180/60 = 3 hours.
Formula or Shortcut: Time = Distance/Speed.
If a person increases speed by 25%, by what percentage does the time taken for the same distance decrease?
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Correct Answer: B. 20%
Explanation: New speed factor = 1.25. New time factor = 1/1.25 = 0.8. Therefore, time decreases by 20%.
Formula or Shortcut: For a fixed distance, speed and time are inversely proportional.
A 180 m long train crosses a pole in 12 seconds. Find its speed in km/h.
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Correct Answer: D. 54 km/h
Explanation: Speed = 180/12 = 15 m/s. Converting to km/h: 15 * 18/5 = 54 km/h.
Formula or Shortcut: To convert m/s to km/h, multiply by 18/5.
A 150 m long train crosses a 250 m platform in 20 seconds. What is the train's speed?
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Correct Answer: D. 72 km/h
Explanation: Total distance = 150 + 250 = 400 m. Speed = 400/20 = 20 m/s = 20 * 18/5 = 72 km/h.
Formula or Shortcut: While crossing a platform, distance = train length + platform length.
A person travels 120 km at 40 km/h and returns the same distance at 60 km/h. What is the average speed for the whole trip?
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Correct Answer: B. 48 km/h
Explanation: For equal distances, average speed = 2ab/(a + b) = 2 * 40 * 60/100 = 48 km/h.
Formula or Shortcut: For equal distances at speeds a and b, average speed = 2ab/(a + b).
A boat moves at 18 km/h downstream and 10 km/h upstream. Find the speed of the stream.
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Correct Answer: B. 4 km/h
Explanation: Stream speed = (downstream speed - upstream speed)/2 = (18 - 10)/2 = 4 km/h.
Formula or Shortcut: Stream speed = (D - U)/2.
Two trains 120 m and 180 m long move in opposite directions at 54 km/h and 36 km/h. How long will they take to cross each other?
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Correct Answer: B. 12 seconds
Explanation: Relative speed = 54 + 36 = 90 km/h = 25 m/s. Total length = 300 m. Time = 300/25 = 12 seconds.
Formula or Shortcut: Opposite-direction relative speed is the sum of speeds.
Walking at 5 km/h, a man reaches office 24 minutes late. Walking at 6 km/h, he reaches 6 minutes early. What is the distance to the office?
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Correct Answer: B. 15 km
Explanation: The difference in travel time is 30 minutes = 1/2 hour. If distance is d, then d/5 - d/6 = d/30 = 1/2. Hence d = 15 km.
Formula or Shortcut: Difference in travel times = distance * (1/slower speed - 1/faster speed).
Mensuration 2D and 3D
Find the perimeter of a rectangle whose length is 18 cm and breadth is 12 cm.
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Correct Answer: D. 60 cm
Explanation: Perimeter = 2(l + b) = 2(18 + 12) = 60 cm.
Formula or Shortcut: Rectangle perimeter = 2(length + breadth).
Using pi = 22/7, find the area of a circle of radius 7 cm.
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Correct Answer: B. 154 cm^2
Explanation: Area = pi*r^2 = 22/7 * 7 * 7 = 154 cm^2.
Formula or Shortcut: Circle area = pi*r^2.
Find the area of a triangle with base 20 cm and height 13 cm.
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Correct Answer: D. 130 cm^2
Explanation: Area = 1/2 * base * height = 1/2 * 20 * 13 = 130 cm^2.
Formula or Shortcut: Triangle area = 1/2 * base * perpendicular height.
The diagonal of a square is 14*sqrt(2) cm. Find its area.
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Correct Answer: D. 196 cm^2
Explanation: For a square, diagonal = side * sqrt(2). Therefore, side = 14 cm and area = 14^2 = 196 cm^2.
Formula or Shortcut: Square area = diagonal^2/2.
Find the volume of a cube whose edge is 6 cm.
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Correct Answer: C. 216 cm^3
Explanation: Volume = edge^3 = 6^3 = 216 cm^3.
Formula or Shortcut: Cube volume = a^3.
Using pi = 22/7, find the volume of a cylinder with radius 7 cm and height 10 cm.
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Correct Answer: C. 1,540 cm^3
Explanation: Volume = pi*r^2*h = 22/7 * 7 * 7 * 10 = 1,540 cm^3.
Formula or Shortcut: Cylinder volume = pi*r^2*h.
A floor is 12 m long and 8 m wide. How many square tiles of side 40 cm are needed to cover it completely?
Show Answer and Solution
Correct Answer: C. 600
Explanation: Floor area = 12 * 8 = 96 m^2. Tile side = 0.4 m, so tile area = 0.16 m^2. Number of tiles = 96/0.16 = 600.
Formula or Shortcut: Number of tiles = floor area / area of one tile, using the same units.
Using pi = 22/7, find the curved surface area of a cone with radius 7 cm and slant height 25 cm.
Show Answer and Solution
Correct Answer: D. 550 cm^2
Explanation: Curved surface area = pi*r*l = 22/7 * 7 * 25 = 550 cm^2.
Formula or Shortcut: Cone curved surface area = pi*r*l.
Elementary Algebra
Solve: 3x - 7 = 20
Show Answer and Solution
Correct Answer: C. 9
Explanation: 3x = 20 + 7 = 27, so x = 9.
Formula or Shortcut: Move the constant to the other side, then divide by the coefficient.
If x + y = 12 and xy = 35, find x^2 + y^2.
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Correct Answer: C. 74
Explanation: x^2 + y^2 = (x + y)^2 - 2xy = 12^2 - 70 = 74.
Formula or Shortcut: x^2 + y^2 = (x + y)^2 - 2xy.
What are the roots of x^2 - 9x + 20 = 0?
Show Answer and Solution
Correct Answer: C. 4 and 5
Explanation: x^2 - 9x + 20 = (x - 4)(x - 5). Therefore, the roots are 4 and 5.
Formula or Shortcut: Find two numbers whose product is 20 and sum is 9.
If a - b = 5 and ab = 14, find a^2 + b^2.
Show Answer and Solution
Correct Answer: C. 53
Explanation: (a - b)^2 = a^2 + b^2 - 2ab. Hence a^2 + b^2 = 25 + 28 = 53.
Formula or Shortcut: a^2 + b^2 = (a - b)^2 + 2ab.
If 2x + 3y = 17 and x - y = 1, find x.
Show Answer and Solution
Correct Answer: B. 4
Explanation: From x - y = 1, x = y + 1. Substituting gives 2(y + 1) + 3y = 17, so 5y = 15 and y = 3. Hence x = 4.
Formula or Shortcut: Use substitution to reduce two equations to one variable.
Which expression is equal to x^2 - 16?
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Correct Answer: B. (x - 4)(x + 4)
Explanation: x^2 - 16 = x^2 - 4^2 = (x - 4)(x + 4).
Formula or Shortcut: a^2 - b^2 = (a - b)(a + b).
Geometry and Trigonometry
The angles of a triangle are in the ratio 2:3:4. Find the largest angle.
Show Answer and Solution
Correct Answer: C. 80 degrees
Explanation: Total ratio parts = 9. One part = 180 degrees/9 = 20 degrees. The largest angle = 4 * 20 degrees = 80 degrees.
Formula or Shortcut: The sum of the interior angles of a triangle is 180 degrees.
An exterior angle of a triangle is 110 degrees. If one of its opposite interior angles is 45 degrees, find the other opposite interior angle.
Show Answer and Solution
Correct Answer: C. 65 degrees
Explanation: An exterior angle equals the sum of the two opposite interior angles. Therefore, the other angle = 110 degrees - 45 degrees = 65 degrees.
Formula or Shortcut: Exterior angle = sum of the two remote interior angles.
What is the sum of the interior angles of a pentagon?
Show Answer and Solution
Correct Answer: C. 540 degrees
Explanation: For n = 5, sum = (n - 2) * 180 degrees = 3 * 180 degrees = 540 degrees.
Formula or Shortcut: Interior-angle sum of an n-sided polygon = (n - 2) * 180 degrees.
A right-angled triangle has perpendicular sides of 9 cm and 12 cm. Find its hypotenuse.
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Correct Answer: C. 15 cm
Explanation: Hypotenuse = sqrt(9^2 + 12^2) = sqrt(225) = 15 cm.
Formula or Shortcut: In a right triangle, h^2 = p^2 + b^2.
What is the value of sin 30 degrees?
Show Answer and Solution
Correct Answer: A. 1/2
Explanation: The standard trigonometric value of sin 30 degrees is 1/2.
Formula or Shortcut: Remember standard values at 0 degrees, 30 degrees, 45 degrees, 60 degrees and 90 degrees.
What is the value of tan 45 degrees?
Show Answer and Solution
Correct Answer: C. 1
Explanation: At 45 degrees, the perpendicular and base of the reference right triangle are equal, so tan 45 degrees = 1.
Formula or Shortcut: tan theta = perpendicular/base.
If cos theta = 12/13 and theta is acute, find sin theta.
Show Answer and Solution
Correct Answer: B. 5/13
Explanation: Using sin^2(theta) + cos^2(theta) = 1, sin theta = sqrt(1 - 144/169) = sqrt(25/169) = 5/13.
Formula or Shortcut: sin^2(theta) + cos^2(theta) = 1.
The shadow of a vertical pole is 10*sqrt(3) m long when the angle of elevation of the sun is 30 degrees. Find the pole's height.
Show Answer and Solution
Correct Answer: B. 10 m
Explanation: tan 30 degrees = height/shadow. Therefore, height = 10*sqrt(3) * 1/sqrt(3) = 10 m.
Formula or Shortcut: tan theta = height/horizontal distance.
Elementary Statistics and Data Interpretation
Find the mean of 6, 8, 10, 12 and 14.
Show Answer and Solution
Correct Answer: B. 10
Explanation: Sum = 6 + 8 + 10 + 12 + 14 = 50. Mean = 50/5 = 10.
Formula or Shortcut: Mean = sum of observations / number of observations.
Find the median of 3, 5, 7, 9, 11 and 13.
Show Answer and Solution
Correct Answer: B. 8
Explanation: There are six ordered observations. Median = average of the third and fourth values = (7 + 9)/2 = 8.
Formula or Shortcut: For an even number of observations, median is the mean of the two middle values.
Find the mode of 4, 6, 6, 7, 8, 6 and 9.
Show Answer and Solution
Correct Answer: B. 6
Explanation: The number 6 occurs three times, more often than any other value. Therefore, the mode is 6.
Formula or Shortcut: Mode is the observation with the highest frequency.
A shop sold 120 units in January and 150 units in February. If the average monthly sale for January, February and March was 150 units, how many units were sold in March?
Show Answer and Solution
Correct Answer: C. 180
Explanation: Required three-month total = 150 * 3 = 450. March sale = 450 - 120 - 150 = 180 units.
Formula or Shortcut: Missing observation = required total - sum of known observations.
In a pie chart representing 500 students, a sector of 72 degrees represents students choosing Mathematics. How many students chose Mathematics?
Show Answer and Solution
Correct Answer: C. 100
Explanation: Students = 72/360 * 500 = 100.
Formula or Shortcut: Category value = sector angle/360 degrees * total.
In a test, students A, B, C and D scored 48, 62, 55 and 75 marks respectively. By what percentage is D's score more than A's score?
Show Answer and Solution
Correct Answer: C. 56.25%
Explanation: Difference = 75 - 48 = 27. Percentage more than A = 27/48 * 100 = 56.25%.
Formula or Shortcut: Percentage increase = increase/original value * 100.
What Is the RRB NTPC Maths Mock Test 2026?
This is an independent Mathematics practice tool for RRB NTPC Graduate and Undergraduate aspirants. It has 100 original questions built around the broad topics listed in the RRB syllabus, including Number System, Ratio and Proportion, Percentage, Mensuration, Time and Work, Time and Distance, Interest, Profit and Loss, Algebra, Geometry, Trigonometry and Statistics.
The complete bank is larger than the Mathematics part of one actual CBT. That is intentional. You can use the same page for daily chapter practice and for timed mixed tests. The CBT-1 mode selects 30 random questions, while the CBT-2 mode selects 35. If one topic is creating problems, choose Topic-Wise Test and work only on that section.
How to Use This Topic-Wise Test
Do not begin with the longest mode just because it has more questions. Choose the mode according to your present preparation.
- Learning stage: select one topic and solve it without rushing. Read every explanation after submission.
- Practice stage: choose CBT-1 Maths Practice and try to keep both your attempt rate and accuracy under control.
- Advanced stage: use CBT-2 Maths Practice or the complete question bank to test longer concentration.
- After the test: filter incorrect and unattempted questions. Note the formula or method you missed.
Use one notebook as an error log. Write the question ID, topic, reason for the mistake and the correct method. Revising this small notebook is usually more useful than attempting new random questions every day without checking old errors.
RRB NTPC CBT-1 and CBT-2 Exam Pattern
| Stage | General Awareness | Mathematics | Reasoning | Total | Full-test time |
|---|---|---|---|---|---|
| CBT-1 | 40 | 30 | 30 | 100 questions | 90 minutes |
| CBT-2 | 50 | 35 | 35 | 120 questions | 90 minutes |
Each question carries 1 mark and one-third mark is deducted for an incorrect answer. The section-wise question distribution is described as indicative in the notice, so students should always check the notification for their own recruitment cycle. The actual examination has one overall timer. The 30-minute and 35-minute timers used here are only for focused Mathematics practice.
Topics Covered in This Maths Question Bank
The bank is divided into 14 useful groups. Some closely connected chapters are kept together so you can revise them in one sitting.
| Topic group | Questions | Main areas |
|---|---|---|
| Number System and Divisibility | 8 | Remainders, factors, unit digit and divisibility |
| Simplification and Roots | 8 | BODMAS, square roots, cube roots and surds |
| Fractions, LCM and HCF | 8 | Decimals, common multiples and common factors |
| Ratio and Percentage group | 14 | Ratio, proportion, partnership and percentage change |
| Commercial Mathematics | 13 | Profit, loss, discount, simple and compound interest |
| Average and Work group | 13 | Averages, ages, time and work, pipes |
| Speed and Mensuration group | 16 | Trains, boats, 2D and 3D mensuration |
| Algebra, Geometry and Statistics | 20 | Equations, identities, trigonometry, mean and data questions |
How Negative Marking Changes Your Score
In RRB NTPC, three wrong answers together remove one mark. Suppose you attempt 25 questions and get 19 correct and 6 wrong. Your net score will be 19 - (6 / 3) = 17 marks. Attempting all questions without checking accuracy can therefore reduce a decent score.
Do not treat this as a reason to leave every doubtful question. Instead, use elimination properly. If you can remove two options and solve the remaining choice logically, an attempt may be reasonable. If you have no method and are only guessing, leave the question and use the saved time on a question you can solve.
How to Analyse Your Mock-Test Result
First check accuracy, then check speed. A fast test with many wrong answers is not a strong result. Similarly, very high accuracy with only a few attempted questions shows that speed and question selection still need work.
- Accuracy below 55%: return to concepts and solve easier examples before another timed test.
- Accuracy from 55% to 69%: identify two weak chapters and practise them separately.
- Accuracy from 70% to 84%: your base is useful; now reduce calculation time and repeated errors.
- Accuracy of 85% or more: keep the same accuracy while gradually increasing the number of attempts.
These ranges are only practice feedback. They are not RRB cutoffs. Actual cutoffs change with the post, category, zone, paper level, vacancies and normalisation.
Seven-Day RRB NTPC Maths Improvement Plan
Day 1: Number System and Simplification
Revision: divisibility, remainders, BODMAS, fractions, LCM and HCF.
Practice: 25 mixed questions. Revise factor-count and remainder rules, then log every calculation error.
Day 2: Ratio, Percentage and Average
Revision: ratio conversion, percentage change and weighted thinking.
Practice: 25 questions. Write successive-change and average formulas on one page. Rework wrong base-value questions.
Day 3: Profit, Loss and Interest
Revision: cost price, selling price, discount, SI and CI.
Practice: 20 questions plus five calculation drills. Mark where you confused the base amount.
Day 4: Time and Work
Revision: work rates, efficiency, men-days and inlet-outlet signs.
Practice: 20 questions. Write each worker's one-day work before using a shortcut.
Day 5: Speed, Trains and Boats
Revision: unit conversion, relative speed, average speed and upstream-downstream formulas.
Practice: 25 questions. Record every m/s to km/h conversion mistake.
Day 6: Mensuration, Algebra and Geometry
Revision: 2D/3D formulas, identities, triangle rules and standard trigonometric values.
Practice: 25 questions. Redraw any geometry question you could not visualise.
Day 7: Statistics and Mixed Test
Revision: mean, median, mode and basic data interpretation.
Practice: take one 30-question mixed test. Spend the final 30 minutes updating and revising your error log.
Common RRB NTPC Maths Mistakes
- Using the wrong base while calculating percentage increase, loss or discount.
- Forgetting to convert km/h into m/s in train questions.
- Adding an outlet rate instead of subtracting it in a pipes question.
- Using a simple average when distances are equal but speeds are different.
- Reading "marked price" as "cost price."
- Starting a long calculation before checking whether options allow a shorter method.
- Attempting every doubtful question even when one-third negative marking applies.
Keep one main source for concepts and use mock tests for checking application. Watching more lectures will not automatically improve your score if you do not solve questions and review mistakes.
Frequently Asked Questions
1. Is this RRB NTPC Maths mock test free?
Yes. The complete question bank, timer, scoring, topic analysis and solutions on this page are free to use.
2. How many Mathematics questions are asked in RRB NTPC CBT-1?
The indicative CBT-1 pattern contains 30 Mathematics questions out of 100 total questions.
3. How many Mathematics questions are asked in RRB NTPC CBT-2?
The indicative CBT-2 pattern contains 35 Mathematics questions out of 120 total questions.
4. Is there negative marking in RRB NTPC?
Yes. One-third of a mark is deducted for every incorrect answer in the CBTs covered by the cited notices.
5. Is the timer in this Maths test an official sectional timer?
No. RRB provides an overall test duration. The timers used here are custom practice timers for Mathematics.
6. Can I practise only one Mathematics topic?
Yes. Select Topic-Wise Test, choose one of the available topic groups and start the test.
7. Are these official previous-year questions?
No. These are original RRB NTPC-level practice questions based on the syllabus pattern, not an official RRB question paper.
8. Will my test progress remain saved after refreshing the page?
The active attempt is saved in local storage on the same browser when that storage is available. You can then choose Resume Test after a refresh.
Build Accuracy Before Chasing Speed
Choose one primary method for every chapter, make a small formula notebook and solve questions with a pen instead of only reading solutions. Start with topic tests, then move to a mixed RRB NTPC Maths mock test when you can solve basic questions without checking notes.
After every attempt, retry the incorrect and unattempted questions from the result page. Your goal is not to complete the largest number of mocks. Your goal is to stop repeating the same mistake in the next mock.
