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.

Question related to Mathematics

  1. Sonu and Raj have to collect different kinds of leaves for a science project. They go to a park where Sonu collects 12 leaves and Raj collects x leaves. After some time, Sonu loses 3 leaves and Raj collects 2x more leaves. Write an algebraic expression to find the total number of leaves collected by both of them.
  2. What is the common difference of an arithmetic progression (A.P.) in which a₍₂₁₎ − a₍₇₎ = 84?
  3. The temperature dropped by 4°C every hour for 6 hours. How much did the temperature drop in total?
  4. A triangle has one side 17 cm, and the difference between the other two sides is 3 cm. If the perimeter is 42 cm, find the area.
  5. What is the additive inverse of -25?
  6. A thief runs with a uniform speed of 100 m/minute. After one minute a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief.
  7. The area of a rectangle is uv, where u is the length and v is the breadth. If the length is increased by 5 units and the breadth is decreased by 3 units, find the new area of the rectangle.
  8. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3:2. Find the area of the triangle.
  9. Subtract 5xy(x + y − 5) from x(6x² − 7y + 5) + xy(x + y)
  10. In a school there are two sections – section A and section B of class X. There are 32 students in section A and 36 students in section B. Determine the minimum number of books required for their class library so that they can be distributed equally among students of section A or section B.
  11. What must be added to the sum of (x² − 4x + 7) and (2x² + 5x − 9) to get 0?
  12. The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
  13. Express 0.666… in the form p/q.
  14. The side of a cube is doubled. How many times will its volume increase?
  15. Rahul borrowed Rs 5,000 at 12% simple interest per year. How much will he have to pay after 3 years?
  16. Rationalize the denominator: 1 / (√5 + √2).
  17. The product of HCF and LCM of 60,84 and 108 is
  18. Simplify: (-8) + 15 - (-6)
  19. 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.
  20. Find the value of x and y if x + y = 5xy and 3x + 2y = 13xy . Also, x ≠ 0 and y ≠ 0
  21. The sum of the cubes of two numbers is 189. If one number is twice the other, find both numbers.
  22. How long will Rs 1,500 take to become Rs 1,950 at 10% simple interest?
  23. Which of the following cannot be the probability of an event? (A) 2/3 (B) –1.5 (C) 15% (D) 0.7
  24. The temperature was -5°C in the morning and rose by 12°C by noon. What is the new temperature?
  25. What is 0 divided by 0?
  26. If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
  27. Find the cube root of 125 × 64
  28. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) the queen of diamonds
  29. Divide (-36) by 9.
  30. The simple interest on a sum for 4 years at 9% per annum is Rs 720. Find the principal.