Mathematics questions and answers
Arithmetic, algebra, geometry, trigonometry, statistics and probability.
These are practice variations, many generated from templates and numeric inputs, not an official question bank. They remain outside search indexing until at least 100 independently reviewed questions across five chapters are available.
Questions and clear answers
01Algebra · foundation · Editorial previewSolve 2x + 5 = 17.+
Subtract 5 to get 2x = 12, then divide by 2: x = 6.
02Geometry · foundation · Editorial previewWhat is the Pythagorean theorem?+
For a right triangle, the squares of the two shorter sides sum to the square of the hypotenuse.
03Calculus · foundation · Editorial previewWhat is the derivative of x squared?+
By the power rule, the derivative of x squared with respect to x is 2x.
04Statistics · foundation · Editorial previewHow do you find the arithmetic mean?+
Add all observations and divide by the number of observations; for 2, 4 and 6 the mean is 4.
05Linear equations · advanced · Editorial previewIn mathematics — Linear equations: Solve 15x + 25 = 31795 for x.+
Subtract 25 and divide by 15: x = 2118.
06Arithmetic · foundation · Editorial previewIn mathematics — Arithmetic: A practice worksheet lists 2729 objects and then 57 more. How many objects are there in total?+
Add the two quantities: 2729 + 57 = 2786 objects in total.
07Percentages · foundation · Editorial previewIn mathematics — Percentages: A sample has 3370 units, of which 3340 meet the stated condition. What percentage meet it, rounded to two decimals?+
99.11% because 3340 ÷ 3370 × 100 = 99.11%.
08Averages · intermediate · Editorial previewIn mathematics — Averages: Four measurements are 3951, 3, 3963 and 15. What is their arithmetic mean?+
Sum = 7932; divide by 4 to get 1983.
09Geometry · foundation · Editorial previewIn mathematics — Geometry: A rectangular study space is 4562 m long and 35 m wide. Find its area.+
Area = length × width = 4562 × 35 = 159670 m².
10Pythagoras · advanced · Editorial previewIn mathematics — Pythagoras: A right triangle has perpendicular sides of 12 cm and 4 cm. Find the hypotenuse to three decimals.+
By Pythagoras, c = √(144 + 16) ≈ 12.649 cm.
11Probability · intermediate · Editorial previewIn mathematics — Probability: A bag contains 785 blue tokens and 40 red tokens. What is the probability of randomly drawing a red token?+
There are 825 tokens, so P(red) = 40/825 ≈ 0.0485.
12Quadratic equations · foundation · Editorial previewIn mathematics — Quadratic equations: Solve x² − 1409x + 18148 = 0.+
Factor as (x − 1396)(x − 13) = 0; x = 1396 or x = 13.
13Simple interest · foundation · Editorial previewIn mathematics — Simple interest: Calculate simple interest on ₹200700 at 2% per year for 5 years.+
SI = PRT/100 = 200700 × 2 × 5/100 = ₹20070.
14Ratios · intermediate · Editorial previewIn mathematics — Ratios: Split 23724 items between two groups in the ratio 2618:18. How many go to the first group?+
The total ratio is 2636 parts. First group = 23724 × 2618/2636 = 23562.
15Speed distance time · advanced · Editorial previewIn mathematics — Speed distance time: A vehicle travels at a constant 3229 km/h for 16 hours. How far does it travel?+
Distance = speed × time = 3229 × 16 = 51664 km.
16Trigonometry · foundation · Editorial previewIn mathematics — Trigonometry: In a right triangle, sides opposite and adjacent to angle θ are 69 cm and 36 cm. Find sin θ to 4 decimals.+
Hypotenuse = √(4761 + 1296) ≈ 77.8267 cm; sin θ = 69/hypotenuse ≈ 0.8866.
17Linear equations · intermediate · Editorial previewIn mathematics — Linear equations: Solve 7x + 55 = 31212 for x.+
Subtract 55 and divide by 7: x = 4451.
18Arithmetic · foundation · Editorial previewIn mathematics — Arithmetic: A practice worksheet lists 63 objects and then 28 more. How many objects are there in total?+
Add the two quantities: 63 + 28 = 91 objects in total.
This is an educational practice preview. Answers and board-specific alignment are undergoing editorial review; these are not official exam questions.