1.Algebra Booster

Recommendations

Info

Matrices and Determinants 7.33 4. We have, X 2 5 3 6 + Ê ˆ Ê ˆ Á = Ë3 -2 ˜ ¯ Á Ë2 7 ˜ ¯ fi fi 5. Clearly, fi and fi X 3 6 2 5 = Ê ˆ Ê ˆ Á - Ë2 7 ˜ ¯ Á Ë3 -2 ˜ ¯ X 1 1 = Ê ˆ Á Ë-1 9 ˜ ¯ 1 ÊÊ2 5 ˆ Ê4 2 ˆˆ X = 2 ÁÁ + 3 2 ˜ Á 8 2 ˜ ËË - ¯ Ë - ¯˜ ¯ 1 Ê 6 7 ˆ Ê 3 7/2ˆ X = 2 Á = Ë11 -4 ˜ ¯ Á Ë11/2 -2 ˜ ¯ 1 ÊÊ2 5 ˆ Ê4 2 ˆˆ Y = 2 ÁÁ - 3 2 ˜ Á 8 2 ˜ ËË - ¯ Ë - ¯˜ ¯ 1 Ê-2 3ˆ Ê -1 3/2ˆ Y = 2 Á = Ë-5 0 ˜ ¯ Á Ë-5/2 0 ˜ ¯ 6. Given A + 2B + X = O fi X = –(A + 2B) ÊÊ2 -1ˆ Ê-1 1ˆˆ =- Á + 2 Ë Á Ë3 5˜ ¯ Á Ë 0 2˜ ¯˜ ¯ ÊÊ2 -1ˆ Ê-2 2ˆˆ =- Á + Ë Á Ë3 5˜ ¯ Á Ë 0 4˜ ¯˜ ¯ Ê0 1ˆ Ê 0 -1ˆ =- Á = Ë3 9˜ ¯ Á Ë-3 -9˜ ¯ Ê 7. Given || x 2 ˆ Ê< 3 2 ˆ Á = Ë 5 | y - 2| ˜ ¯ Á Ë 5 < 4 ˜ ¯ fi |x| < 2, |y – 2| < 3 fi –2 < x < 2, –3 < (y – 2) < 3 fi –2 < x < 2, –1 < y < 5 8. We have Ê 3 x - 3x+ 2 2 ˆ Ê0 2ˆ Á 3 2 ˜ = Á 3 y 7y 35 Ë3 1 ˜ Ë + - ¯ ¯ x 3 – 3x + 2 = 0, y 3 + 7y 2 – 35 = 1 x 3 – 3x + 2 = 0, y 3 + 7y 2 – 36 = 1 Now, x 3 – 3x + 2 = 0 fi x 3 – x 2 + x 2 – x – 2x + 2 = 1 fi x 2 (x – 1) + x(x – 1) – 2(x – 1) = 0 fi (x – 1)(x 2 + x – 2) = 0 fi (x – 1)(x + 2)(x – 1) = 0 fi (x – 1) 2 (x + 2) = 0 fi x = 1, –2 Also, y 3 + 7y 2 – 36 = 0 fi y 3 – 2y 2 + 9y 2 – 18y + 18y – 36 = 1 fi y 2 (y – 2) + 9y(y – 2) + 18(y – 2) = 0 fi (y – 2)(y 2 + 9y + 18) = 0 fi (y – 2)(y + 3)(y + 6) = 0 fi y = 2, –3, –6 Thus, S(x + y) = (1 – 2 + 2 – 3 – 6) = –8 9. We have Êx yˆ Ê1 -2ˆ Ê3 5ˆ 2Á + 3 = 4 Ëz t ˜ ¯ Á Ë0 4 ˜ ¯ Á Ë4 6 ˜ ¯ Êx yˆ Ê3 5ˆ Ê1 -2ˆ fi 2Á = 4 -3 Ëz t ˜ ¯ Á Ë4 6 ˜ ¯ Á Ë0 4 ˜ ¯ fi Ê2x 2yˆ Ê12 20ˆ Ê3 -6ˆ Á = - Ë2z 2t ˜ ¯ Á Ë16 24 ˜ ¯ Á Ë0 12 ˜ ¯ Ê 9 26ˆ = Á Ë16 12 ˜ ¯ fi x = 9/2, y = 13, z = 8, t = 6 10. Let Ê2 3ˆ Ê-1 2 ˆ A= Á and B= Ë4 0 ˜ ¯ Á Ë 1 -5 ˜ ¯ Solving, we get 1 1 X = (3B - 2 A) and Y = (3A-2 B) 5 5 1 ÊÊ-3 6 ˆ Ê4 6ˆˆ Thus, X = 5 ÁÁ - 3 15 ˜ Á 8 0 ˜ ËË - ¯ Ë ¯˜ ¯ fi and fi 11. Given 1 Ê-7 0 ˆ Ê-7/5 0 ˆ X = 5 Á = Ë-5 -15 ˜ ¯ Á Ë -1 -3 ˜ ¯ 1 ÊÊ 6 9ˆ Ê-2 4 ˆˆ Y = 5 ÁÁ - 12 0 ˜ Á 2 10 ˜ ËË ¯ Ë - ¯˜ ¯ 1 Ê 8 5ˆ Ê8/5 1ˆ Y = 5 Á = Ë10 10 ˜ ¯ Á Ë 2 2 ˜ ¯ Ê2 0ˆ A = Á Ë0 2 ˜ ¯ Ê1 0ˆ = 2Á = 2I Ë0 1 ˜ ¯ We have, f(x) = 1 + x + x 2 + … to 1 = 1 - x fi I f( A) = I - A I = I - 2I I =- I 2 I =- I =-I
7.34 Algebra <strong>Booster</strong> 12. Then AB = [1 ¥ 2 + 2 ¥ 3] = [8] 13. Then AB = [a ¥ a 2 + b ¥ b 2 + c ¥ c 2 ] = [a 3 + b 3 + c 3 ] 1 2 2 4 14. Then AB = Ê ˆ Ê ˆ Á ¥ Ë3 4 ˜ ¯ Á Ë5 7 ˜ ¯ Ê1.2 + 2.5 1.4 + 2.7ˆ = Á Ë3.2 + 4.5 3.4 + 4.7 ˜ ¯ Ê12 18ˆ = Á Ë26 40 ˜ ¯ Also, Ê2 4ˆ Ê1 2ˆ Ê2.1 + 4.3 2.2 + 4.7ˆ Á ¥ Ë5 7 ˜ ¯ Á Ë3 4 ˜ = ¯ Á Ë5.1 + 7.3 5.2 + 7.4 ˜ ¯ Ê14 32ˆ = Á Ë26 38 ˜ ¯ Thus, AB π BA Clearly, the matrix multiplication is not commutative. 15. Given A is a 2 ¥ 3 matrix and AB is a 2 ¥ 5 matrix. Thus, B is a matrix of 3 ¥ 5. 16. Clearly, the matrix multiplication is not defined. 1 0 17. Given A = Ê ˆ Á Ë-1 1 ˜ ¯ Now, A 2 = A.A Ê 1 0ˆ Ê 1 0ˆ = Á ¥ Ë-1 1 ˜ ¯ Á Ë-1 1 ˜ ¯ Ê 1 0ˆ = Á Ë-2 1 ˜ ¯ Also Ê 1 0ˆ Ê 1 0ˆ Ê1 0ˆ A 2 – 2A + I 2 = Á - 2 + Ë-2 1 ˜ ¯ Á Ë-2 1 ˜ ¯ Á Ë0 1 ˜ ¯ Ê 1 0 ˆ Ê–2 0 ˆ Ê1 0ˆ = Á + + Ë-2 1 ˜ ¯ Á Ë 2 –2 ˜ ¯ Á Ë0 1 ˜ ¯ Ê0 0ˆ = Á Ë0 0 ˜ ¯ = 0 Hence, the result 18. We have, Ê1ˆ AB = Á2 ˜(2 Á ˜ 3 4) Ë3¯ Ê2 3 4ˆ = Á4 Á 6 8˜ ˜ Ë6 9 12¯ Also, Ê1ˆ BA = (2 3 4) Á2˜ Á ˜ Ë3¯ = (2 + 6 +12) = (20) 19. We have, Ê2 3ˆÊ2 3ˆ A 2 = A.A = Á Ë4 1 ˜Á ¯Ë4 1 ˜ ¯ Ê4+ 12 6+ 3ˆ Ê16 9ˆ = Á = Ë 8 + 4 12 + 1 ˜ ¯ Á Ë12 13 ˜ ¯ Now, A 3 = A 2 .A Ê16 9 ˆÊ2 3ˆ = Á Ë12 13 ˜Á ¯Ë4 1 ˜ ¯ Ê32 + 36 48 + 9 ˆ Ê68 57ˆ = Á = Ë24 + 52 36 + 39 ˜ ¯ Á Ë76 69 ˜ ¯ Also, A 4 = A 3 .A Ê68 57ˆÊ2 3ˆ = Á Ë76 69 ˜Á ¯Ë4 1 ˜ ¯ Ê136 + 228 204 + 57ˆ Ê364 261ˆ = Á = Ë152 + 276 228 + 69 ˜ ¯ Á Ë428 297 ˜ ¯ Êa bˆ 20. Let X = Á Ëc d ˜ ¯ Ê2 1ˆÊa bˆ Ê3 5ˆ So, Á = Ë1 4 ˜Á ¯Ëc d ˜ ¯ Á Ë0 6 ˜ ¯ Ê2a + c 2b+ dˆ Ê3 5ˆ fi = Ë Á a+ 4c b+ 4d¯ ˜ Ë Á 0 6¯ ˜ 2a + c= 3 2b+ d = 5 fi a + 4c= 0 b+ 4d = 6 fi –8c + c = 3, 2(6 – 4d) + d = 5 3 fi c=- , - 7 d = 5 - 12 =- 7 7 3 fi c=- , d = 1 7 12 Therefore, a = , b= 2 7 Ê12/7 2ˆ Thus, the matrix X = Á Ë-3/7 1 ˜ ¯ . 21. We have, Ê1 2 2ˆÊ1 2 2ˆ A 2 = A.A = Á2 Á 1 2˜Á2 ˜Á 1 2˜ ˜ Ë2 2 1¯Ë2 2 1¯
Page 2 and 3:
Algebra Booster with Problems & Sol
Page 4 and 5:
Algebra Booster with Problems & Sol
Page 6:
Dedicated to light of my life (Rush
Page 9 and 10:
viii Preface I owe a special debt o
Page 11 and 12:
x Contents Descartes Rule of Signs
Page 13 and 14:
xii Contents Chapter 8 Probability
Page 15 and 16:
1.2 Algebra Booster (ii) a 1 - k, a
Page 17 and 18:
1.4 Algebra Booster fi a + (n + 1)d
Page 19 and 20:
1.6 Algebra Booster (i) Maximum Val
Page 21 and 22:
1.8 Algebra Booster 25. In an AP, (
Page 23 and 24:
1.10 Algebra Booster b 86. If b = a
Page 25 and 26:
1.12 Algebra Booster 145. Find the
Page 27 and 28:
1.14 Algebra Booster and n= 0 2n 2n
Page 29 and 30:
1.16 Algebra Booster 51. In a serie
Page 31 and 32:
1.18 Algebra Booster 37. Observing
Page 33 and 34:
1.20 Algebra Booster 7. If a, b and
Page 35 and 36:
1.22 Algebra Booster (B) (C) (D) If
Page 37 and 38:
1.24 Algebra Booster 22. No questio
Page 39 and 40:
1.26 Algebra Booster 17 1 50. Ê ˆ
Page 41 and 42:
1.28 Algebra Booster 8. 3 - 1 2 9.
Page 43 and 44:
1.30 Algebra Booster fi a(a 2 - d 2
Page 45 and 46:
1.32 Algebra Booster On subtraction
Page 47 and 48:
1.34 Algebra Booster 1 1 1 1 fi - =
Page 49 and 50:
1.36 Algebra Booster 61. We have (a
Page 51 and 52:
1.38 Algebra Booster fi 3 n > 14001
Page 53 and 54:
1.40 Algebra Booster and 2 sin n n=
Page 55 and 56:
1.42 Algebra Booster 102. We have,
Page 57 and 58:
1.44 Algebra Booster 115. It is giv
Page 59 and 60:
1.46 Algebra Booster Now, Ê a + b
Page 61 and 62:
1.48 Algebra Booster 136. (i) We ha
Page 63 and 64:
1.50 Algebra Booster 152. Let t n 3
Page 65 and 66:
1.52 Algebra Booster fi 161. As we
Page 67 and 68:
1.54 Algebra Booster 177. We have (
Page 69 and 70:
1.56 Algebra Booster 193. We know t
Page 71 and 72:
1.58 Algebra Booster Thus, (1 + x)(
Page 73 and 74:
1.60 Algebra Booster Alternate meth
Page 75 and 76:
1.62 Algebra Booster fi 1007d = a -
Page 77 and 78:
1.64 Algebra Booster 2 2 fi Ê 1 1
Page 79 and 80:
1.66 Algebra Booster and b + br = 9
Page 81 and 82:
1.68 Algebra Booster = 1 ◊ cos(1
Page 83 and 84:
1.70 Algebra Booster 6. We have 1 1
Page 85 and 86:
1.72 Algebra Booster fi fi Dividing
Page 87 and 88:
1.74 Algebra Booster fi 7 4 4 4 (1
Page 89 and 90:
1.76 Algebra Booster n 35. We have
Page 91 and 92:
1.78 Algebra Booster 5. We know tha
Page 93 and 94:
1.80 Algebra Booster Hence, the val
Page 95 and 96:
1.82 Algebra Booster Since the equa
Page 97 and 98:
1.84 Algebra Booster 2 S2 = = 3 1 1
Page 99 and 100:
1.86 Algebra Booster 37. Let a and
Page 101 and 102:
1.88 Algebra Booster fi fi Ê n Ê
Page 104 and 105:
CHAPTER 2 Quadratic Equations and E
Page 106 and 107:
Quadratic Equations and Expressions
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
CHAPTER 3 Logarithm 1. INTRODUCTION
Page 182 and 183:
Logarithm 3.3 = log 2 (4) = log 2 (
Page 184 and 185:
Logarithm 3.5 x fi Ê1ˆ Á = 3 Ë
Page 186 and 187:
Logarithm 3.7 fi fi 10 log10x log10
Page 188 and 189:
Logarithm 3.9 16. If a 2 + b 2 = 7a
Page 190 and 191:
Logarithm 3.11 2 log 2 + log 3 y =
Page 192 and 193:
Logarithm 3.13 (Q) (R) (S) The valu
Page 194 and 195:
Logarithm 3.15 1 1 13. { , 2 4} 14.
Page 196 and 197:
Logarithm 3.17 Also, (a - b) = log
Page 198 and 199:
Logarithm 3.19 Again, log a b = 2 f
Page 200 and 201:
Logarithm 3.21 Now, log( a + c) + l
Page 202 and 203:
Logarithm 3.23 fi Ê1 2 ˆ log 3/4
Page 204 and 205:
Logarithm 3.25 fi 2x 2 = 12 fi x 2
Page 206 and 207:
Logarithm 3.27 fi fi 1 2 x 2 = 3 3,
Page 208 and 209:
Logarithm 3.29 = log 10 (64 ¥ 31)
Page 210:
Logarithm 3.31 fi 2x = 8, 4 = 2 3 ,
Page 213 and 214:
4.2 Algebra Booster EXAMPLE 2: The
Page 215 and 216:
4.4 Algebra Booster (i) If z lies i
Page 217 and 218:
4.6 Algebra Booster (iii) w 3 = 1 (
Page 219 and 220:
4.8 Algebra Booster Note The sum of
Page 221 and 222:
4.10 Algebra Booster In an equilate
Page 223 and 224:
4.12 Algebra Booster 3. Straight Li
Page 225 and 226:
4.14 Algebra Booster (vii) We consi
Page 227 and 228:
4.16 Algebra Booster 55. If |z 1 +
Page 229 and 230:
4.18 Algebra Booster 8. The area of
Page 231 and 232:
4.20 Algebra Booster 53. The number
Page 233 and 234:
4.22 Algebra Booster 49. Find the r
Page 235 and 236:
4.24 Algebra Booster 30. Resolve z
Page 237 and 238:
4.26 Algebra Booster 1. The value o
Page 239 and 240:
4.28 Algebra Booster 12. Show that
Page 241 and 242:
4.30 Algebra Booster X¢ P(-1, 0) Y
Page 243 and 244:
4.32 Algebra Booster 41. (d) 42. (c
Page 245 and 246:
4.34 Algebra Booster HINTS AND SOLU
Page 247 and 248:
4.36 Algebra Booster Hence, the val
Page 249 and 250:
4.38 Algebra Booster p q fi = = l(s
Page 251 and 252:
4.40 Algebra Booster p fi < 2q< p 2
Page 253 and 254:
4.42 Algebra Booster 2 2Êq1- q2ˆ
Page 255 and 256:
4.44 Algebra Booster x◊ 3 p + y
Page 257 and 258:
4.46 Algebra Booster 92. We have x
Page 259 and 260:
4.48 Algebra Booster fi fi fi fi Ê
Page 261 and 262:
4.50 Algebra Booster Putting z 3 =
Page 263 and 264:
4.52 Algebra Booster i e p 122. Let
Page 265 and 266:
4.54 Algebra Booster fi fi 3(2 + co
Page 267 and 268:
4.56 Algebra Booster 19. Let z = r(
Page 269 and 270:
4.58 Algebra Booster 2 1 w w = + +
Page 271 and 272:
4.60 Algebra Booster fi Ê 2p 4p 6p
Page 273 and 274:
4.62 Algebra Booster A B 50. Given
Page 275 and 276:
4.64 Algebra Booster fi 2 2 (3x + y
Page 277 and 278:
4.66 Algebra Booster fi fi |(x - 4)
Page 279 and 280:
4.68 Algebra Booster Comparing the
Page 281 and 282:
4.70 Algebra Booster = |(cos (3q) -
Page 283 and 284:
4.72 Algebra Booster Thus, 18. Let
Page 285 and 286:
4.74 Algebra Booster 2 Ê a ˆ = 2
Page 287 and 288:
4.76 Algebra Booster 1È Ê3pˆ Ê5
Page 289 and 290:
4.78 Algebra Booster 12 Ê2k + 1ˆ
Page 291 and 292:
4.80 Algebra Booster 16. We have, s
Page 293 and 294:
4.82 Algebra Booster 3 fi x =± 2 T
Page 295 and 296:
4.84 Algebra Booster fi fi 4 Ê3z -
Page 297 and 298:
4.86 Algebra Booster 53. fi 2 2 2 (
Page 299 and 300:
4.88 Algebra Booster Now, 1 iq -iq
Page 302 and 303:
CHAPTER 5 Permutations and Combinat
Page 304 and 305:
Permutations and Combinations 5.3 (
Page 306 and 307:
Permutations and Combinations 5.5 =
Page 308 and 309:
Permutations and Combinations 5.7 5
Page 310 and 311:
Permutations and Combinations 5.9 1
Page 312 and 313:
Permutations and Combinations 5.11
Page 314 and 315:
Page 316 and 317:
Page 318 and 319:
Page 320 and 321:
Page 322 and 323:
Page 324 and 325:
Page 326 and 327:
Page 328 and 329:
Page 330 and 331:
Page 332 and 333:
Page 334 and 335:
Page 336 and 337:
Page 338 and 339:
Page 340 and 341:
Page 342 and 343:
Page 344 and 345:
Page 346 and 347:
Page 348 and 349:
Page 350 and 351:
Page 352 and 353:
Page 354:
Page 357 and 358:
6.2 Algebra Booster 5. Subtracting
Page 359 and 360:
6.4 Algebra Booster Proof 1. ( a +
Page 361 and 362:
6.6 Algebra Booster EXERCISES LEVEL
Page 363 and 364:
6.8 Algebra Booster 80. Find the su
Page 365 and 366:
6.10 Algebra Booster 10. In the exp
Page 367 and 368:
6.12 Algebra Booster 11. Find the c
Page 369 and 370:
6.14 Algebra Booster 64. Find the c
Page 371 and 372:
6.16 Algebra Booster 43. Find the s
Page 373 and 374:
6.18 Algebra Booster 3. Match the f
Page 375 and 376:
6.20 Algebra Booster (a) 0 (c) (-1)
Page 377 and 378:
6.22 Algebra Booster LEVEL IV COMPR
Page 379 and 380:
6.24 Algebra Booster 30 2 30 2 2 30
Page 381 and 382:
6.26 Algebra Booster Now, (33 43 -
Page 383 and 384:
6.28 Algebra Booster 57. We have, 1
Page 385 and 386:
Page 387 and 388:
Page 389 and 390:
6.34 Algebra Booster Comparing the
Page 391 and 392:
6.36 Algebra Booster 1 1 1 1 + + +
Page 393 and 394:
6.38 Algebra Booster 127. We have,
Page 395 and 396:
6.40 Algebra Booster n n 2 n 3 7. W
Page 397 and 398:
6.42 Algebra Booster n r n r n r n
Page 399 and 400:
6.44 Algebra Booster n n Â Ck k =
Page 401 and 402:
6.46 Algebra Booster A1 Ê 1 1 1 1
Page 403 and 404:
6.48 Algebra Booster Multiplying Eq
Page 405 and 406:
6.50 Algebra Booster Ê12 ˆ Middle
Page 407 and 408:
6.52 Algebra Booster 72. Let t n 1
Page 409 and 410: 6.54 Algebra Booster Putting x = 1,
Page 411 and 412: 6.56 Algebra Booster Â Â Thus, 2I
Page 413 and 414: 6.58 Algebra Booster fi fi 2n 2n Ê
Page 415 and 416: 6.60 Algebra Booster Cn ( ,4) 36. L
Page 417 and 418: 6.62 Algebra Booster Thus, S = t 1
Page 419 and 420: 6.64 Algebra Booster 7. We have 10
Page 421 and 422: 6.66 Algebra Booster = ( 49 C 4 + 4
Page 423 and 424: 6.68 Algebra Booster Differentiatin
Page 425 and 426: 6.70 Algebra Booster 37. We have, 3
Page 427 and 428: 6.72 Algebra Booster 51. Let the th
Page 429 and 430: 7.2 Algebra Booster (vii) Identity
Page 431 and 432: 7.4 Algebra Booster (xii) If A is s
Page 433 and 434: 7.6 Algebra Booster where Proof: fi
Page 435 and 436: 7.8 Algebra Booster Replace A by ad
Page 437 and 438: 7.10 Algebra Booster 10. Unitary ma
Page 439 and 440: 7.12 Algebra Booster 46. Expand the
Page 441 and 442: 7.14 Algebra Booster 88. If A be a
Page 443 and 444: 7.16 Algebra Booster 7. For non-zer
Page 445 and 446: 7.18 Algebra Booster 2x + 4p p + 6a
Page 447 and 448: 7.20 Algebra Booster 4. Prove that
Page 449 and 450: 7.22 Algebra Booster 4. If S r = a
Page 451 and 452: 7.24 Algebra Booster 2 2 2 2 2 2 a
Page 453 and 454: 7.26 Algebra Booster The value of (
Page 455 and 456: 7.28 Algebra Booster 17. The determ
Page 457 and 458: 7.30 Algebra Booster 43. If a 0 A
Page 459: 7.32 Algebra Booster 65. Let M be a
Page 463 and 464: 7.36 Algebra Booster Êa bˆÊ1 2ˆ
Page 465 and 466: 7.38 Algebra Booster 1 a a 47 The g
Page 467 and 468: 7.40 Algebra Booster 2 2 2 1 0 = (1
Page 469 and 470: 7.42 Algebra Booster Thus, D1 ( d -
Page 473 and 474: 7.46 Algebra Booster 90. We know th
Page 475 and 476: 7.48 Algebra Booster 108. We have,
Page 477 and 478: 7.50 Algebra Booster 118. We have,
Page 481 and 482: 7.54 Algebra Booster = ([x] + [y] +
Page 483 and 484: 7.56 Algebra Booster It is given th
Page 485 and 486: 7.58 Algebra Booster 27. The given
Page 487 and 488: 7.60 Algebra Booster and 12 -3 5 D1
Page 489 and 490: 7.62 Algebra Booster fi Ê a ˆ Ê
Page 491 and 492: 7.64 Algebra Booster a b c b c a =
Page 493 and 494: 7.66 Algebra Booster 2bc -2c -2b 2
Page 495 and 496: 7.68 Algebra Booster 1 1 1 1 = 2 n
Page 497 and 498: 7.70 Algebra Booster 3 m m m 3 m =
Page 499 and 500: 7.72 Algebra Booster fi (49 - 42)si
Page 501 and 502: 7.74 Algebra Booster fi p + q + r =
Page 503 and 504: 7.76 Algebra Booster 34. We have fi
Page 505 and 506: 7.78 Algebra Booster where a 2 + b
Page 507 and 508: 7.80 Algebra Booster 55. (iii) Let
Page 509 and 510: 7.82 Algebra Booster fi 2 2 (1 + a)
Page 511 and 512:
8.2 Algebra Booster For example, th
Page 513 and 514:
8.4 Algebra Booster (ii) P(AB) £ P
Page 515 and 516:
8.6 Algebra Booster (ii) a black ca
Page 517 and 518:
8.8 Algebra Booster 64. If two dice
Page 519 and 520:
8.10 Algebra Booster ferred from th
Page 521 and 522:
8.12 Algebra Booster 168. The proba
Page 523 and 524:
8.14 Algebra Booster 28. A fair coi
Page 525 and 526:
8.16 Algebra Booster product is 0.7
Page 527 and 528:
8.18 Algebra Booster event that thr
Page 529 and 530:
8.20 Algebra Booster Questions aske
Page 531 and 532:
8.22 Algebra Booster The probabilit
Page 533 and 534:
8.24 Algebra Booster 72. A is targe
Page 535 and 536:
8.26 Algebra Booster 5, 6, 7. A car
Page 537 and 538:
8.28 Algebra Booster 137. Ê 9 m ˆ
Page 539 and 540:
8.30 Algebra Booster 24. 25. 3 10 1
Page 541 and 542:
8.32 Algebra Booster So, the probab
Page 543 and 544:
8.34 Algebra Booster (iv) Let D be
Page 545 and 546:
8.36 Algebra Booster Hence, the req
Page 547 and 548:
8.38 Algebra Booster 58. Here, S =
Page 549 and 550:
8.40 Algebra Booster 81. Here, S =
Page 551 and 552:
8.42 Algebra Booster The probabilit
Page 553 and 554:
8.44 Algebra Booster Thus, 1 36 =
Page 555 and 556:
8.46 Algebra Booster 128. Hence, th
Page 557 and 558:
8.48 Algebra Booster tively and let
Page 559 and 560:
8.50 Algebra Booster Hence, the pro
Page 561 and 562:
8.52 Algebra Booster Ê 5 1 ˆ = 1-
Page 563 and 564:
8.54 Algebra Booster We are interes
Page 565 and 566:
8.56 Algebra Booster 193. Clearly,
Page 567 and 568:
8.58 Algebra Booster 15. Let E be t
Page 569 and 570:
8.60 Algebra Booster = P( A or CA o
Page 571 and 572:
8.62 Algebra Booster 20. Out of 2 c
Page 573 and 574:
8.64 Algebra Booster Clearly, a = 5
Page 575 and 576:
8.66 Algebra Booster = (0.17) ¥ (0
Page 577 and 578:
8.68 Algebra Booster 1 Ê13ˆÊ1ˆ
Page 579 and 580:
8.70 Algebra Booster 46. We have, P
Page 581 and 582:
8.72 Algebra Booster 3 2 3 3 2 1 1
Page 583 and 584:
8.74 Algebra Booster and the number
Page 585 and 586:
8.76 Algebra Booster 88. Let G = Or
show all

1.Algebra Booster

Create successful ePaper yourself

Delete template?

Save as template?