Curriculum-aligned Mathematics questions for Class 10 under CBSE. Shortlist topics, practice at your pace, and make every answer count.
In a right-angled triangle, one of the angles measures 30 degrees. Using the properties of trigonometric ratios of complementary angles, find the sine and cosine values of the other angles in the triangle. Illustrate your calculations clearly, and explain how these ratios are derived. Furthermore, discuss the application of these ratios in real-world scenarios, such as in construction or navigation.
A survey was conducted in a class of 50 students regarding their favorite fruits. The data collected is as follows: Apples - 10, Bananas - 15, Oranges - 5, Mangoes - 12, Grapes - 8. Calculate the mode of this grouped data and explain its significance in understanding the preferences of the students. Additionally, discuss how this information could be useful for planning a fruit-based event in the school.
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random, calculate the probability of drawing a red ball. Then, if you draw a second ball without replacement, what is the probability of drawing a blue ball? Discuss the concept of probability using these two scenarios and provide a detailed explanation of your calculations, including the theoretical approach to probability.
In a coordinate plane, point A is located at (3, 4) and point B is at (7, 1). Using the distance formula, find the distance between points A and B. Explain each step of the calculation and the significance of the distance in the context of a real-world scenario, such as finding the shortest path between two locations.
An observer is standing at point A, looking at the top of a tower at point B. If the angle of elevation from point A to the top of the tower is 45° and the angle of elevation from point A to a point C, which is halfway up the tower, is 30°, calculate the height of the tower using trigonometric ratios of complementary angles. Clearly outline your calculations and reasoning.
A sector of a circle has a radius of 7 cm and a central angle of 60°. Calculate the area of the sector and the area of the corresponding segment of the circle. Provide a detailed explanation of the formulas used and the steps taken to arrive at your answer.
In a triangle, if two angles measure 50° and 60°, and the sides opposite these angles are in proportion to the lengths of the sides opposite to the angles of another triangle measuring 80° and 50°, respectively, demonstrate whether the two triangles are similar using the criterion of angle-angle similarity. Provide a detailed explanation of your reasoning and calculations.
In triangle ABC, if the area of triangle ABC is 30 cm² and the base BC is 10 cm, find the height from A to BC. What does this tell you about the relationship between area, base, and height?
Using the section formula, find the coordinates of a point that divides the line segment joining A(2, 3) and B(8, 15) in the ratio 1:3.
If the equations 3x + 2y = 6 and 6x + 4y = 12 are given, determine if they are reducible to a pair of linear equations. What does this imply about their graph?
Find the value of sin(30°) and cos(60°). How are these values related to each other in terms of trigonometric ratios?
Solve the quadratic equation x^2 - 5x + 6 = 0 by factorization. What are the roots of this equation?
Convert the rational number 0.75 into its decimal expansion and express it in the form of a fraction. What does this tell you about its characteristics as a rational number?
Calculate the area of a combination of a circle with radius 7 cm and a rectangle with length 10 cm and width 4 cm. What is the total area?
A tree is 15 meters tall. From a point 20 meters away from the base of the tree, what is the angle of elevation to the top of the tree? Use trigonometric ratios to find your answer.
A polynomial p(x) has zeroes at x = 2 and x = -3. If the polynomial is represented graphically, what is the geometric interpretation of these zeroes on the x-axis?
Find the 10th term of the arithmetic progression: 2, 5, 8, 11, ...
From a point outside a circle, draw a tangent to the circle and explain its properties.
Calculate the value of sin(30°) and cos(30°).
If the zeroes of the polynomial x^2 - 5x + 6 are alpha and beta, find the relationship between the zeroes and coefficients.