Class 10 Mathematics questions for CBSE

For the quadratic equation x^2 - 5x + 6 = 0, which of the following describes the nature of its roots?

A tree casts a shadow of 15 meters when the angle of elevation of the sun is 45 degrees. How tall is the tree?

A ladder is leaning against a wall, making an angle of 60 degrees with the ground. If the foot of the ladder is 4 meters away from the wall, what is the height at which the ladder touches the wall?

In a right triangle, if the angle A is 30 degrees, what is the value of sin A?

Consider two complementary angles A and B. If the sine of angle A is 0.6, compute the cosine of angle B using the relationship between the trigonometric ratios of complementary angles. Additionally, explore the implications of this relationship by calculating the values of sine and cosine for specific angles and discussing how this might apply in real-world scenarios such as engineering or physics.

In a school project, two students are tasked with creating similar triangles using a scale of 1:2. They constructed a triangle with sides of lengths 3 cm, 4 cm, and 5 cm, creating a similar triangle by doubling the lengths of its sides. Explain the criteria for similarity of triangles and demonstrate how the areas of these two triangles relate to each other. Calculate the area of both triangles and discuss the proportional relationship between their areas based on their similarity.

A tower stands vertically on the ground. From a point 50 meters away from the base of the tower, the angle of elevation to the top of the tower is measured to be 30 degrees. Calculate the height of the tower using the concept of heights and distances. Additionally, if a second observer stands 70 meters away from the base of the tower, determine the angle of elevation for this observer. Analyze how the distance from the tower affects the angle of elevation and the overall height calculation.

From a point P, which is 8 cm away from the center O of a circle, determine the number of tangents that can be drawn to the circle with radius 5 cm. Justify your answer with the appropriate geometric principles and calculations.

In a triangle ABC, if the lengths of sides AB and AC are 6 cm and 9 cm respectively, and the angle A is 60 degrees, verify if triangle ABC is similar to triangle DEF with sides DE = 3 cm, DF = 4.5 cm, and angle D = 60 degrees. Provide the reasoning and calculations behind your conclusion.

A person standing 50 meters away from a tree observes the angle of elevation to the top of the tree as 30 degrees. Calculate the height of the tree using trigonometric concepts. Provide the necessary calculations and any relevant formulas used.

A ladder 10 meters long leans against a wall. The foot of the ladder is 6 meters away from the wall. Calculate the height at which the ladder touches the wall using trigonometric ratios. Show all steps in your calculation.

Find the coordinates of the point that divides the line segment joining A(2, 3) and B(8, 15) in the ratio 3:5.

Prove that sin²θ + cos²θ = 1 using the unit circle definition of trigonometric identities.

A line segment drawn from a point outside a circle to touch the circle is 12 cm long. Calculate the distance from the point to the center of the circle if the radius of the circle is 5 cm.

In a triangle, if two sides are in the ratio 3:4 and the included angle is 60 degrees, find the area of the triangle using the formula for area based on similarity of triangles.

A tower stands tall and casts a shadow of 30 meters. If the angle of elevation from the tip of the shadow to the top of the tower is 60 degrees, find the height of the tower.

A tower casts a shadow of 15 m. If the angle of elevation from the tip of the shadow to the top of the tower is 30°, find the height of the tower.

Using trigonometric identities, simplify sin^2(x) + cos^2(x).

Calculate the sum of the first 10 terms of the AP: 2, 5, 8, ...

From point P(2, 3), how many tangents can be drawn to the circle x^2 + y^2 = 25?