Prove the following trigonometric identities: Question 29. Solution: We have, L.H.S. = = = = 1 + cos θ = = = = R.H.S. Hence… Read More

# Tag Archives: RD Sharma Class-10

Question 1: Find the roots of the following quadratic (if they exist) by the method of completing the square: . Solution: Given: We have to make… Read More

Question 1. A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in the figure. If AB = 60… Read More

Question 1. Points A and B are 70km. apart on a highway. A car starts from A and another car starts from B simultaneously. If… Read More

Question 35. In the figure, AB and CD are two diameters of a circle perpendicular to each other and OD is the diameter of the… Read More

Question 18. In the given figure, Find the area of the shaded region. (Use π = 3.14). Solution: The side of the square =… Read More

Question 1. Find the centroid of the triangle whose vertices are: (i) (1, 4), (-1, -1), and (3, -2) Solution: Given, vertices of triangle are… Read More

Question 20. The three vertices of a parallelogram are (3, 4), (3, 8), and (9, 8). Find the fourth vertex. Solution: Let ABCD be a… Read More

Question 40. Prove that the points (3, 0), (4, 5), (-1, 4), and (-2, -1) taken in order, form a rhombus. Also, find its area.… Read More

Solve each of the following systems of equations by the method of cross multiplication. Question 15. 2ax + 3by = a + 2b and 3ax… Read More

Question 1. A father is three times as old as his son. After twelve years, his age will be twice as that of his son… Read More

Solve each of the following systems of equations by the method of cross multiplication. Question 1. x + 2y + 1 = 0 and 2x… Read More

Question 1. Find the discriminant of the following quadratic equations: (i) 2x2 – 5x + 3 = 0 Solution: Given quadratic equation: 2x2 – 5x… Read More

Question 1. Find the distance between the following pair of points: (i) (-6, 7) and (-1,-5) (ii) (a + b, b + c) and (a… Read More

Question 1. If cos θ = 4/5, find all other trigonometric ratios of angle θ. Solution: We are given, cos θ = 4/5. So,… Read More