Class 10 Mathematics questions for CBSE

Using Euclid's Division Lemma, what is the remainder when 20 is divided by 3?

What is the value of sin(30°)?

In the given right-angled triangle ABC, AB = 6 cm, BC = 8 cm and AC = 10 cm. What is sin A?

The quadratic equation x^2 - 6x + 9 = 0 has what kind of roots?

Solve the quadratic equation x^2 - 7x + 10 = 0 by factorization. What are the roots?

The roots of the equation x^2 + 4x + 4 = 0 are both equal. What does this imply about the nature of the roots?

For the polynomial p(x) = x^2 - 5x + 6, what is the relationship between the sum of the zeroes and the coefficients?

If a polynomial f(x) is divided by (x - 1) and gives a remainder of 5, what can be concluded about the polynomial?

A polynomial has zeroes at x = 2 and x = -3. What is the geometrical representation of these zeroes on the x-axis?

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?