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Polynomials -Exercise 2.2 – Class 10

1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.  (i) x2 – 2x – 8 (ii) 4s2 – 4s + 1 (iii) 6x2 – 3 – 7x (iv) 4u2 + 8u (v) t2 – 15 (vi) 3x2 – x – 4 Solution: (i) x2 – 2x… Continue reading Polynomials -Exercise 2.2 – Class 10

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Polynomials – Exercise 2.1 – Class 10

1. The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case. (i) (ii) (iii) (iv) (v) (vi) Solution: (i) The number of zeroes is 0 as the graph does not cut the x-axis at any point. (ii)The number of zeroes is… Continue reading Polynomials – Exercise 2.1 – Class 10

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Constructions – Exercise 11.2 – Class 10

1. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Give the justification of the construction.  Solution: A pair of tangents to the given circle can be constructed as follows. Taking any point O of the given… Continue reading Constructions – Exercise 11.2 – Class 10

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Constructions – Exercise 11.1 – Class 10

1. Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. Give the justification of the construction.  Solution: A line segment of length 7.6 cm can be divided in the ratio of 5:8 as follows. Draw line segment AB of 7.6 cm and draw a ray AX… Continue reading Constructions – Exercise 11.1 – Class 10

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Circles-exercise 10.1-Class 10

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 (B) 12 cm (C) 15 cm (D) 24.5 cm Solution: Let O be the centre of the circle. Given that,… Continue reading Circles-exercise 10.1-Class 10

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Introduction to Trigonometry – Exercise 8.4 – Class 10

1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.  Solution: We know that, 2. Write all the other trigonometric ratios of ∠A in terms of sec A.  Solution: We know that 3. Evaluate (i) (sin263° + sin227°)/(cos217°+cos273°) (ii) sin25° cos65° + cos25° sin65°  Solution: (i) (ii)sin25° cos65° + cos25° sin65°  =… Continue reading Introduction to Trigonometry – Exercise 8.4 – Class 10

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Introduction to Trigonometry-Exercise 8.3-Class 10

1. Evaluate (i) sin18˚/cos72˚ (ii) tan26˚/cot64˚ (iii) cos48˚ - sin42˚ (iv) cosec31˚ - sec59˚ Solution: (i) sin18˚/cos72˚ = [sin(90˚-72˚)]/cos72˚ = cos72˚)]/cos72˚ =1   (ii) tan26˚/cos64˚ = tan(90˚-64˚)/cos64˚ = cot64˚/cot64˚ = 1   (III) cos 48° − sin 42° = cos (90°− 42°) − sin 42° = sin 42° − sin 42° = 0   (iv) cosec… Continue reading Introduction to Trigonometry-Exercise 8.3-Class 10

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Introduction to Trigonometry-Exercise 8.2-Class 10

Evaluate the following (i) sin60° cos30° + sin30° cos 60° (ii) 2tan2 45° + cos2 30° − sin2 60° (iii)  (cos45°)/(sec30°+cosec30°) (iv) (v) Solution: (i) sin60° cos30° + sin30° cos 60° =  √3/2   x  √3/2 +  1/2  x ½ = 3/4 + 1/4 = 4/4 = 1   (ii) 2tan2 45° + cos2 30° − sin2 60° =… Continue reading Introduction to Trigonometry-Exercise 8.2-Class 10

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Introduction to Trigonometry-Exercise 8.1-Class 10

1. In ∆ABC right angled at B, AB = 24 cm, BC = 7 m. Determine (i) sin A, cos A (ii) sin C, cos C  Solution: (i) Applying Pythagoras theorem for ∆ABC, we obtain AC2 = AB2 + BC2 = (24 cm)2 + (7 cm)2 = (576 + 49) cm2 = 625 cm2 ∴ AC… Continue reading Introduction to Trigonometry-Exercise 8.1-Class 10