Chapter 10 Circles Ex 10.2
Chapter 10 Circles Ex 10.2 Question 1. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (a) 7 cm Sol. (b) 12 cm (c) 15 cm (d) 24.5 cm Solution: Question 2. […]
Chapter 10 Circles Ex 10.1
Chapter 10 Circles Ex 10.1 Question 1. How many tangents can a circle have? Solution: There can be infinitely many tangents to a circle. Question 2. Fill in the blanks: (i) A tangent to a circle intersects it in ………… point(s). (ii) A line intersecting a circle in two points is called a ………… . (iii) A circle […]
Chapter 9 Some Applications of Trigonometry Ex 9.1
Chapter 9 Some Applications of Trigonometry Ex 9.1 Question 1. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30° […]
Chapter 8 Introduction to Trigonometry Ex 8.4
Chapter 8 Introduction to Trigonometry Ex 8.4 Question 1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A. Solution: From trigonometric identity, cosec² A – cot² A = 1, we get Question 2. Write all the other trigonometric ratios of ∠A in terms of sec A. Solution: Since […]
Chapter 8 Introduction to Trigonometry Ex 8.3
Chapter 8 Introduction to Trigonometry Ex 8.3 Question 1. Solution: Question 2. Show that: (i) tan 48° tan 23° tan 42° tan 67° = 1 (ii) cos 38° cos 52° – sin 38° sin 52° = 0 Solution: (i) LHS = tan 48° tan 23° tan 42° tan 67° = tan 48° tan 23° tan […]
Chapter 8 Introduction to Trigonometry Ex 8.2
Chapter 8 Introduction to Trigonometry Ex 8.2 Question 1. Evaluate the following: Solution: Question 2. Choose the correct option and justify your choice: Solution: Question 3. Question 4. State whether the following statements are true or false. Justify your answer. (i) sin (A + B) = sin A + sin B. (ii) The value of […]
Chapter 8 Introduction to Trigonometry Ex 8.1
Chapter 8 Introduction to Trigonometry Ex 8.1 Question 1. In ∆ABC right angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A (ii) sin C, cos C Solution: Question 2. In given figure, find tan P – cot R. Solution: Question 3. Question 4. Given 15 cot A […]
Chapter 7 Coordinate Geometry Ex 7.4
Chapter 7 Coordinate Geometry Ex 7.4 Question 1. Determine the ratio, in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, -2) and B(3, 7). Solution: Question 2. Find a relation between x and y, if the points (x, y), (1, 2) and (7, 0) are […]
Chapter 7 Coordinate Geometry Ex 7.3
Chapter 7 Coordinate Geometry Ex 7.3 Question 1. Find the area of the triangle whose vertices are: (i) (2, 3), (-1, 0), (2, -4) (ii) (-5, -1), (3, -5), (5, 2) Solution: Question 2. In each of the following find the value of ‘k’ for which the points are collinear. (i) (7, -2), (5, 1), […]
Chapter 7 Coordinate Geometry Ex 7.2
Chapter 7 Coordinate Geometry Ex 7.2 Question 1. Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2 : 3. Solution: Question 2. Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3). Solution: Question 3. Solution: […]