1.Algebra Booster

Recommendations

Info

Permutations and Combinations 5.21 130. 5! ¥ (9!) 2 30 1 P20 131. ¥ 2 20 132. 140 133. 210 134. 792 135. 4410 21 136. C 5 137. n = 20, –19 138. 24 139. 56 20! 140. 4!5!3!8! 141. 9! ¥ ( 13 C 4 ) 142. (13) 4 143. 246 144. D f = {3} 145. 1 146. 4 147. 6 148. 5 149. 0 150. n > 7 52 151. C 4 152. n = 9 and r = 3 153. x = 3 nn ( -1)( n- 2)( n+ 1) 154. 8 155. n = 2 156. (i) 98 C 18 (ii) 95 C 20 157. 30 158. 44 ¥ 43 ¥ 14 ¥ 41 159. 4 C 1 ¥ 48 C 9 + 4 C 2 ¥ 48 C 8 + 4 C 3 ¥ 48 C 7 + 4 C 4 ¥ 48 C 6 160. 5 C 2 ¥ 6 C 3 161. 246 162. 1283 163. 780 164. 2700 165. 41 166. 255 167. 1023 168. 31 169. 217 170. (i) 9 (ii) 9 171. n = 10 172. 6 173. 17 174. 4 175. 3 176. 1 177. 13 178. 13727 179. 209 180. 210 181. 330 182. 241 183. 215 184. 197 185. 1919 186. 53 187. 758 188. 136 189. 2454 190. 26 191. 486 192. 256 193. 16650 194. (i) 60 (ii) 48 (iii) 12 (iv) 30 195. 8 196. 315 197. 9360 198. 78 199. 15 200. 403 201. 100 202. 23 203. 30 204. 4 205. 8 206. 3 207. 6 208. 720 209. 300 210. 14 211. 150 212. 540 213. 36 214. 6 215. 3 216. 1771 217. 2 15 – 121 218. (i) 501 (ii) 256 219. 1 220. 2 221. 9 222. 44 223. 44 224. 5280 225. 20 226. 31 227. 56 228. 264 229. 476 230. 72 231. 10 232. 35 233. (i) 1771 (ii) 969
5.22 Algebra <strong>Booster</strong> 234. 117 235. 66 236. 1540 237 336 50 238. C 3 – 19 C 3 239. 55 240 27 241. 2048 242. 25 243. 84 244. 26 245. 18720 246. (i) 57 (ii) 210 (iii) 420 247. 35 248. 10 249. 16 250. 1260 251. 7 252. 280 253. 791 254. 20 255. 104 256. m 2 n 2 257. n = 5 258. 258.205 259. 98 LEVEL II 1. (c) 2. (a) 3. (a) 4. (b) 5. (c) 6. (d) 7. (c) 8. (b) 9. (d) 10. (c) 11. (a) 12. (c) 13. (c) 14. (c) 15. (a) 16. (c) 17. (d) 18. (b) 19. (c) 20. (b) 21. (b) 22. (d) 23. (a) 24. (c) 25. (b) 26. (c) 27. (c) 28. (b) 29. (d) 30. (c) 31. (b) 32. (c) 33. (b) 34. (b) 35. (a) 36. (b) 37. (b) 38. (c) 39. (b) 40. (c) 41. (c) 42. (c) 43. (a) 44. (c) 45. (c) 46. (b) 47. (b) 48. (a) 49. (a) 50. (b) 51. (a) LEVEL III 1. 325 2. 100 1 3. ( 4)( 5) 6 nn- n- 4. 126 5. 9216 6. 7. 191 8. 150 9. 35 10. 116280 11. 110556 12. 552 13. (n + 2)2 n – 1 14. 72 15. 286 16. 240 17. 56 18. 4 19. 70 20. 2600 21. 536 22. 117 23. 25 24. (2)! ¥ (18)! 2 25. 1 ( 1)(2 4 3) 3 m+ m + m+ 26. 13 27. 210 28. (i) 24 (ii) 96 29. 10 30. 120 INTEGER TYPE QUESTIONS 1. r = 5 2. n = 9 3. 6, where x = 5, 6, 7, 8, 9, 10 4. 4 5. n = 8 6. 3 7. 5 8. 7 9. 5 10. 6 11. 6 12. 8 13. 8 14. 2 15. 9 16. 8 17. 4 18, 8 19. 9 20. 3 COMPREHENSIVE LINK PASSAGES Passage I : 1. (a) 2. (c) 3. (b) 4. (b) 5. (d) Passage II : 1. (c) 2. (b) 3. (a) 4. (d) 5. (a) Passage III: 1. (c) 2. (a) 3. (b) 4. (d) 5. (d) Passage IV : 1. (c) 2. (b) 3. (b) 4. (c) 5. (b) MATRIX MATCH 1. A Æ (P, R); B Æ (Q, S, T); C Æ (Q, R, S, T) 2. A Æ (P, Q, S); B Æ (P, Q, R, S, T); C Æ (P, Q, S) 3. A Æ (P, Q, R, S); B Æ (Q); C Æ (P, Q, R, S, T) 4. A Æ (P, Q, S), B Æ (Q, S); C Æ (R, T)
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 354: Permutations and Combinations 5.53
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:
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:
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 and 460:
7.32 Algebra Booster 65. Let M be a
Page 461 and 462:
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:
Page 473 and 474:
7.46 Algebra Booster 90. We know th
Page 475 and 476:
Page 477 and 478:
Page 479 and 480:
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?