Class 10 Mathematics questions for CBSE

A student lists the first five terms of an arithmetic progression where the first term is 3 and the common difference is 5. What is the fourth term?

In a local community, two friends are trying to determine how many hours they will work together on a project. They have the equations 2x + 3y = 12 and 4x - y = 5, representing the hours they can contribute. Solve this pair of linear equations using the elimination method, and interpret the solution in the context of their work hours. Include all steps in your solution.

A park is designed such that a triangular flower bed is formed with vertices at points A(2, 3), B(8, 7), and C(5, y) where point C divides the line segment AB in the ratio 2:3. Calculate the value of y using the section formula. Then, find the area of triangle ABC using the coordinates of the vertices. Provide all necessary calculations and steps taken.

A farmer is planting a new crop in rows that form an arithmetic progression. The first row has 5 plants, and the number of plants in each subsequent row increases by 3. Calculate the number of plants in the 10th row and find the total number of plants from the first to the 10th row. Show your calculations and reasoning clearly.

A scientist is studying the growth of a certain plant species and has found that the height of the plant can be modeled by the quadratic equation h(x) = x^2 - 4x + 4, where h is the height in cm and x is the number of days since planting. Determine the nature of the roots of the quadratic equation and interpret what this means in the context of the plant's growth.

A gardener is planting flowers in a row. The gardener plans to plant a total of 30 flowers, with the first flower being planted 2 feet apart and each subsequent flower being planted 1 foot farther apart than the previous one. Determine the total distance covered by the flowers when planted in this arithmetic progression. Use the formula for the sum of the first n terms of an AP to find the answer.

During a construction project, an engineer needs to calculate the height of a building using trigonometric ratios. If the engineer stands 50 meters away from the building and measures the angle of elevation to the top of the building as 30 degrees, calculate the height of the building using the appropriate trigonometric ratios.

A local school is organizing a mathematics competition. The organizers need to determine how many students can participate based on the ratio of students to teachers. If there are 12 students for every 1 teacher, and there are 5 teachers available, how many students can participate in the competition? Formulate this situation as a pair of linear equations in two variables and solve it.

Using the Fundamental Theorem of Arithmetic, express the number 60 as a product of its prime factors.

If sin(θ) = 1/2, find the value of θ in degrees, knowing that θ lies in the first quadrant. Use trigonometric ratios.

A polynomial p(x) has its zeroes at x = 2 and x = -3. What is the geometrical meaning of these zeroes on the graph of the polynomial?

In a bag of colored balls, there are 3 red, 2 blue, and 5 green balls. What is the probability of picking a red ball from the bag?

On a graph, the lines represented by the equations 2x + 3y = 6 and 4x - y = 5 intersect at point P. Find the coordinates of point P using the graphical method.

A point A is located at (3, 4) and point B is at (7, 1). Calculate the distance between points A and B using the distance formula.

Find the 10th term of the arithmetic progression: 5, 10, 15, ...

If a bag contains 3 red and 2 blue balls, what is the probability of drawing a red ball?

Solve the quadratic equation x^2 - 5x + 6 = 0 by completing the square.

Calculate sin(30°) using trigonometric ratios.

prove root 3 is irrational

Using the division algorithm, what is the quotient when the polynomial 2x³ + 3x² - 2 is divided by x + 1?