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
- α and β are zeroes of the quadratic polynomial x² – 6x + y. Find the value of ‘y’ if 3α + 2β = 20
- If the product of zeroes of the polynomial p(x)=3x² + kx − 2 is 2/3 , find the value of k.
- The sum of first 16 terms of the AP: 10, 6, 2,… is
- Solve: 45 + (-18) - (-12).
- An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
- Give an example of a monomial and a binomial having degrees of 82 and 99, respectively.
- Without actual division, prove that 2x^4 – 5x^3 + 2x^2 – x + 2 is divisible by x^2 – 3x + 2.
- A cube has a volume of 512 m³. Find its surface area.
- 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.
- Find the smallest number that when divided by 12, 16, and 24 leaves a remainder of 4 in each case.
- Evaluate: (-20) + 18 - (-7).
- Determine the area of an isosceles triangle with a perimeter of 30 cm and equal sides measuring 12 cm each.
- Reshma wanted to save at least ₹ 6,500 for sending her daughter to school next year (after 12 months). She saved ₹ 450 in the first month and raised her saving by ₹ 20 every next month. How much will she be able to save in next 12 months? Will she be able to send her daughter to the school next year? What value is reflected in this question?
- Find the value of "p" from the polynomial x² + 3x + p, if one of the zeroes of the polynomial is 2.
- Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is less than 9.
- Simplify: (p + q)² – (p – q)²
- A ladder has rungs placed at equal distances. If the first rung is at 15 cm and the last at 120 cm, with 10 rungs, find the distance between two consecutive rungs.
- When 33 is divided by which number the quotient will be 55?
- Ramkali required ₹ 2500 after 12 weeks to send her daughter to school. She saved ₹ 100 in the first week and increased her weekly saving by ₹ 20 every week. Find whether she will be able to send her daughter to school after 12 weeks. What value is generated in the above situation?
- 9² ÷ 9 × 9 + 9 = ?
- Complete the following statements: (i) Probability of an event E + Probability of the event ‘not E’ = ________ . (ii) The probability of an event that cannot happen is ________. Such an event is called ___________. (iii) The probability of an event that is certain to happen is . Such an event is called __________. (iv) The sum of the probabilities of all the elementary events of an experiment is _________. (v) The probability of an event is greater than or equal to _________ and less than or equal to _________.
- Find the sum: (-6) + (-15) + 10.
- 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?
- A two-digit number is 4 more than 6 times the sum of its digit. If 18 is subtracted from the number, the digits are reversed. Find the number.
- Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is (i) 6 (ii) 12 (iii) 7
- The sum of the cubes of two numbers is 189. If one number is twice the other, find both numbers.
- If the sum of two integers is -14 and one integer is -9, find the other integer.
- A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 , and these are equally likely outcomes. What is the probability that it will point at (i) 8 ? (ii) an odd number? (iii) a number greater than 2? (iv) a number less than 9?
- Find the value of 9x² + 4y² if xy = 6 and 3x + 2y = 12.
- A coin is tossed two times. Find the probability of getting at most one head.