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Chapter 1, , Knowing Our Numbers, , Exercise 1.1, 1., 2., 3., 4., 7., 9., , (a) 8, (b), Fall in temperature, (a) +3000 m, (b), –11 , 5., Rs 12, (a) 6062, (b), , –8, is greater in Roorkee by 5ºC ., + Rs 5000, (c) – Rs 500, 160, 6. –50 km, –20 km , 0, , (c) –168, , (d) 1599, , (b) False, , (c) True, , (d) True, , Exercise 1.2, 1. (a) True, 3., X, , –11, , –10, , 9, , –8, , –7, , 6, , –6, , 66, , 60, , –54, , 48, , 42, , –36, , 5, , –55, , –50, , 45, , –40, , –35, , 30, , –4, , 44, , 40, , –36, , 32, , 28, , –24, , –3, , 33, , 30, , –27, , 24, , 21, , –18, , 4. (a) –60, 6. (a) 139800, 7. 16 min, , (b) 0, (b) –234500, 8. Rs 350, , (c) 1265, (c) 485000, , (d) 0, (d) –32017, , (b) –27, (b) True, , (c) –14, (c) False, , (d) 13, (d) False, , Exercise 1.3, 1. (a) 1, 2. (a) False, , (e) False, 3. 22 , 7. 7 days, 8. a) 3, , 4. –81, , 5. 7 hours, , 6. 56, , b) 6, , c) 576, , d) –138, , 3. –12ºC, 7. 48, , 4. 449300, 8. 17, , MCQ - 1, 1. –1 , 5. –1325600, 9. 1 , , 2. none, 6. not defined, 10. 81, , Revision Exercise, 1., 2., 3., 4., 5., 7., 8., 10., 11., , –6, –5 –4, –3,, 1, 2, 3, 4, 5, –13, –7, –5, 2, 5,, 304, 253, 212, 53,, (a) 7, 11, (b), (a) 345, (b), 254 , 9., (a) 4, (b), –192, 12., , UM - 7, , –2, 6, –67, –142, –467, –19, –24, –5, (c) –810, 29 units, 156, –13, 13. Rs 4100, , (d) 68, , 3

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Chapter 2, , Fractions, , Exercise 2.1, 1. (a) =, 2. (a) 2 , 8 , 2, 3 21 9, 6, 3., , 9 , 12 , 15, 22 33 44 55, 4. (a) 27, 6, , (e) 6 1, 24, 1, 5. 2 , 2, 7. (a) 10 1, 2, Exercise 2.2, 1. (a) 1, 14, , (e) 24, 144, , (i) 286, 405, 2. (a) 3, 2, , (e) 13, 9, , (i) 95, 8, 3. (a) 11, 2, , (e) 3, 4. – 31, 30, , (b) >, (b) 7 , 3 , 1, 10 7 5, , (c) =, (c) 7 , 22 , 3, 15 45 5, , (d) <, (d) 13 , 5 , 11, 24 8 16, , (b) 2 7, 24, , (c) 1, 25, , (d) 5 29, 30, , 6. 15 1 cm, 5, (b) 17 1, 2, (b) 2, 56, (f) 28, 504, (j) 156, 624, (b) 7, 4, (f) 1, 18, (j) 1, , 8. 2 , Sona ate more by 1, 5, 5, (c) 20, 117, (g) 459, 169, (k) 1215, 2700, (g) 266, 27, (k) 885, 28, (c) 5, 2, , (d) 319, 35, 28, (h), 72, 600, (l), 720, (d) 4, 3, (h) 574, 39, (l) 777, 20, (d) 7, 4, , (c) 7, 5, (g) 8, 3, (c) 3, 91, (g) 3, 104, (c) 21, 16, 155, (g), 226, , (d) 64, 15, (h) 25, 47, (d) 3, 289, (h) 31, 49, (d) 91, 18, (h) 10, 17, , (c) 1, , (b) 23, 5, (f) – 22 , 5, , Exercise 2.3, 1. (a) 16, , (b) 25, , , (e) 2, 2. (a) 1, 16, , (e) 2, 143, 3. (a) 4, 5, 169, , (e), 225, Exercise 2.4, 1. 16 , 5. Rs 373, , 4, , 7, 20, , (f) 121, 2, 1, (b), 55, (f) 11, 36, (b) 5, 6, (f) 5, 7, , 2. 4 32 kg, 3. 11 m, 4. 2 litre, 35, 105, 3, 6. (a) 540 hectares (b) 300 hectares, UM - 7

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7. Rs 110, 11., , 41, , 66, , 11, 27, 5, 12. 25 kg, 7, 8. 11, , 15. Rs 171, Rs 410.4, Rs 444.6, MCQ - II, 4, 1., 5, 8, 4., , 45, 27, 8., , 40, Revision Exercise, 4, 1. (a) 7, 5, 1, , (e) 3, 2, 25, 2. (a), 11, 153, , (e), 7, 6 9 12 15, 3. ,, ,, ,, 8 12 16 20, 1 2 7 4, 4. (a) , , ,, 6 3 9 5, 5 2 7 5, 5. (a) , ,, ,, 6 3 12 9, 11, 6. (a), 15, 1, 7. Rs 12, 2, , 2, 5, 5. 625 g, 1, 9. 2, 3, 2. 1, , 11, 12, 2, (f) 22, 7, 23, (b), 6, 197, (f), 17, , (b) 11, , 3 1 2 5, , , ,, 8 2 3 6, 19 7 3 5, (b), , , ,, 6 4 2 8, 19, (b) –, 98, , (b), , 1, 10. 15 km, 9, 217, 14. 4, 242, , 9. 3344, 13. 15, , 2, 3, , 16. Rs 200, Rs 300, Rs 400, , 3. Sonu ate more than Ritu, 1, 7, 6. 2, 7. 150, 9, 8, 5, 10., 7, , (c) 4, , (c), , 1, 2, , 30, 7, , 1 3, , ,, 4 8, 8 3, (c) , ,, 9 4, 1, (c), 10, (c), , (d) 4, , (d), , 4, 5, , 65, 4, , 7 5, ,, 12 6, 6 1, ,, 9 3, (d) 3, , 17, 45, , 8. Rs 1806, Rs 2107, Rs 602, 9., , 21, 11, , 11. (a) Rs 7700, , 10., , 88, 43, , (b) Rs 2100, , (c) Rs 1400, , Chapter 3, Exercise 3.1, 1. (a) –4, (e) –12, 3. (a) Numerator, , (b) Numerator, , (c) Numerator, , (d) Numerator, , (e) Numerator, , (f) Numerator, –7 7 –9, 4., ,, ,, –8 14 –17, UM - 7, , Rational Numbers, (b) –13, (c) 4, (d) –17, (f) 17, 2. (a), (c), (e) and (f), = –3, denominator = 4, = –7, denominator = 18, = –11, denominator = –13, = 14, denominator = 21, = 0,, denominator = 5 , = –3, denominator = 7, 5. (a), (b), (c), (e), , 5

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Exercise 3.2, 2. (a) 20, 3. (a) 10, 5, 4. (a), 11, 61, , (e), 161, , (b) –49, (b) –24, –1, (b), 8, 3, (f), 16, , 5. (a) 24, (b) 24, 81, 7, , (e), (f), 39, 77, 6. (a) In ascending order, In descending order, , (b) In ascending order, In descending order, Exercise 3.3, 5, 1. (a), 4, –1, , (e), 5, 4, 2. (a), 3, –1, (e), 14, 7, (i), 30, –15, 3. (a), 28, –2, 4. (a), 7, 2, 5., , 9, –23, 8., 28, , (b), (f), (b), (f), (j), (b), (b), 6., 9., , Exercise 3.4, 7, 1. (a), 10, 28, , (e), 169, , (b), , 2. (a) 0, , (b), , –4, , (e), 7, 22, 3. (a), 91, 122, , (e), 9, –4, 4., , 17, –77, 8., 25, , 6, , (f), , (f), (b), (f), 5., 9., , 6, 31, 9, 23, –1, 9, –1, 15, 15, 14, 141, 280, 1, 8, 11, 3, 59, 30, –26, 45, –1, 3, –49, 169, –403, 561, 2, 117, 44, 45, –481, 731, –34, 15, , (c) –48, (c) –56, –11, (c), 25, (c), , 3, 4, , (d) –176, (d) –15, 9, (d), 8, (d), , 7, 71, , –3 5 2 5 11, , , , ,, 4 8 3 6 12, 11 5 2 5 –3, :, , , , ,, 12 6 3 8 4, –9 –13 6 7 3, :, ,, ,, ,, ,, 10 10 15 12 5, 3 7 6 –13 –9, : ,, ,, ,, ,, 5 12 15 10 10, :, , (c) –1, , (c), (g), (k), (c), (c), 7., , –1, 10, –97, 66, –1, 12, –671, 910, –61, 40, 41, 33, , –7, 16, –13, (g), 136, –221, (c) 36, (c), , (g) 1, –2, 5, 2, (g), 3, 39, 6., 82, (c), , (d), , –1, 3, , 1, 4, –21, (h), 20, 45, (l), 76, , (d), , (d), , (d), (h), (d), (h), (d), (h), , 47, 40, , 8, 39, 48, 403, –8, 15, 2, 3, –1, 5, 21, 40, , 7. 10, , UM - 7

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Exercise 3.5, 1. (a), , (e), 2. (a), , (e), , 2.8, (b), 3.0625, (f), 1.33…, (b), 18.09…, (f), 301, 3. (a), (b), 25, 401, , (e), (f), 50, 4. (a) 2.4705, (b), (e) 0.6470, (f), 5. (a) Terminating, , (d) Terminating, 6. Terminating, 187, 7. (a), (b), 200, 51, , (e), (f), 50, 8. (a), (b) and (f), , 1.625, (c) 7.5, 11.48, 1.714285… (c) 0.18…, 0.375, 13, 1913, (c), 40, 40, 573, 400, 0.1250, (c) 0.6666, 0.1500, (b) Non–terminating, (e) Non–terminating, 789, 1000, 193469, 20000, , (c), , (d) 2.3125, (d) 2.86…, (d), , 1081, 2500, , (d) 0.8750 , (c) Terminating, (f) Non–terminating, , 253, 50, , (d), , 2839, 500, , Exercise 3.6, 1. (a) 103.68, , (e) 36.2965, , (b) 33.9552, , (c) 280.254, , (d) 218.9, (h) 0.0021, , (f) 15.796, , (g) 2670.6176, , 2. (a) 686.925, , (b) 87857.472, , (c) 47.616, , 3. (a) 8.5, , (b) 11.06, , (c) 2.12, , (d) 8.7, , (f) 2.7, , (g) 20.5, , (h) 8.94, , , (e) 0.13, 4. Rs 1971.25, , 5. Rs 1749.12, , 6. Rs 29347.55, , 8. Rs 1080.625, , 9. 132601.5 kg 10. 55.8 litre, , 7. 1.85, 11. 3.75 km/hr, , 12. 13.7, Exercise 3.7, 1. (a) 0.230 km, (e) 3.275 kg, , (b) 270 hm, (f) 0.4 century, , (c) 8 year, , (d) 3000 litre , , 2. (a) 11250 mm, , (b) 0.02876 m, , (c) 13320 sec, , (d) 2.75 dag, , , (e) 0.00376 g, , (f) 20160 min, , (g) 1.28 kg, , (h) 3250 litres, , , (i) 875 dg, , 3. 58.8 m, , 4. 9.24 kg, , 5. 1125, , 7. 422, , 8. 456 kg, , 9. 1682 hr, , 6. 40 , 10. 38.725 kg, , 11. Rs 23667.12, , MCQ - III, –7 –49, ,, 6 42, 48, 5., 149, 9. a × (b + c), 1., , UM - 7, , 7 2, ,, 12 3, –3, 6., 4, 10. terminating, 2., , 3., , 29, 20, , 7. 9470, , –29, 20, 135, 8., 47, 4., , 7

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Revision Exercise, , –9, 1. (a) 7, (b) 6, (c), 4, –7, 64, , (e), (f), 4, 3, 3 7 2 3 5, –7 4 11 –5, 3. , , , ,, 4., , ,, ,, 8 12 3 4 6, –12 9 –24 6, 41, 235, –11, 5. (a), (b), (c), 10, 24, 72, –2, –3 –2 –1 0 1 2, 6. 5, 7., , , , , ,, 8 8 8 8 8 8, 9. (a) 0.875, (b) –1.0625, (c) 3.142857…, , (e) –0.19230…, 10. (a), , (e), 11. (a), 12. (a), , (d), , (f), , (d), , 8, 3, , (d), , 17, 24, , (d) –0.133…, , (f) 0.4333…, , 63, –411, 469, 809, (b), (c), (d), 4, 16, 20, 25, 9, 7326, (f), 2000, 25, 4.064, (b) 0.192, (c) 480, (d) 3.2, terminating (b) non–terminating recurring (c) terminating, terminating (e) terminating, non–terminating recurring, , 13. 868.275 km, , Chapter 4, , Exponents and Powers, , Exercise 4.1, 1. (a) 512, , (e) 6561, 6, , 2. 576 = 2 × 3, 3. (a) 6, , (b) 14641, 64, (f), 343, , 2, , 3, , (b) 10, 3, , 3, , 4. 74088 = 2 × 3 × 7, , 3, , (c) 125, , (d) -1, , (c), , (d), , , , 3, , Exercise 4.2, 1. (a) –1, 17, , 3, , –3, (b) , 2, , 4, , 11, (c) , 17, , 13, , (d), , , , , (e), 2. (a) –16384, 2187, 125, , (e), 512, 128, 3. (a), 243, 2, , (e), 15, , (b), , 27, 343, , 343, 2239488, 16, (f), 9, , (b), , (c), , 16, 2401, , (d) 1, , (c), , 11, 54, , (d), , (c), , –64, 125, , 175, 36, , Exercise 4.3, , 8, , 1. (a), , 32, 243, , (b), , 32, 243, , UM - 7

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2. (a), , (b), , (c), , 3. (a), , (b), , (c), , , (e), , (f), , 4. (a) 1, , (b), , 5. (a) 1, , (b), , , (e) 1, , (f), , , (i), , , (d), , =1, –128, 2187, , 1, 25, , (c), , 16, 25, , (d) 0, , (c), , 4096, 81, , (d), , 5, 9, , (g), , 625, 81, , (h), , 9, , 49, , (c) 128, , (d), , –2, 2187, , 21, 64, , 6. (a) 2, , (b), , , (e) 1, , (f), , 1458, 625, , Exercise 4.4, 1. (a), , (b), , 2. (a) 18, , (b), , –128, 19683, , 64, 27, 1, 4., 7, , 7. 2 , , 8. 36, , 3., , (c), 32, , 81, –3, 5., 6. -1 , 2, 5, 81, 9. (a), (b), 2, 100, , (c), , Exercise 4.5, 1. (a) 3.47 × 10, , 6, , 2. (a) 7540000, , (b) 7.689 × 10, , 8, , (b) 0.000932, , (c) 4.579 × 10, , -1, , -4, , (d) 3.45 × 10 , , (c) 0.00000000000573, , , (d) 3485000000000, 8, , 3. 3 × 10 m/s, 6. 1.602 × 10, , 4. 12756000 m, , -19, , 2, , 5. 0.000000000067 Nm /kg, , 2, , C, , MCQ - 1V, –1, 2. 9, , 1. –8 , 5., , –1, , 8, , 6. 1, 12, , 9. 9.4605 × 10 km , UM - 7, , 3, , 3. 1, , 4. 4, , 7. 4, , 8. 5, , 10., , 8, 27, , 9

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Revision Exercise, 128, 2187, 16, (b), 81, 2, (b), 3, , 1. (a) 256, , (b), , 2. (a) 25, 3. (a), , 32, 243, , (c), , 15625, 117649, , (d) 7776, , (c) 4 , 25, 16, , (c) 0, , (d), , (d) –13, , 4. (a) 5, , (b) 0, , (c) 3, , 1, , 18, 36, 8. (a), 49, , 25, 676, 16, (b), 9, , 2187, , 128, 64, (c), , 15625, , 5., , 6., , 9. (a) 5.43 × 10, , -3, , 7., , 5, , (b) 2.49218 × 10 (c) 2.63 × 10, , 10. (a) 0.0000243, , (b) 61200000, , -7, , (d) 4.529 × 10, , 11, , (c) 0.00000000009025, , , (d) 801050, 0, , -3, , 11. 2.56 m, 0.00256 km, 2.56 × 10 m, 2.56 × 10 km, 512, 12. 149600000000 km , 13., 125, , Chapter 5, , Algebraic Expressions, , Exercise 5.1, 1. (a) x – 5, , (b) 7 + y – x, (c) x + y – z, x, (e) 7y + 3, (f), +y, 4, 2, 2. (a) The terms and their factors are : 2x (2, x),, , (d) 3x + y , –3y (3, y),, , 7 (7), , , (b) The terms and their factors are : –3xy (3, x, y), 5yz (5, y, z), , 6xy (6, x, y), 2, , , (c) The terms and their factors are : x y (x, y),, , 2, , y x (x, y),, , 2 2, , x y (x, y), 3 2, , 4 3, , 3. (a) 7a b c, , 2, , 2, , 6 6, , (b) –2x y, , (c) –24x y, , 2, , (d) 2t, , 10, , 4. (a) (–3xy , 13y x, 6xy ), (5xy, 5yx, 10xy), (–17, 55), 2, , 2, , 2, , 2, , 2, , 2, , , (b) (10pqr, –7pqr), (–5p qr , 11p qr ), (8pq r, pq r), 5. (a) 23, , (e) 31, , (b) –12, (f) –122, , (c) 28, , (d) –84, , Exercise 5.2, 2 2, , 2, , 2, , 1. (a) (3x y , 3y ), (–16x y, –16y), 2, (c) 4x y, 4y, , 2, , 2, , (b) (–5x , –5), (–11x yz, –11yz), , 2. The degree and coefficient of each term are :, 2, 2, 2, , (a) (3x , 2, 3), (–5xy, 2, –5), (–4y , 2, –4), (–11x y, 3, –11), degree of expression = 3, 2 2, , 2 3, , (b) (23xy, 2, 23), (–4x y , 4, –4), (5x y , 5, 5), (–17, 0, –17), degree of expression = 5, , 10, , UM - 7

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Exercise 6.4, 1., 5., 8., 11., 15., 18., , 14, 20, 2., 10 yr, 7 yr 6., 10, 9., 15, 12., 36, 16., 12 yr, 40 yr, , 3, 3. 54 m, 20 m, 4. 9 m, 23 m, 23 m, 7, 75, 125, 7. Rs 165, Rs 125, 25, 10. 11 yr, 13 yr, 31, 38, 13. 13, 37, 14. 65º, 44º, 71º, 44 yr, 17 yr , 17. 15 yr, , Exercise 6.5, 1. (a) x < 2, , (e) x ≤ 2, , (i) x ≤ 4, , (b) x ≥ 6, (f) x ≥ –2, (j) x < –4, , 2. 35 , , 3. 9 cm, , (c) x < –4, (g) x < –3, , (d) x > –2, (h) x ≤ –3, , MCQ - VI, 1. 22 , , 2. 9, , 5. 13 , , 6. 8, 10. 3, 5, , 9. x > –3, , Revision Exercise, 3, 1. (a) x = y + 15, 4, 2. (a) Yes, 1, 3. (a), (b), 2, 4. 12 yr, 5., 8. 50 m, 25 m, 9., 11. 30, 18, 5, 12. (a) x <, (b), 2, 13. 77, , 3. 16, , 4. 18, , 7. 27, 36, , 8. x ≥ 4, , (b) x + 2x + 8 = 56, (b) No, 47, 7, (c), 8, 7, 6. 63, 20, 30, 10. Rs 80, Rs 60, , (c), (c), (d), 7., , x>4, , (d) x <, , Chapter 7, , (c) x ≤ –3, , x + 2x – 1 = 8, No, 3, 7, 13, 1, 5, , Ratio, Proportion And Percentage, , Exercise 7.1, 1. (a) 2 : 7, , (b) 1 : 20, , (c) 3 : 10, , (d) 1 : 8, , (f) 49 : 73, , (g) 1 : 4, , (h) 20 : 1, , 2. (a) 3 : 8, , (b) 1 : 3, , (c) 3 : 5, , (d) 7 : 1, , , (e) 1 : 8, , (f) 1 : 4, , (g) 9 : 19, , (h) 2 : 5, , , (i) 20 : 1, , (j) 720 : 7, , (k) 1 : 8, , (l) 1 : 4, , , (e) 3 : 2, , 3. (a) 9 : 14, , (b) 5 : 6, , (c) 3 : 7, , (b) 7 : 18, , (c) 18 : 11, , (d) 3.2 : 5.2, , 4. 5 : 4, 5. (a) 7 : 11, , 6. (a) 2 : 5, 4 : 10 (b) 8 : 6, 12 : 9 (c) 22:30, 33:45 (d) 9:2, 27:6, , 14, , UM - 7

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7. 8 , 11. 6, 8, , 8. 75 m, , 9. 675, , 10. Rs 2000, , 12. 3:10, 3:8, Class VIII has a better result, , 13. 259, 407, Exercise 7.2, 1. 5.6 m, , 2. 24 cm, , 3. (a) No, , (b) No, , (c) Yes, , (d) Yes, , 4. (a) 135, , (b) x = 16, y = 64, , (c) 200, , (d) 1, , 5. 780 m, 7. (a) Rs 84000, 8. (a) 880 km, 10. Rs 670, , 6. Rs 240, (b) 25, (b) 40 hr, , 9. (a) 10 kg, , (b) 48, , 11. Rs 300, , Exercise 7.3, 1. (a) 28%, 8, , (e) 68 %, 9, 2. (a) 345%, , (e) 23.1%, 3. (a) 150%, , (e) 44%, 11, 625, 3, , (e), 25000, 4. (a), , 1, (b) 62 %, 2, , (b) 73%, (f) 6.2%, 2, (b) 26 %, 3, 1, (f) 108 %, 3, 3, (b), 4000, 1, (f), 8000, (b) 0.0005, , , (e) 0.00135, , (f) 0.0072, , , (e) Rs 845, , (b) 75 g, , 5, %, 11, , (c) 80%, , (d) 404.5%, , 5, (c) 85 %, 7, , 2, (d) 66 %, 3, , (c), , 161, 20000, , (d), , 3, 500, , (c) 0.00625, , (d) 0.004, , (c) 210 m, , (d) 225 l, , (f) 24 min, , 7. Rs 3750, Rs 8250 , 9. 200 , , (d) 45, , (f) 80%, , 5. (a) 0.00762, 6. (a) Rs 140, , 3, (c) 13 %, 5, , 8. Rs 640, , 10. 360 g, 400 g, 240 g, , 11. 200, , Exercise 7.4, 1. (a) 180%, 2. 75%, 6. 48 kg, 7. (a) 50%, UM - 7, , 5, (b) 55 %, 9, 2, 3. 106 %, 3, 1, (b) 33 %, 3, , 1, 4. 37 %, 2, , 2, 5. 83 %, 3, , 15

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1, 8. 37 %, 2, 10. (a) 25%, , 2, 9. 26 %, 3, (b) 25%, , Exercise 7.5, 1. (a) Profit Rs 50, , (b) Loss Rs 150, , (c) Profit Rs 50, , 1, (b) Loss 12 %, 2, , (c) Profit 4%, , , (d) Profit Rs 150, 2. (a) Profit 50%, 2, , (d) Loss 16 %, 3, 3. Profit Rs 60, 25%, , 4. Rs 200, 10%, , 1, 5. Rs 200, 12 %, 2, , 6. Profit 50%, , 7. Loss 25%, , 8. 20%, , 9. (a) Rs 53.50, , (b) Rs 1356, , (c) Rs 1200, , (d) Rs 5720, , 10. (a) Rs 400, , (b) Rs 1000, , (c) Rs 450, , (d) Rs 300, , 11. Rs 337.50, , 12. Rs 300, , 13. Rs 1200, , 15. Rs 750, , 1, 16. 3 %, 8, , 1, 14. Loss, Rs 50, 6 %, 4, , 17. Rs 2000, Rs 2250, , Exercise 7.6, 1. (a) Rs 192, Rs 992 (b)Rs 210, Rs 7210, , (c) Rs 400, Rs 10400, 2. (a) Rs 4000, 1, 3. (a) 2 year, 2, 4. Rs 300, , (b) Rs 350, , (c) Rs 4000, , (b) 6 year, , (c) 7 year, 1, 6. 12 %, 2, , 8. (a) Rs 23400, , (b) 12 year, , 9. Rs 9100, , 10. Rs 4125, , 5. 12%, , 1, 7. 12 %, 2, , MCQ - VII, 1. 2 : 3, , 2. 18.3 g, , 4. 100 , , 5. 75, , 2, 8. 8 %, 3, 1, 12. 33 %, 3, , 9. 4, , 1, year, 2, , 3. Rs 96, Rs 320, Rs 120, 19, 6., 7. 10%, 500, 1, 10. 56 % gain 11. 25 years, 4, , Revision Exercise, 1. (a) 4:5, , (e) 12:5, , 16, , (b) 3.2:1, , (c) 10:1, , (d) 25:6, , (f) 1:8, UM - 7

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2. (a) 60, , (b) 32, , (c) 12, , 3. (a) 4:3, , (b) 4:1, , (c) 1:320, , (d) 6:1, , , (e) 2:1, , (f) 8:3, , 2, (c) 56 %, 3, , (d) 37.5%, , 4. Rs 300, Rs 400, Rs 500, 5. (a) 1750 m, , (b) 7.2 cm, , 6. (a) 36 year, , (b) 24 year, , 7. (a) 72 km, , (b) 8 hr, , 8. (a) 37.5%, , (b) 375%, 2, (f) 26 %, 3, 59, (b), 25000, (b) 90, , , (e) 2.5%, 8, 9. (a), 25, 10. (a) 5 kg, 3, , (e) 200 days (f) 100, 4, 1, 11. (a) 62 %, (b) 20%, 2, 2, 12. 25%, 13. 16 %, 3, 15. 240, , 49, 20, (c) 3 m, , 29, 40, (d) Rs 18750, , (c), , (d), , (c) 30%, , (d) 6%, , 14. y = 9600, z = 40000, , 16. 240 mango trees, 360 lemon trees and 1400 orange trees, 1, 19, 14, 28, 17. (a) 29 %, (b) 51 %, (c) 6 %, (d) 12 %, 31, 31, 31, 31, 1, 18. 25%, 19. Profit 33 % 20. Profit 10% 21. 25%, 3, 22. (a) Rs 702, (b) Rs 7050, 23. (a) Rs 800, 24. Profit 20%, 27. Loss 4%, , (b) Rs 1800, , 2, %, 11, 28. Rs 10500 , 25. Profit 13, , 26. Loss 10%, , 29. (a) Rs 900, Rs 5400 (b)Rs 96, Rs 8096, 30. (a) Rs 1000, , (b) Rs 2500, , 31. (a) 2 years 1 month , , (b) 4 years, , 32. 15 year, , 34. Rs 15000, Rs 45000, , 33. 6.25 %, , Chapter 8, , Lines and Angles, , Exercise 8.1, 1. (a) 60º, , (b) 131º, , (c) 11º, , (d) 157º, , 2. (a) 62º, , (b) 1º, , (c) 71º, , (d) 13º, , 3. (a) Complementary , , (b) Supplementary, , (c) Complementary , , (d) Supplementary, , (e) Complementary , , (f) Supplementary, , UM - 7, , 17

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Chapter 10, , Symmetry, , Exercise 10.1, 1., , (a), , (b), , (c), , (d), , (e), , (f), , (g), , (h), , 2., , (a), , (b), , 3., , (a), , (e), , 20, , (b), , (f), , (c), , (g), , (d), , (h), UM - 7

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4., , (a), , (b), , (c), , (d), , (e), , (f), , (g), , (h), , (a), , (b), , (c), , (d), , (a), , (b), , (c), , 5., , 6., , 7. (a) 3, , (e) 0, , (i) 2, 0, 1, 1, , (b) 1, (f) 2, , (c) 0, (g) 12, , (d) infinite, (h) 16, , Exercise 10.2, 1., 2., 4., 5., 6., 7., 9., , (a) infinite, Z , (a) 3, (a) 5, (a) 90º, O, X, (a) 180º, , b), 3., (b), (b), (b), 8., (b), , 3, a, d, 6, 2, 120º, M, B, E, 90º, , Chapter 11, , c) 3, , d) 4, , (c) 5, (c) 2, (c) 90º, , (d) 72º, , (c) 60º, , (d) 72º, , Representing 3D in 2D, , Exercise 11.1, 1. a) vertices 12, faces 8, edges 18, , b) vertices 6, faces 6, edges 10, , c) vertices 9, faces 9, edges 16, d) vertices 8, faces 6, edges 12, 2. (a), (b), (c), UM - 7, , 3. (b), , 21

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6. 11.1 cm, 7.4 cm 7. 12.5 cm, , 9. 7.2 km, , 8. Rs 594, , 10. Rs 24000, , 11. 10.5 cm, 7 cm , , 13. 6.1cm, , 14. 45 cm, , 12. 10 cm, 15 cm , 5 cm, , 15. Rs 12800, , 16. Shakeela covers 60m more, Exercise 14.2, 1. (a) 71 cm, , (b) 34.5 cm, , 2. (a) 45 cm, , (b) 10.5 cm, , 3. (a) 47 cm, , (b) 24 cm, , 4. (a) 88 cm, , (b) 22 cm, , (c) 220 m, , (d) 66 dm, , 5. (a) 7 cm, , (b) 21 dm, , (c) 17.5 dm, , (d) 10.5 mm, , (c) 1350 cm, , 7. 132 m, 21 m, , 6. Rs 3872, , (d) 35.25 cm, , 8. 40 cm, , 9. 40.5 cm, , 10. Rs 5250, , 11. 157 m, , 12. 154 cm, , 13. 50000, , 14. 84 m, , 15. 7 m, , 16. Rs 528, , 17. 1.54 km, , Exercise 14.3, 1. (a) 24.5 cm, , 2, , 2. (a) 24.01 cm, 3. (a) 46 dm, , 2, , 2, , 2, , 4. 12 cm, 8. 55 cm, , 2, , (b) 14 m, 9 2, (b), m, 25, 2, (b) 1.32 m, , (c) 9600 cm, 121 2, (c), m, 169, , 5. 126 m, , 6. 144 cm, , 9. 6.5 cm, , 12. 144.8 m, , 17. 1376 cm, , 20. (a) 13.3 cm, , (b) 15 cm, , 2, , 10. 4 cm, 2, , 18. 173 cm, , (d) 1260 m, , 2, , (d) 102400 cm, 7. 432 m, , 2, , 2, , 11. 240, , 14. 30 m, , 13. Rs 2800, , 16. 16 cm, , 2, , 15. 6 cm, 8 cm , 2, , 19. Rs. 18225, , 21. 12.5 cm, 22. (a) 60 cm, 23. 84 cm, 27. 135, , 2, , 2, , (b) 6000 cm, , 2, , 24. 152.88 m, , 2, , 25. 32, , 26. 625 cm, , 2, , 2, , Exercise 14.4, 1., 2., 3., 4., 5., 6., 8., 9., , 2, , 154 cm, (a) 9.8 cm, (a) 19.6 cm, 326.85 cm, 2, 616 cm, Circle, by 3993, 2, (a) 10.5 cm, 2, 203 cm, , UM - 7, , (b) 61.6 cm, 2, (b) 1207.36 cm (c) Area becomes 4 times, , 2, , cm , 7. 4:9, 2, 2, (b) 129.714 cm (c) 31.5 cm, 2, 10. 22.88 m, 11. 19.796 cm, , (d) 28 cm, 12. 52 m, , 2, , 23

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Exercise 14.5, 1., 2., 6., 7., 9., 10., , 2, , (a) 96 m, Rs 11.25, 2, (a) 875 m, Rs 74800, 2, (a) 4750 m, 2, 1300 cm, , (b), 3., (b), 8., (b), 11., , Rs 480, Rs 2277, 2, 154 m, 2, 61009 m, 2, 90450 m, 2, 2656 m, , 5. 10300 m, (d) 44 m, , 4. Rs 14244, 2, (c) 721 m, , 2, , (c) Rs 2,28,000, , MCQ - IX, 2, , 1. 15 cm, 5. 44 cm, 2, 9. 50 cm, , 2. 200 cm, 2, 6. 2604 m, 10. 16:25, , 3. 88 cm, 7. 8 cm, , 4. 264 m, 2, 8. 196 cm, , 3. 40, 2, 7. 7550 cm, , 4. 5 m, 2, 8. 200 cm, , Revision Exercise, 1., 5., 9., 11., , Rs 3033.84, 44 cm, 14:11, 24:25, 2, (a) 308 m, , 2., 6., 10., (b), , 49 m, 2, 113.14 cm, 100, 2, 2700 m, , 2, , 12. 984 m , Rs 49200, , Chapter 15, , Surface Area and Volumes, , Exercise 15.1, 1. 6 cm, , 2. 6 cm, , 5. (a) 240 cm, 6. (a) 64 cm, , 3, , 3, , 3. 8 cm, , 7. 10 cm, , (c) 3000 cm, , 3, , (c) 15625 mm, , (b) 56250 cm, (b) 3.375 dm, , 4. Rs 2880, , 3, , 3, 3, , (d) 42.875 m, , 8. 156 kg, , 9. 72, , 2. Rs 376, , 3. 88 m , Rs 440, , 3, , 10. 416, , Exercise 15.2, 1. 544 cm, , 2, , 4. 1000 cm, , 2, , 6. (a) 856 cm, 7. 216 cm, , 2, , 5. Rs 8640, 2, , 2, , (b) 376 dm, , 2, , 8. 4750 cm, , 2, , (c) 502000 cm or 50.2 m, 2, , 9. 260 m, , 2, , 2, , 10. Rs 1110, , MCQ - XI, 3, , 1. 180 cm, 5. Rs 3960, 3, 9. 15.625 dm, , 2. 300 m, 6. 5 cm, 10. 2 cm, , 2, , 3. 216 cm, 7. 27 : 1, , 2, , 4. 125, 8. 4, , Revision Exercise, , 24, , 2, , 1. 640, , 2. 27 times, , 3. 30 m, , 5. 90 , , 6. 10, , 7. 25886 cm , 238521 cm, , 8. (a) 12 cm, , (b) 1728 cm, , 9. (a) Rs 11200, , (b) Rs 9000, , 4. 12000 litre, 2, , 3, , (c) 864 cm, , 3, , 2, , 10. 57.6 kg, UM - 7

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Chapter 16, , Data Handling, , Exercise 16.1, 1. (a) , Marks, , Tally Marks, , (b), , 1 , , 5, , 3 , , 15, , 4 , , 20, , 5 , , 3, , 7 , , 5, , 9 , , 1, , 10 , , 141, 142, 143, 147, 148, 149, 150, 151, 152, 153, , (b) 35, Tally Marks, , (c) 15, Frequency, , ||||, |, |, |, ||, ||||, ||||, |, |, |, , 5., , 4., , 4, 1, 1, 1, 2, 4, 4, 1, 1, 1, , Total, , Tally Marks, , 145, |||| ||||, 146, ||||, 147, |||, 148, |||| ||||, 149, |||| |||| ||||, 150, |||| |||| ||||, 151, |||, 152, ||||, Total , , 50, , 2. (a) 20, Heights, , (cms), , 1, , Total, , 3., , Heights, , Frequency, , Frequency, , 9 , 4, 3, 9, 14, 14, 3, 4, 60, , (d) 5, Marks, , 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, 90-100, Total, , Tally Marks, , |||| |||, |||, ||, |||| |, ||||, |||| ||, |||| |||| |, , Frequency, , 8, 3, 2, 6, 5, 7, 9, 40, , 20, , Class interval Tally Marks Frequency, , 10 - 14, ||||, 14 - 18, |||| |||, 18 - 22, |||| |||, 22 - 26, |||| ||, 26 - 30, ||||, 30 - 34, ||||, 34 - 38, |||, Total , 6., , Class interval, , 5, 8, 8, 7, 5, 4, 3, 40, , Tally Marks, , 15 - 20, |||| |||| |||| |, 20 - 25, |||| |||| ||, 25 - 30, |||| |||| |, 30 - 35, |, Total , UM - 7, , Frequency, , 16, 12, 11, 1, 40, , 25

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Exercise 16.2, 1. 9 , 2. 9.625, 3. 39.2, 4. (a) highest marks = 100, lowest marks = 19, , (b) Mean = 64.42 , (c) Range = 81, 5. 1800, 6. (a) 9.33 cm, , (b) 3, , 7. 27.5, , (c) 3, , 8. 50, , 11. 55 , 13., , 9. 9, , (d) 14 cm, 10. 70.25 kg, , 12. 7, Marks, , Numbers of Students, , 30 - 39, 40 - 49, 50 - 59, 60 - 69, 70 - 79, 80 - 89, 90 - 99, 100 - 109, , 2 , , (a), 3, , (b), 8, , (c), 8, , (d), 4, (e), 2, , (f), 2, (g), 1, , 100, 37, 63, 2, 8, 51, 54, 57, 5, , Exercise 16.3, 1. Mode = 28, Median = 21, No, they are not same., 2. Mean = 47, Mode = 12, Median = 13. No, they are not same., 3. Mode = 14, Median = 14, 4. Mode = 16, 5. Mean = 2.7, Median = 3, Mode = 3, 6. Mode = 120, 7. Median = 32, New Median = 35, 8. Mean = 2.4, Median = 2.35, Mode = 2.2, 9. a) False, b) True, c) False, d) True, , e) True, f) False, Exercise 16.4, 1., , Scale 1 unit = 50 marks, , 450, , Marks Obtained, , 400, 350, 300, 250, 200, 150, 100, 50, 0, , 26, , Joy, , John, , Karan, , Akshay, , Students, , Ritu, , Afza, , UM - 7

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2., , Scale 1 unit = 100 books, , 1000, , Maths, , Biology, , 900, 800, , Sales, , 700, 600, 500, 400, 300, , Difference is, least in year, 2004., , 200, 100, 0, , 2002, , 3. (a) Dogs, , 2003, , (b) 5, , 2005, , 2006, , Scale 1 unit = 5 students, , 145, , 4., , 2004, , Years, , 140, No. of Students, , 135, 130, 125, 120, 115, 110, 105, 100, 0, , First, , Second, , Third, , Fourth, , Fifth, , Sixth, , , (a) Fourth class has maximum marks of students., , Third class has minimum numbers of students., , (b) 21 : 25, , No. of People, , 5., , 1700, 1600, 1500, 1400, 1300, 1200, 1100, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 0, , Scale 1 unit = 100 people, Watching, Playing, , Basketball, , , (b) Hockey, UM - 7, , Volleyball, , Hockey, Cricket, Sports, , Tennis, , Golf, , 27

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Revision Exercise, 1., Value, , 2 ., , Tally Marks Frequency, , 12, 13, 14, 15, 16, 17, , ||||, |||| |||| ||, |||| ||||, ||, ||, |, , 4, 12, 9, 2, 2, 1, , Total , 3., , 450, , Tally Marks, , Frequency, , 1-3, , ||||, , 3-5, , |||| ||||, , 10, , 5-7, , |||| |||| |||, , 13, , 7-9, , |||| ||||, , 9, , |||, , 3, , 9 - 11, , 5, , Total , , 30, , (a) 8, , (b) 8, , 40, (c) 13, , Scale 1 unit = 50 students, , 400, , No. of Students, ,   Class interval, , 350, 300, 250, 200, 150, 100, 50, 0, , 4., , 8 - 9, , 9-10, , 10-11, , 11-12, , 12-13, , Time Interval, , 14-15, , Scale 1 unit = 10 students, , 100, 90, , No. of Students, , 13-14, , School A, , 80, , School B, , 70, 60, 50, 40, 30, 20, 10, 0, , VI, , VII, , VIII, , Class, , IX, , X, , 5. (a) The bar graph gives the production of coal, in million tonnes, in, several states during the years 2006 -2007 and 2007-2008., , (b) Bihar and M.P., , (c) U.P. , (d) U.P., , (e) Bihar, West Bengal and M.P., UM - 7, , 29

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6. (a) 9.5, , (b) 50, , 7. 34.4 , , (c) 10.5, , 8. 154.5, , 10. (a) 56, , (b) 53.5, , 11. (a) 4, , (b) 23, , 9. 7, , 12. (a) Mean = 5.4, Median = 6, Mode = 6, , (a) Mean = 44.7, Median = 36, Mode = 21, 13., Item, Food , Electricity , Clothes , Transport , Others , 14., , Sector angle, 120º, 60º, 90º, 60º, 30º, , Electricity, , Books , Mobile Phone, Movies, Games , Food , Misc , , Clothes, , 1000 Others, 2000, , 60º, , 3000, , Transport, Mobile Phone, 150, , Movies, , 200, 100, , Games, , 45º, , 250, , 60º, 30º, , Books, 75º, , 60º, , 200, , 90º, , Misc, , 300, Food, , (July, 550), , (May, 500), , 450, , Sales (In lakh Rs), , 30º, , 90º, , Scale 1 unit = Rs50 lakh, , 500, , 350, , 120º, , 60º, , 75º, 45º, 60º, 30º, 90º, 60º, , 550, , 400, , 4000, , 2000, , Sector angle, , Need, , 15., , Food, , (June, 450), (March, 350), , 300, , (April, 300), , 250, , (August, 300), , 200, 150, 100, 50, 0, , 30, , March, , April, , May, , June, , Month, , July, , August, , UM - 7

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Chapter 17, , Chance and Probability, , Exercise 17.1, (b) Possible, , (c) Possible, , (d) Impossible, , , (e) Impossible, , 1. (a) Certain, , (f) Impossible, , (g) Possible, , (h) Possible, , , (i) Impossible, , (j) Possible, , Exercise 17.2, 5, 1. (a), 11, 3, 2. (a), 13, 1, 3. (a), 2, 1, 4. (a), 6, 2, 6. (a), 21, 1, 7. , 7, 3, 8. (a), 8, 3, , (e), 4, 2, 9., , 5, 2, 12. (a), 5, 1, 14. (a), 2, 1, 15. (a), 3, , (b), (b), (b), (b), (b), , (b), , 6, 11, 4, 13, 1, 2, 1, 6, 4, 21, 5, 12, , (c), , 6, , 13, , (c) 0, (c), , 5, 21, , (c), , 1, 4, , 1, 1, 11., 2, 2, 3, 5, (b), 13. (a), 5, 6, 1, (b), , 3, 2, 2, (b), (c), 9, 9, , 1, , 9, 1, (d) , 3, 5., , (d), , 3, 8, , (b), , 1, 6, , (d), , 1, 9, , 10., , Revision Exercise, 1. (a) Impossible, , (d) Impossible, , (b) Possible, (e) Impossible, , (c) Possible, (f) Certain, , 2. (a) Less likely, , (d) Equally likely, , (b) Less likely, (e) Equally likely, , (c) Equally likely, (f) Highly likely, , 1, (b), 3, 1, (a), (b), 2, 1, , 10, 2, (a), (b), 5, 2, (a), (b), 13, , 3. (a), 4., 5., 6., 7., , UM - 7, , 2, 5, 1, 2, , 1, 2, 4, 13, , (c) 0, (c), , 1, 2, , 1, 5, 5, (c), 13, (c), , 11, , 15, 1, (d), 2, , (d), , 7, (d) 10, (d), , 2, 13, , 31

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Chapter 18, , Coordinates and Graphs, , Exercise 18.1, 1., , Y, 7 0, 7, 6, , 2, 5, , 5, 4, 3, , –3, 2, X’, , 2, 1, , –4, 0, –7 –6 –5 –4 –3 –2 –1, , 7, 0, , o, , 1, , 2, , 3, , 4, , 5, , 6, , 7, , X, , –1, –2, –3, –4, , –5, –7, , 4, –3, 7, –4, , 0, –4, , –5, –6, –7, Y’, , 2., , 3., , Y, , –2, 1, A, X’, , –5 –4 –3 –2 –1, , Y, , 5, , 5, , 4, , 4, , 3, , 1, , 2, , 3, , 4, , X, , 5, , 1, , X’, , –5 –4 –3 –2 –1, , –1, , o, , 1, , 2, , 3, , 0, 4, A, 4 5, , –2, , –2, , –3, , –3, , –4, , –4, , –5, , –5, , Y’, , Y’, , b) (7, 0), , c) (0, 7), , d) (–3, 0), , e) (–4, 3), , f) (0, –5), , g) (–2, –4), , h) (3, –6), , i) (7, –3), , j) (7, 6), , 5. a) Yes, , b) No, , 6. a) , Y, , b), , 3, , 3, , 2, , 2, , –3 –2 –1 o, –1, , 1, , –2, –3, , 32, , Y, , 1, , 1, X’, , X, , –1, , The figure is triangle., 4. a) (3, 1), , C 5, 4, , 2, , 1, , o, , 5, 0, , 3, , B 3, 2, , 2, , B, , 2, , 3, , X, , X’, , –3 –2 –1 o, –1, , 1, , 2, , 3, , 4, , 5, , 6, , X, , –2, Y’, , –3, , Y’, , UM - 7

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Y, , d), , c) , 3, , X’, , –4 –3 –2, , 2, , 3, , 1, , 2, , –1 o, , 1, , –1, , 1, , 2, , X’, , –2, –3, , Y, , 8., , 2, , 3, , 4, , 5, , 6, , X, , 12, , –3, , Y, , Y’, , 11, 10, 9, , 1, –3 –2 –1 o, –1, , 1, , –2, , 2, X’, , –4 –3 –2 –1 o, –1, , Y’, , 7. , 3, , Y, , 4, , 8, , 1, , 2, , 3, , X, , 7, 6, 5, , –2, , 4, , –3, , 3, , Y’, , (a) (–5, –4), (b) (7, 2), , Y, , Yes, (3, 3) lies on, the line., , 2, 1, X’, , –4 –3 –2 –1 o, –1, –2, , 1, , 2, , 3, , 4, , X, , Y’, , Chapter 19, , Sets, , Exercise 19.1, 1. (a) No, (b) No, (c) No, (d) No, , (e) No, (f) Yes, 2. (a) True, (b) True, (c) False, (d) True, , (e) False, 3. (a) A = {6, 7, 8, 9, 10, 11, 12, 13, 14}, , (b) B = {I, J, K, L, M, N}, (c) C = {–3, –2, –1, 0, 1, 2, 3, 4, 5}, , (d) D = {P, E, R, M, U, T, A, I, O, N, S}, 4. (a) A= { x: x is an odd number and 0 < x < 8 }, (b) B= { x : x is an even positive number and 0 < x < 13 }, (c) C= { x : x is positive multiple of 4 and 0 < x < 25 }, (d) D= { x : x is square of N and 0 < N < 5 }, 5. (a) No, (b) Yes, (c) Yes, 6. (a) Finite, (b) Infinite, (c) Finite, (d) Infinite, 7. (a) 2, (b) 3, (c) 0, (d) 1, , (e) 0, (f) 5, 8. A = B = C, D = G = H, E = F, UM - 7, , 9. A and B, D and E., , 33

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Exercise 19.2, 1. (a) { }, {–1}, {0}, {1}, {–1, 0}, {–1, 1}, {0, 1}, {–1, 0, 1}, (b) { }, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c }, {b, d}, {c, d}, {a, b, c},, {a, b, d}, {b, c, d}, {a, b, c, d}, {a, c, d}, (c) { }, {+}, {–}, {+, –}, 2. (a) False, , (e) False, 3. (a) 7, , (b) True, , (c) True, , (d) False, , (f) True, , (g) False, , (h) False, , (b) 32, , (c) { }, {a}, {b}, {c}, {a, b}, {b, c}, {a,c}, , 4. (a) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, , (c) {x : x is a circle} , , (b) {x : x is a triangle}, (d) {x : x is a quadrilateral}, , Exercise 19.3, 1. (a) {1, 2, 3, 4, 5, 7, 9}, , (b) {1, 2, 3, 4, 5, 7, 8, 9, 10}, , , (c) {1, 2, 3, 4, 5, 8, 10}, 2. (a) {5}, , (b) {5, 8}, , (c) {5}, , 3. (a) {x : x is an even natural number} or {2, 4, 6, 8, ...}, , (b) {x : x is a natural number} or {1, 2, 3, 4, ...}, , (c) {x : x is an odd natural number} or {1, 3, 5, 7, ...}, , (d) {x : x is a prime number} or {2, 3, 5, 7, 11, 13, ...}, (e) { }, , (f) {x : x is an even prime number} or {2}, , (g) {x : x is an odd natural number} or {3, 5, 7, 11, 13, ...}, , (h) {x : x is a natural number}, 4. (a) No, , (b) Yes, , (c) Yes, , 5. (a) {10, 11, 12, 13, 15, 16, 17, 18, 19} , , (b) {10, 15}, , (c) {10, 15, 16} (d) {11, 13, 14, 17, 18, 20}, , (e) {12, 19}, , (f) {14, 20}, , (g) {14, 20}, , (h) {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}, , (i) {12, 19}, , (j) {10, 11, 13, 14, 15, 16, 17, 18, 20}, (k) {11, 13, 14, 17, 18, 20}, , (l) {14, 20}, , 7. (a) {5, 6, 7, 8, 9} , , (b) {1, 2, 5, 6, 7, 8, 9}, , , (c) {1, 2, 3, 4} , , (d) {1, 3, 4, 5, 6, 7, 9}, , 8. (a) {1, 2, 3, 4, 5, 6, 7, 8, 11}, , (b) {2, 3, 7}, , (c) {1, 8}, , Exercise 19.4, 1. 10 , , 2. 16, , 3. 50, , 4. 24, , 5. 200, 50, 140, , 6. 125, 275, 75, , 7. English-40, Only English-15, , 8. 30, , 34, , UM - 7

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9. 19, 10. (a) 26, , (b) 16, , (c) 22, , 11. (a) È = {a, b, c, d, e, f, g, h, i, j, k, l, m, n}, , (b) A = {a, b, d, e, f, i}, , (c) B = {a, c, d, g, k}, , (d) AÈB = {a, b, c, d, e, f, g, i, k}, (e) A’ = {c, g, h, j, k, l, m, n}, , (f) AÇB = {a, d}, , (g) B - A = {c, g, k} , , (h) (AÈB)’ = {h, j, l, m, n}, , (i) (AÇB)’ = {b, c, e, f, g, h, i, j, k, l, m, n}, (j) A – B = {b, e, i, f}, 12., 2, , 4, 16, , 8, 20, , 10, , , (a), (b), (c), , (d), , U, , B, , A, , 12, 24, , 22, , 6, , 14, , 30, 18, 26, , A’ = {2, 6, 10, 14, 18, 22, 26, 30}, B’ = {2, 4, 8, 10, 14, 16, 20, 22, 26, 28}, AÈB = {4, 6, 8, 12, 16, 18, 20, 24, 28, 30}, AÇB = {12, 24}, , Chapter 20, , Relation and Mapping, , Exercise 20.1, 1. x = 2, y = 1, 2. x = 3, y = –1, 3. (a) R = {(-1, 2), (0, 1), (2, 5)} Range = {2, 1, 5}, , (b) R = {(1,2), (2,4), (3,6), (4,8), (5,10), (6,12), (7,14), (8,16), (9,18),, , , (10,20)}, , 4. R = {(3, 2), (4, 2), (5, 2), (6, 2), (6, 5), 5. (a) It is a mapping., , 2, 3, 4, 5, 6, , 2, 5, 6, , (b) It is not a mapping., (c) It is a mapping., UM - 7, , 35

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6. (a) R = {(1, 3), (1, 7), (2, 2), (2, 10)}, Domain = {1, 2}, Range = {2, 3, 7, 10}, , , (b) R = {(1, 3), (1, 7), (3, 3), (3, 7), (7, 3), (7, 7)}, Domain = {1, 3, 7}, Range = {3, 7}, , , (c) R = {(1, 2), (1, 10), (2, 3), (2, 7), (3, 2),, , , (3, 10), (7, 2), (7, 10), (8, 3), (8, 7)}, , Domain = {1, 2, 3, 7, 8}, Range = {2, 3, 7, 10}, , , (d) R = {(2, 2), (2, 10), (8, 2), (8, 3), (8, 7), (8, 10) }, Domain = {2, 8}, Range = {2, 3, 7, 10}, , 1, 2, 3, 7, 8, , 1, 2, 3, 7, 8, , 1, 2, 3, 7, 8, , 1, 2, 3, 7, 8, , 2, 3, 7, 10, , 2, 3, 7, 10, , 2, 3, 7, 10, , 2, 3, 7, 10, , Revision Exercise, 1. (a) A = {–2, –1, 0, 1, 2, 3, 4, 5, 6}, (b) B = {18, 27, 36, 45, 54, 63, 72, 81, 90}, (c) C = {T, R, I, G, N, O, M, E, Y}, (d) D = {2, 3, 5}, 2. (a) A = {x : x is a cube of a natural number less upto 10}, (b) B = {x : x is one of the first ten multiples of 3}, (c) C = {x : x is a letter of the word GEOGRAPHY}, (d) D = {x : x is a symbol for the operations of addition, subtraction,, division and multiplication}, 3. (a) Subsets of A are : f, {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5}, {2, 3, 5}, (b) Subsets of B are : f, {m}, {n}, {o}, {m, n}, {m, o}, {n, o}, {m, n, o}, (c) Subsets of C are : f, {H}, {T}, {H, T}, 4. (a) {3, 5, 7, 9, 11, 13} , , (b) {11, 13} , , , (c) { } , , (d) {7, 9, 11}, , (e) {3, 5, 7, 9} , , (f) {13} , , , (g) {7, 9, 11} , , (h) {3, 5, 7, 9}, , 36, , UM - 7

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5. (a), (b), (c), (d), , =, =, =, =, , {1,, {1,, {2,, {1,, , 4,, 3,, 3,, 5,, , 9,, 5,, 5,, 7,, , 16}, 7, 9, 11, 13, 15, 17, 19}, 7, 11, 13, 17, 19}, 11, 13, 17, 19}, U, , 6. a) , A, , b), , U, , B, , B, A, , c) , , d), U, , A, , 7. (a), (b), (c), (d), (e), (f), (g), (h), (i), , U, A, , B, , B, , {b, c, f, g, m, u}, {a, c, g, h, i}, {a, b, c, d, f, g, h, i, m, n, u}, {b, f, m, u}, {a, h, i}, {a, b, c, f, g, h, i, m, u}, {c, g}, {a, d, h, i, n}, {d, n}, U, A, , 8. 48, , 23, , B, 12, , 13, , 9. a) R = {(1, 2), (1, 5), (1, 8), (2, 4), (2, 7), (5, 4), (5, 7), (8, 4), (8, 7)}, Domain of R = {1, 2, 5, 8}, A, B, 2, 1, Range of R = {2, 5, 7, 8}, 4, 2, 5, 3, 5, 7, 6, 8, 8, UM - 7, , 37

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A, , b) R = {(2, 2), (5, 5), (8, 8)}, Domain of R = {2, 5, 8}, Range of R = {2, 5, 8}, , A, , c) R = {(1, 2), (2, 4)}, Domain of R = {1, 2}, Range of R = {2, 4}, , 1, 2, 3, 5, 6, 8, , 2, 4, 5, , 1, 2, 3, 5, 6, 8, , 2, 4, 5, , B, , 7, 8, , B, , 7, 8, , Sample Paper, Section - A, 1. 11 , , 2. 6, , 3. 264 cm, , 4. A = {2, 3, 5, 7}, , 5. , , 6. 5, , 7. 21, , 8., , 3, 5, , 5., , 31, 4, , 9. ÄABC À ÄRPQ 10., , 2 cm, A, D, , 5 cm, B, , C, , Section - B, 2, , 1. 998001, , 2. 8x – 18y, , 2, , 3. 3, , 1, year, 2, , Y, , Section - C, 1., 5, 4, 3, 2, X’, , 1, –3 –2 –1, , o, , 1, , 2, , 3, , 4, , 5, , 6, , X, , –1, –2, Y’, , 38, , UM - 7

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3. x = 56, y = 54, z = 70, , 2. Loss, 4%, 6., , A, , B, , 2, 5, 8, 12, 15, , 7, 11, 14, 20, , 7. 13 m, , 8. a), 3, , 2, , 9. a) 7x – 3x – 4x – 4, , 4. 14:11 or 10 cm, , Domain = {8, 12, 15}, Range = {7, 11, 14), , 16, 81, , 3, 25, 12, b) 5x + 6y –, 5, , b), , 10. 1000, Section - D, 1. a) 808 m, , 2, , , a) 198 m, , 2, , b) Rs 40400, b) Rs 27800, , c) 5192 m, c) 480 m, , 2, , 3, , or, 2. 63, , 3. mean = 64, median = 65, mode = 50, , 4. a), b), c), , d), , e), , AUB = {1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 17, 19, 23, 24}, A–C = {2, 3, 5, 7, 23}, B’ÇC’ = {5, 7, 9, 21, 22, 23}, AÇ (BUC) = {2, 3, 11, 13, 17, 19}, AU (B–C) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 19, 23, 24}, or, a) 200, B, A, 600 200 700, b) 600, c) 700, 5. a) Rs. 9900, 9, 2, , 6. a), , b) Rs. 7920, , c) Loss 12%, , b) 153.6, , Mental Ability Test, 1. 129 , 5. 34 , 9. 57 , 13. , , 17. 320 cm, UM - 7, , 2., 6., 10., 14., , 2, , 7, 5, 2, 360 cm, 66, , 18. 112 cm, , 2, , 3., 7., 11., 15., , 32, 32, y, 125º, 55º, , 19. 112, , 4., 8., 12., 16., , 54, 6, 3, 3 + 3 +3, 40 km, , 20. 62.4 litre, , 39