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ANSWERS/HINTS 357 5. 40 3 m 6. 19 3 m ✁ 7. 20 3 1 m 0.8 3 1 m 9. 2 16 m 7 3 1 m 3 10. 20 3m,20m,60m 11. 10 3 m, 10m 12. ✝ ✞ 8. ✄ ☎ ✆ ✂ ✟ 13. 50 3 m 14. 294 3m 5 15. 3 seconds EXERCISE 10.1 1. Infinitely many 2. (i) One (ii) Secant (iii) Two (iv) Point of contact 3. D EXERCISE 10.2 1. A 2. B 3. A 6. 3 cm 7. 8 cm 12. AB = 15 cm, AC = 13 cm EXERCISE 12.1 1. 28 cm 2. 10 cm 3. Gold : 346.5 cm 2 ; Red : 1039.5 cm 2 ; Blue : 1732.5 cm 2 ; Black : 2425.5 cm 2 ; White : 3118.5 cm 2 . 4. 4375 5. A EXERCISE 12.2 1. 132 cm 2 7 2. 77 cm 2 8 4. (i) 28.5 cm 2 (ii) 235.5 cm 2 5. (i) 22 cm (ii) 231 cm 2 (iii) 3. 154 cm 2 3 6. 20.4375 cm 2 ; 686.0625 cm 2 7. 88.44 cm 2 ✠ ☞ ✍ 441 ✡ 3 231 cm 4 ☛ ✌ ✎ 2 8. (i) 19.625 m 2 (ii) 58.875 cm 2 9. (i) 285 mm (ii) 10. 22275 cm 2 28 11. 13. Rs 162.68 14. D 158125 cm 2 126 385 mm 2 4 12. 189.97 km 2
358 MATHEMATICS EXERCISE 12.3 1. 4523 cm 2 28 2. 154 cm 2 3 3. 42 cm 2 4. 660 7 ✂ ✁ 36 ☎ 3 cm 2 ✄ ✝ 5. 68 cm 2 7 6. 22528 ✞ ✟ 768 ✠ ✡ ☛ 3 cm 7 ☞ ✌ 2 ✆ 7. 42 cm 2 8. (i) 2804 m 7 (ii) 4320 m 2 9. 66.5 cm 2 10. 1620.5 cm 2 11. 378 cm 2 12. (i) 77 cm 2 8 (ii) 49 cm 2 8 13. 228 cm 2 14. 308 cm 2 3 15. 98 cm 2 16. 256 cm 2 7 EXERCISE 13.1 ✍ ✎ ✒ ✓ ✂ ✓ ✂ ✓ ✄ ☎ ✆ ✝ Required Volume = ✔ ✕ 1. 160 cm 2 2. 572 cm 2 3. 214.5 cm 2 4. Greatest diameter = 7 cm,surface area = 332.5 cm 2 1 2 5. 24 4 l 6. 220 m 2 7. 44 m 2 , Rs 22000 8. 18 cm 2 9. 374 cm 2 EXERCISE 13.2 1. cm 3 2. 66 cm 3 . Volume of the air inside the model = Volume of air inside (cone + cylinder + cone) = 1 2 2 1 2 rh , 1 rh2 rh1 where r is the radius of the cone and the cylinder, h 3 3 1 is the height (length) of the cone and h 2 is the height (length) of the cylinder. 1 2 1 3 2 1 3 r h h h . 3. 338 cm 3 4. 523.53 cm 3 5. 100 6. 892.26 kg 7. 1.131 m 3 (approx.) 8. Not correct. Correct answer is 346.51 cm 3 .
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Foreword Preface Contents 1. Real N
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xi 9. Some Applications of Trigonom
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REAL NUMBERS 1 1.1 Introduction In
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REAL NUMBERS 3 moment we write down
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REAL NUMBERS 5 This algorithm works
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REAL NUMBERS 7 EXERCISE 1.1 1. Use
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REAL NUMBERS 9 An equivalent versio
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REAL NUMBERS 11 So, HCF (6, 72, 120
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3 = a b ✂ REAL NUMBERS 13 Substit
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REAL NUMBERS 15 1.5 Revisiting Rati
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REAL NUMBERS 17 We are now ready to
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REAL NUMBERS 19 You have seen that
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POLYNOMIALS 21 a cubic polynomial a
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POLYNOMIALS 23 Table 2.1 x - 2 -1 0
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POLYNOMIALS 25 Case (iii) : Here, t
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POLYNOMIALS 27 Note that 0 is the o
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a = k, b =- k(✞ + ✟) and c = k
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POLYNOMIALS 31 Example 4 : Find a q
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POLYNOMIALS 33 EXERCISE 2.2 1. Find
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POLYNOMIALS 35 Solution : Note that
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POLYNOMIALS 37 3. If the zeroes of
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PAIR OF LINEAR EQUATIONS IN TWO VAR
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QUADRATIC EQUATIONS 71 Sridharachar
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QUADRATIC EQUATIONS 73 (ii) Since x
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QUADRATIC EQUATIONS 75 Note that we
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QUADRATIC EQUATIONS 77 Therefore, (
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QUADRATIC EQUATIONS 79 So, 9x 2 - 1
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QUADRATIC EQUATIONS 81 Therefore, t
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QUADRATIC EQUATIONS 83 If b 2 - 4ac
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QUADRATIC EQUATIONS 85 x = 3 25 2 B
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QUADRATIC EQUATIONS 87 Example 15 :
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QUADRATIC EQUATIONS 89 b b b If b 2
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QUADRATIC EQUATIONS 91 EXERCISE 4.4
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ARITHMETIC PROGRESSIONS 5 5.1 Intro
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ARITHMETIC PROGRESSIONS 95 In the e
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ARITHMETIC PROGRESSIONS 97 Similarl
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ARITHMETIC PROGRESSIONS 99 (iv) a 2
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ARITHMETIC PROGRESSIONS 101 Now, lo
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ARITHMETIC PROGRESSIONS 103 Example
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ARITHMETIC PROGRESSIONS 105 It is a
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ARITHMETIC PROGRESSIONS 107 17. Fin
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ARITHMETIC PROGRESSIONS 109 Here, a
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ARITHMETIC PROGRESSIONS 111 Therefo
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ARITHMETIC PROGRESSIONS 113 4. How
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ARITHMETIC PROGRESSIONS 115 EXERCIS
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TRIANGLES 6 6.1 Introduction You ar
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TRIANGLES 119 What can you say abou
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TRIANGLES 121 From the above, you c
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TRIANGLES 123 6.3 Similarity of Tri
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TRIANGLES 125 Therefore, from (1),
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TRIANGLES 127 Example 2 : ABCD is a
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TRIANGLES 129 5. In Fig. 6.20, DE |
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TRIANGLES 131 Let rays BP and CQ in
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TRIANGLES 133 Cut DP = AB and DQ =
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TRIANGLES 135 Now, PQ || EF and ABC
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TRIANGLES 137 Now, BD = 1.2 m × 4
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TRIANGLES 139 Fig. 6.34 2. In Fig.
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TRIANGLES 141 11. In Fig. 6.40, E i
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TRIANGLES 143 Example 9 : In Fig. 6
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TRIANGLES 145 So, from (1) and (2),
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TRIANGLES 147 So, ✁ ✂ ✂ ✂ B
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TRIANGLES 149 or, BL 2 = ✄ AC 2
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TRIANGLES 151 8. In Fig. 6.54, O is
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TRIANGLES 153 (ii) AB 2 = AD 2 - BC
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COORDINATE GEOMETRY 7 7.1 Introduct
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COORDINATE GEOMETRY 157 Therefore,
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COORDINATE GEOMETRY 159 Also, PQ 2
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COORDINATE GEOMETRY 161 So, the req
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COORDINATE GEOMETRY 163 Draw AR, PS
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COORDINATE GEOMETRY 165 Therefore,
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COORDINATE GEOMETRY 167 EXERCISE 7.
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COORDINATE GEOMETRY 169 Example 11
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COORDINATE GEOMETRY 171 EXERCISE 7.
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INTRODUCTION TO TRIGONOMETRY 8 8.1
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INTRODUCTION TO TRIGONOMETRY 175 No
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INTRODUCTION TO TRIGONOMETRY 177 Fr
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INTRODUCTION TO TRIGONOMETRY 179 Th
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INTRODUCTION TO TRIGONOMETRY 181 EX
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INTRODUCTION TO TRIGONOMETRY 183 As
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INTRODUCTION TO TRIGONOMETRY 185 Ta
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INTRODUCTION TO TRIGONOMETRY 187 1.
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INTRODUCTION TO TRIGONOMETRY 189 Ex
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INTRODUCTION TO TRIGONOMETRY 191 Is
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INTRODUCTION TO TRIGONOMETRY 193 =
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SOME APPLICATIONS OF TRIGONOMETRY 9
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CIRCLES 207 You might have seen a p
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CIRCLES 209 Take a point Q on XY ot
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CIRCLES 211 Theorem 10.2 : The leng
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CIRCLES 213 Now, TPR + RPO = 90° =
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CIRCLES 215 10.4 Summary In this ch
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CONSTRUCTIONS 217 Let us see how th
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CONSTRUCTIONS 219 Solution : Given
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CONSTRUCTIONS 221 Steps of Construc
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AREAS RELATED TO CIRCLES 12 12.1 In
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AREAS RELATED TO CIRCLES 225 You ca
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AREAS RELATED TO CIRCLES 227 In a w
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AREAS RELATED TO CIRCLES 229 Soluti
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AREAS RELATED TO CIRCLES 231 10. An
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AREAS RELATED TO CIRCLES 233 Altern
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AREAS RELATED TO CIRCLES 235 2. Fin
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AREAS RELATED TO CIRCLES 237 11. On
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SURFACE AREAS AND VOLUMES 13 13.1 I
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SURFACE AREAS AND VOLUMES 241 First
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SURFACE AREAS AND VOLUMES 243 Examp
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SURFACE AREAS AND VOLUMES 245 7. A
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SURFACE AREAS AND VOLUMES 247 Examp
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SURFACE AREAS AND VOLUMES 249 How a
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✁ ✂ ✂ ☎ ✄ SURFACE AREAS A
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SURFACE AREAS AND VOLUMES 253 How c
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SURFACE AREAS AND VOLUMES 255 So, t
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SURFACE AREAS AND VOLUMES 257 Now,
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SURFACE AREAS AND VOLUMES 259 3. Gi
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STATISTICS 261 x = n ✁ fx i 1 n i
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STATISTICS 263 Table 14.3 Class int
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STATISTICS 265 Substituting the val
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STATISTICS 267 Example 2 : The tabl
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STATISTICS 269 Example 3 : The dist
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STATISTICS 271 4. Thirty women were
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STATISTICS 273 Clearly, 2 is the nu
Page 280 and 281: STATISTICS 275 of the students. In
Page 282 and 283: STATISTICS 277 14.4 Median of Group
Page 284 and 285: STATISTICS 279 From the table above
Page 286 and 287: STATISTICS 281 Table 14.14 Marks ob
Page 288 and 289: STATISTICS 283 Example 7 : A survey
Page 290 and 291: STATISTICS 285 Solution : Class int
Page 292 and 293: STATISTICS 287 EXERCISE 14.3 1. The
Page 294 and 295: STATISTICS 289 5. The following tab
Page 296 and 297: STATISTICS 291 Remark : Note that b
Page 298 and 299: STATISTICS 293 EXERCISE 14.4 1. The
Page 300 and 301: PROBABILITY 15 The theory of probab
Page 302 and 303: PROBABILITY 297 For another example
Page 304 and 305: PROBABILITY 299 Solution : Kritika
Page 306 and 307: PROBABILITY 301 That is, the probab
Page 308 and 309: PROBABILITY 303 Example 7 : There a
Page 310 and 311: PROBABILITY 305 Let E be the event
Page 312 and 313: PROBABILITY 307 4 6 5 4 6 5 1 2 3 4
Page 314 and 315: PROBABILITY 309 10. A piggy bank co
Page 316 and 317: PROBABILITY 311 25. Which of the fo
Page 318 and 319: ANSWERS/HINTS EXERCISE 1.1 1. (i) 4
Page 320 and 321: ANSWERS/HINTS 347 his daughter. To
Page 322 and 323: ANSWERS/HINTS 349 EXERCISE 3.5 1. (
Page 324 and 325: ANSWERS/HINTS 351 5. Marks in mathe
Page 326 and 327: ANSWERS/HINTS 353 n 4. 12. By putti
Page 328 and 329: ANSWERS/HINTS 355 3. 61m; 5th line
Page 332 and 333: ANSWERS/HINTS 359 EXERCISE 13.3 1.
Page 334 and 335: ANSWERS/HINTS 361 EXERCISE 15.1 1.
Page 336 and 337: ANSWERS/HINTS 363 ✆ ✂ ✂ ✂ 2
Page 338 and 339: PROOFS IN MATHEMATICS A1 A1.1 Intro
Page 340 and 341: PROOFS IN MATHEMATICS 315 (v) Some
Page 342 and 343: PROOFS IN MATHEMATICS 317 used to d
Page 344 and 345: PROOFS IN MATHEMATICS 319 Number of
Page 346 and 347: PROOFS IN MATHEMATICS 321 4. Using
Page 348 and 349: PROOFS IN MATHEMATICS 323 Remark :
Page 350 and 351: PROOFS IN MATHEMATICS 325 For examp
Page 352 and 353: PROOFS IN MATHEMATICS 327 In genera
Page 354 and 355: PROOFS IN MATHEMATICS 329 2. Write
Page 356 and 357: PROOFS IN MATHEMATICS 331 Since np
Page 358 and 359: PROOFS IN MATHEMATICS 333 EXERCISE
Page 360 and 361: MATHEMATICAL MODELLING 335 (v) Pred
Page 362 and 363: MATHEMATICAL MODELLING 337 For inst
Page 364 and 365: MATHEMATICAL MODELLING 339 A2.3 Som
Page 366 and 367: MATHEMATICAL MODELLING 341 Example
Page 368 and 369: MATHEMATICAL MODELLING 343 3. A T.V
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