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
- Determine the product of (3a + 2b) and (9a² – 6ab + 4b²).
- 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
- 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.
- If x = √2 + √3, find the value of x² – 10
- For what value of k will k + 9, 2k − 1 and 2k + 7 are the consecutive terms of an A.P.?
- The product of HCF and LCM of 60,84 and 108 is
- A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the cone and of the remaining solid left out after the cone carved out.
- What is the absolute value of -19?
- Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?
- Find the product: (x – 3y) (x + 3y) (x² + 9y²)
- Verify that (11pq + 4q)² – (11pq – 4q)² = 176pq²
- 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?
- A cube has a volume of 512 m³. Find its surface area.
- 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?
- For what value of k will the consecutive terms 2k + 1, 3k + 3 and 5k − 1 form an A.P.?
- 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.
- A kite-shaped field is made of two congruent right triangles with sides 13 m, 12 m, and 5 m. Find the total area of the field.
- Find a quadratic polynomial whose zeroes are 5 and −3.
- If a shopkeeper gives a discount of Rs.5 per item and a customer buys 20 items, what is the total discount?
- If the zeroes of the quadratic polynomial p(x) = ax² + bx + c are reciprocal of each other, prove that c = a.
- Factorize completely: a^4 – 4a²b² + 4b^4
- 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?
- A metal pipe is 77 cm long. The inner diameter of its cross-section is 4 cm and the outer diameter is 4.4 cm. What is its inner curved surface area?
- The LCM of 60, 84 and 108 is
- If (x – 1/x) = 4, then evaluate (x² + 1/x²) and (x⁴ + 1/x⁴).
- 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.
- If the 2nd term of an AP is 13 and the 5th term is 25, then its 7th term is
- Find the area of a quadrilateral field ABCD where angle C is 90 degrees, AB = 9 meters, BC = 12 meters, CD = 5 meters and AD = 8 meters.
- The value of 104 × 96 is
- How to convert fractions to decimals?