Class 10 Mathematics questions for CBSE

A vertical pole of height 10 meters is standing on a level ground. From a point on the ground, the angle of elevation to the top of the pole is 30 degrees. Calculate the distance of the point from the base of the pole. Additionally, if a second pole of height 20 meters is standing at the same point where the first pole is, find the angle of elevation from the ground to the top of the second pole. Show all calculations clearly and explain the trigonometric ratios used in your solution.

A quadratic equation is given by the expression ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. Explain the different methods to solve a quadratic equation. Illustrate your explanation with an example for each method: factorization, completing the square, and using the quadratic formula. Discuss the nature of the roots based on the discriminant and provide an example with a discriminant value that indicates real and distinct roots, real and equal roots, and complex roots.

Solve the following pair of linear equations using the cross-multiplication method: 2x + 3y = 6 and 4x - y = 5.

If sin θ = 1/2, find the value of cos θ using trigonometric identities.

Find the 10th term of the arithmetic progression: 3, 7, 11, 15,...

Prove that the number √2 is an irrational number.

In two similar triangles, the ratio of their corresponding sides is 3:5. If the area of the smaller triangle is 27 cm², find the area of the larger triangle.

In the given triangle ABC, AB = 6 cm, BC = 8 cm and AC = 10 cm. Use the figure to verify that the triangle is right-angled.

What is the nature of the roots of the quadratic equation x² + 4x + 4 = 0?

Which of the following numbers is an irrational number?

Using the cross-multiplication method, what is the solution for the system of equations 2x + 3y = 6 and 4x - y = 5?

If the zeroes of the polynomial p(x) = x² - 5x + 6 are α and β, what is the value of α + β?

Which of the following is a trigonometric identity?

Which of the following criteria can be used to determine if two triangles are similar?

If the height of a tower is 20 meters and the angle of elevation from a point 30 meters away from the base is 30 degrees, what is the height of the tower?

In the given coordinate graph, what are the coordinates of point A?