Mathematics

Mathematics is the science of numbers, quantity, structure, space, and change. It plays a crucial role in our daily lives—from basic calculations to complex problem-solving in science, engineering, technology, and finance.

Often described as the "language of the universe," mathematics helps us understand patterns, formulate new conjectures, and build logical frameworks for solving real-world problems. Its branches include arithmetic, algebra, geometry, trigonometry, calculus, and statistics, each with unique applications and significance.

Mathematics nurtures reasoning, critical thinking, and analytical skills, making it a foundational subject in education and a powerful tool across disciplines.

List of Mathematics Topics
ProbabilityMath Essentials
Relations & FunctionsSurface Areas and Volumes
Arithmetic ProgressionPair of Linear Equations
Real NumbersPercentage
PolynomialsArea and Perimeter
Integer 

Question related to Mathematics

  1. If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) ∶ (4n + 27), then find the ratio of their 9th terms.
  2. If 1 + 4 + 7 + 10 + ⋯ + x = 287, find the value of x.
  3. What is the difference between mean, median, and mode?
  4. A car is moving at a speed of -60 km/h (backward). How much distance will it cover in 3 hours?
  5. What is the additive inverse of -25?
  6. A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
  7. The sum of two numbers is 137 and their difference is 43. Find the numbers.
  8. The diameter of a roller is 84 cm, and its length is 120 cm. It takes 500 complete revolutions to move once over and level a playground. What is the area of the playground in m²?
  9. Find the smallest number that is divisible by 6, 10, and 15, and leaves a remainder of 5 in each case.
  10. The students of a class are made to stand in rows. If 4 students are extra in a row, there would be 2 rows less. If 4 students are less in a row, there would be 4 rows more. Find the number of students in the class.
  11. If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is
  12. Evaluate: (-4) × (-3) × (-2).
  13. The length, breadth and height of a room is 5m, 4m and 3m. The cost of white washing its four walls at the rate of Rs. 7.50 per square meter is
  14. Find the value of x³ + y³ + z³ – 3xyz if x² + y² + z² = 83 and x + y + z = 15
  15. The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
  16. What is 0 divided by 0?
  17. Evaluate: (-20) + 18 - (-7).
  18. If p, q, r and s are in A.P. then r – q is
  19. Which term of the A.P. 3, 8, 13, 18, … is 78?
  20. Simplify: (-8) + 15 - (-6)
  21. The sum of first 16 terms of the AP: 10, 6, 2,… is
  22. Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3, respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9 separately.
  23. A hiker climbs 100 meters in 5 minutes. How much will he climb in 30 minutes?
  24. A child puts one five–rupee coin of her saving in the piggy bank on the first day. She increases her saving by one five–rupee coin daily. If the piggy bank can hold 190 coins of five rupees in all, find the number of days she can continue to put the five–rupee coins into it and find the total money she saved. Write your views on the habit of saving.
  25. What is the factorial of 100?
  26. In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students. Which value is shown in this question?
  27. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red ? (ii) not red?
  28. Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .
  29. If the sum of first 7 terms of an AP is 49 and that of first 17 terms is 289, find the sum of its first n terms.
  30. Find the zeroes of the polynomial: p(x) = x² − 7x + 10 and verify the relation between zeroes and coefficients.