- Page 2 and 3: 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,
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1.44 Algebra Booster 115. It is giv
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1.46 Algebra Booster Now, Ê a + b
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1.48 Algebra Booster 136. (i) We ha
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1.50 Algebra Booster 152. Let t n 3
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1.52 Algebra Booster fi 161. As we
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1.54 Algebra Booster 177. We have (
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1.56 Algebra Booster 193. We know t
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1.58 Algebra Booster Thus, (1 + x)(
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1.60 Algebra Booster Alternate meth
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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
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1.72 Algebra Booster fi fi Dividing
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1.74 Algebra Booster fi 7 4 4 4 (1
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1.76 Algebra Booster n 35. We have
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1.78 Algebra Booster 5. We know tha
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1.80 Algebra Booster Hence, the val
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1.82 Algebra Booster Since the equa
- Page 97 and 98:
1.84 Algebra Booster 2 S2 = = 3 1 1
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1.86 Algebra Booster 37. Let a and
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1.88 Algebra Booster fi fi Ê n Ê
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CHAPTER 2 Quadratic Equations and E
- Page 106 and 107:
Quadratic Equations and Expressions
- Page 108 and 109:
Quadratic Equations and Expressions
- Page 110 and 111:
Quadratic Equations and Expressions
- Page 112 and 113:
Quadratic Equations and Expressions
- Page 114 and 115:
Quadratic Equations and Expressions
- Page 116 and 117:
Quadratic Equations and Expressions
- Page 118 and 119:
Quadratic Equations and Expressions
- Page 120 and 121:
Quadratic Equations and Expressions
- Page 122 and 123:
Quadratic Equations and Expressions
- Page 124 and 125:
Quadratic Equations and Expressions
- Page 126 and 127:
Quadratic Equations and Expressions
- Page 128 and 129:
Quadratic Equations and Expressions
- Page 130 and 131:
Quadratic Equations and Expressions
- Page 132 and 133:
Quadratic Equations and Expressions
- Page 134 and 135:
Quadratic Equations and Expressions
- Page 136 and 137:
Quadratic Equations and Expressions
- Page 138 and 139:
Quadratic Equations and Expressions
- Page 140 and 141:
Quadratic Equations and Expressions
- Page 142 and 143:
Quadratic Equations and Expressions
- Page 144 and 145:
Quadratic Equations and Expressions
- Page 146 and 147:
Quadratic Equations and Expressions
- Page 148 and 149:
Quadratic Equations and Expressions
- Page 150 and 151:
Quadratic Equations and Expressions
- Page 152 and 153:
Quadratic Equations and Expressions
- Page 154 and 155:
Quadratic Equations and Expressions
- Page 156 and 157:
Quadratic Equations and Expressions
- Page 158 and 159:
Quadratic Equations and Expressions
- Page 160 and 161:
Quadratic Equations and Expressions
- Page 162 and 163:
Quadratic Equations and Expressions
- Page 164 and 165:
Quadratic Equations and Expressions
- Page 166 and 167:
Quadratic Equations and Expressions
- Page 168 and 169:
Quadratic Equations and Expressions
- Page 170 and 171:
Quadratic Equations and Expressions
- Page 172 and 173:
Quadratic Equations and Expressions
- Page 174 and 175:
Quadratic Equations and Expressions
- Page 176 and 177:
Quadratic Equations and Expressions
- Page 178 and 179:
Quadratic Equations and Expressions
- 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
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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 ,
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4.2 Algebra Booster EXAMPLE 2: The
- Page 215 and 216:
4.4 Algebra Booster (i) If z lies i
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4.6 Algebra Booster (iii) w 3 = 1 (
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4.8 Algebra Booster Note The sum of
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4.10 Algebra Booster In an equilate
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4.12 Algebra Booster 3. Straight Li
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4.14 Algebra Booster (vii) We consi
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4.16 Algebra Booster 55. If |z 1 +
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4.18 Algebra Booster 8. The area of
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4.20 Algebra Booster 53. The number
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4.22 Algebra Booster 49. Find the r
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4.24 Algebra Booster 30. Resolve z
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4.26 Algebra Booster 1. The value o
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4.28 Algebra Booster 12. Show that
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4.30 Algebra Booster X¢ P(-1, 0) Y
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4.32 Algebra Booster 41. (d) 42. (c
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4.34 Algebra Booster HINTS AND SOLU
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4.36 Algebra Booster Hence, the val
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4.38 Algebra Booster p q fi = = l(s
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4.40 Algebra Booster p fi < 2q< p 2
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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
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4.54 Algebra Booster fi fi 3(2 + co
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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
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4.62 Algebra Booster A B 50. Given
- Page 275 and 276:
4.64 Algebra Booster fi 2 2 (3x + y
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4.66 Algebra Booster fi fi |(x - 4)
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4.68 Algebra Booster Comparing the
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4.70 Algebra Booster = |(cos (3q) -
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4.72 Algebra Booster Thus, 18. Let
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4.74 Algebra Booster 2 Ê a ˆ = 2
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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
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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
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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:
Permutations and Combinations 5.13
- Page 316 and 317:
Permutations and Combinations 5.15
- Page 318 and 319:
Permutations and Combinations 5.17
- Page 320 and 321:
Permutations and Combinations 5.19
- Page 322 and 323:
Permutations and Combinations 5.21
- Page 324 and 325:
Permutations and Combinations 5.23
- Page 326 and 327:
Permutations and Combinations 5.25
- Page 328 and 329:
Permutations and Combinations 5.27
- Page 330 and 331:
Permutations and Combinations 5.29
- Page 332 and 333:
Permutations and Combinations 5.31
- Page 334 and 335:
Permutations and Combinations 5.33
- Page 336 and 337:
Permutations and Combinations 5.35
- Page 338 and 339:
Permutations and Combinations 5.37
- Page 340 and 341:
Permutations and Combinations 5.39
- Page 342 and 343:
Permutations and Combinations 5.41
- Page 344 and 345:
Permutations and Combinations 5.43
- Page 346 and 347:
Permutations and Combinations 5.45
- Page 348 and 349:
Permutations and Combinations 5.47
- Page 350 and 351:
Permutations and Combinations 5.49
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Permutations and Combinations 5.51
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Permutations and Combinations 5.53
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6.2 Algebra Booster 5. Subtracting
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6.4 Algebra Booster Proof 1. ( a +
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6.6 Algebra Booster EXERCISES LEVEL
- Page 363 and 364:
6.8 Algebra Booster 80. Find the su
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6.10 Algebra Booster 10. In the exp
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6.12 Algebra Booster 11. Find the c
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6.14 Algebra Booster 64. Find the c
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6.16 Algebra Booster 43. Find the s
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6.18 Algebra Booster 3. Match the f
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6.20 Algebra Booster (a) 0 (c) (-1)
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6.22 Algebra Booster LEVEL IV COMPR
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6.24 Algebra Booster 30 2 30 2 2 30
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6.26 Algebra Booster Now, (33 43 -
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6.28 Algebra Booster 57. We have, 1
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6.30 Algebra Booster 78. We have, 1
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6.32 Algebra Booster 87. We have, 2
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6.34 Algebra Booster Comparing the
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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
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6.42 Algebra Booster n r n r n r n
- Page 399 and 400:
6.44 Algebra Booster n n  Ck k =
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6.46 Algebra Booster A1 Ê 1 1 1 1
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6.48 Algebra Booster Multiplying Eq
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6.50 Algebra Booster Ê12 ˆ Middle
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6.52 Algebra Booster 72. Let t n 1
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6.54 Algebra Booster Putting x = 1,
- Page 411 and 412:
6.56 Algebra Booster   Thus, 2I
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6.58 Algebra Booster fi fi 2n 2n Ê
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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
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6.68 Algebra Booster Differentiatin
- Page 425 and 426:
6.70 Algebra Booster 37. We have, 3
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6.72 Algebra Booster 51. Let the th
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7.2 Algebra Booster (vii) Identity
- Page 431 and 432:
7.4 Algebra Booster (xii) If A is s
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7.6 Algebra Booster where Proof: fi
- Page 435 and 436:
7.8 Algebra Booster Replace A by ad
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7.10 Algebra Booster 10. Unitary ma
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7.12 Algebra Booster 46. Expand the
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7.14 Algebra Booster 88. If A be a
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7.16 Algebra Booster 7. For non-zer
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7.18 Algebra Booster 2x + 4p p + 6a
- Page 447 and 448:
7.20 Algebra Booster 4. Prove that
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7.22 Algebra Booster 4. If S r = a
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7.24 Algebra Booster 2 2 2 2 2 2 a
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7.26 Algebra Booster The value of (
- Page 455 and 456:
7.28 Algebra Booster 17. The determ
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7.30 Algebra Booster 43. If a 0 A
- Page 459 and 460:
7.32 Algebra Booster 65. Let M be a
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7.34 Algebra Booster 12. Then AB =
- 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 471 and 472:
7.44 Algebra Booster 77. We have, 2
- Page 473 and 474:
7.46 Algebra Booster 90. We know th
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7.48 Algebra Booster 108. We have,
- Page 477 and 478:
7.50 Algebra Booster 118. We have,
- Page 479 and 480:
7.52 Algebra Booster 4. We have, 2
- Page 481 and 482:
7.54 Algebra Booster = ([x] + [y] +
- Page 483 and 484:
7.56 Algebra Booster It is given th
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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
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8.8 Algebra Booster 64. If two dice
- Page 519 and 520:
8.10 Algebra Booster ferred from th
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8.12 Algebra Booster 168. The proba
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8.14 Algebra Booster 28. A fair coi
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8.16 Algebra Booster product is 0.7
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8.18 Algebra Booster event that thr
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8.20 Algebra Booster Questions aske
- Page 531 and 532:
8.22 Algebra Booster The probabilit
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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
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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
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8.48 Algebra Booster tively and let
- Page 559 and 560:
8.50 Algebra Booster Hence, the pro
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8.52 Algebra Booster Ê 5 1 ˆ = 1-
- Page 563 and 564:
8.54 Algebra Booster We are interes
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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