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
- 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
- Find the zeroes of the polynomial: p(x) = x² − 7x + 10 and verify the relation between zeroes and coefficients.
- A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day
- If 1 + 4 + 7 + 10 + ⋯ + x = 287, find the value of x.
- Which term of the given AP : 3, 8, 13, 18, . . . ,is 78?
- Factorise: (a – b)³ + (b – c)³ + (c – a)³
- Simplify: (-8) + 15 - (-6)
- Find the 17th term from the end of the AP: 1, 6, 11, 16 ... ... 211, 216.
- A coin is tossed two times. Find the probability of getting at most one head.
- Using identities, evaluate 8.56 × 11.60
- Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish. What is the probability that the fish taken out is a male fish?
- If the zeroes of the quadratic polynomial p(x) = ax² + bx + c are reciprocal of each other, prove that c = a.
- Three cubes of a metal whose edges are in the ratio 3:4:5 are melted and converted into a single cube whose diagonal is 12 3 cm. Find the edges of the three cubes.
- Give an example of a monomial and a binomial having degrees of 82 and 99, respectively.
- Calculate the volume of a cuboidal box whose dimensions are 5x, 3x², and 7x^4.
- If a³ = 729, find the value of a².
- Find the cube root of 64 × 125 × 8 × 27
- If the 2nd term of an AP is 13 and the 5th term is 25, then its 7th term is
- If the cube of a number ends in 1, what will be the unit digit of the number?
- For what value of k will k + 9, 2k − 1 and 2k + 7 are the consecutive terms of an A.P.?
- A cube’s volume increases from 27 cm³ to 64 cm³. Find the percentage increase in its edge.
- A river 3 meters deep and 40 meters wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
- Find the cube root of the product of 64 and 125.
- At what rate will Rs 1,000 amount to Rs 1,250 in 5 years?
- 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.
- For what value of k will the consecutive terms 2k + 1, 3k + 3 and 5k − 1 form an A.P.?
- The number of multiples of 4 between 10 and 250 is:
- A die is thrown once. Find the probability of getting (i) a prime number; (ii) a number lying between 2 and 6; (iii) an odd number
- Subtract (-12) from 8.
- Find the smallest number that is divisible by 6, 10, and 15, and leaves a remainder of 5 in each case.