Chapter 8 Linear Equations in Two Variables Ex 8.2 eng
Chapter 8 Linear Equations in Two Variables Ex 8.2 Question 1. Which one of the following options is true and why? y = 3x + 5 has (i) a unique solution (ii) only two solutions (iii) infinitely many solutions Solution: (iii) A linear equation in two variables has infinitely many solutions. Question 2. Write four solutions […]
Chapter 8 Linear Equations in Two Variables Ex 8.1 eng
Chapter 8 Linear Equations in Two Variables Ex 8.1 Question 1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be ₹ x and that of a pen to be ₹ y) Solution: Let […]
Chapter 7 Heron’s Formula Ex 7.2 eng
Chapter 7 Heron’s Formula Ex 7.2 Question 1. A park, in the shape of a quadrilateral ABCD, has ∠C = 90°, AB = 9m,BC = 12m,CD = 5m and AD = 8 m. How much area does it occupy? Solution: In right ∆ BCD Question 2. Find the area of a quadrilateral ABCD in which […]
Chapter 7 Heron’s Formula Ex 7.1 eng
Chapter 7 Heron’s Formula Ex 7.1 Question 1. A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side a. Find the area of the signal board, using Heron’s formula.If its perimeter is 180 cm, what will be the area of the signal board? Solution: We know that, an equilateral triangle has equal […]
Chapter 6 Coordinate Geometry Ex 6.3 eng
Chapter 6 Coordinate Geometry Ex 6.3 Question 1. In which quadrant or on which axis does each of the points (-2,4), (3, – 1), (-1,0), (1, 2) and (-3, – 5) lie? Verify your answer by locating them on the cartesian plane. Solution: (i) (-2, 4) lies in II quadrant. (ii) (3, -1) lies in IV quadrant. […]
Chapter 6 Coordinate Geometry Ex 6.2 eng
Chapter 6 Coordinate Geometry Ex 6.2 Question 1. Write the answer of each of the following questions (i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane? (ii) What is the name of each part of the plane formed by these two […]
Chapter 6 Coordinate Geometry Ex 6.1 eng
Chapter 6 Coordinate Geometry Ex 6.1 Question 1. How will you describe the position of a table lamp on your study table to another person? Solution: Let us consider the lamp as a point A and table as a plane. Take any two perpendicular edges of the table, say OX and OY. Measure the distance […]
Chapter 5 Triangles Ex 5.5 eng
Chapter 5 Triangles Ex 5.5 Question 1. ABC is a triangle. Locate a point in the interior of ∆ ABC which is equidistant from all the vertices of ∆ ABC. Solution: Suppose OM and ON be the perpendicular bisectors of sides BC and AC of ∆ ABC. So, O is equidistant from two endpoints 0 […]
Chapter 5 Triangles Ex 5.4 eng
Chapter 5 Triangles Ex 5.4 Question 1. Show that in a right angled triangle, the hypotenuse is the longest side. Solution: Let ABC be a right angled triangle, such that ∠ ABC = 90° We know that, ∠ABC + ∠BCA + ∠CAB = 180° (By A property) ⇒ 90° + ∠BCA + ∠CAB = 180° […]
Chapter 5 Triangles Ex 5.3 eng
Chapter 5 Triangles Ex 5.3 Question 1. ∆ABC and ∆DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see figure). If AD is extended to intersect BC at P, show that (i) ∆ABD = ∆ACD (ii) ∆ABP = ∆ACP (iii) AP bisects […]