1.Algebra Booster

Recommendations

Info

Binomial Theorem 6.45 = (1 + x + 2x 2 + 3x 3 + … + nx n ) ¥ (1 + x + 2x 2 + 3x 3 + … + nx n ) Co-efficient of x n = 1 ◊ n + 1 ◊ (n – 1) + 2 ◊ (n – 2) + … + (n – 1) ◊ 1 + n ◊ 1 n 2 ( n + 1) n ( n + 1)(2 n + = - 1) + 2 6 where t r = nr – r 2 nn ( + 1) Ê 2n+ 1ˆ = Án - + 2n 2 Ë ˜ 3 ¯ nn ( + 1) Ên-1ˆ = ◊ Á + 2n 2 Ë ˜ 3 ¯ 2 nn ( - 1) = + 2n 6 2 nn ( + 11) = 6 It is given that 2 nn ( + 11) = 310 6 fi n(n 2 + 1) = 1860 fi n = 12 34. We have F(n) = n+1 C 2 + 2( n C 2 + n–1 C 2 + n–2 C 2 + … + 2 C 2 ) = n+1 C 2 = 2 n+1 C 3 = ( n+1 C 2 + n+1 C 3 ) + n+1 C 3 = n+2 C 3 + n+1 C 3 ( n + 2)( n + 1) n ( n + 1) n( n -1) = + 6 6 nn ( + 1) = ( n + 2 + n - 1) 6 nn ( + 1)(2n + 1) = 6 Hence, the value of F(11) + 4 11.12.23 = + 4 6 = 506 + 4 = 510 35. Let Ê1+ 2+ 3+ + r ˆ tr = Á C Ë ˜ r ¯ Êrr ( + 1) ˆ 2 = Á C Ë ˜ r 2r ¯ Ê( r + 1) ˆ n 2 = Á C Ë ˜ r 2 ¯ 1 ( n 2 n 2 = r Cr + Cr ) 2 Thus, 1 Ê n n n 2 n 2ˆ Sn = r r 2 ÁÂr C + Â C ˜ Ër= 0 r= 0 ¯ 2 r 2n 1 [(1 n 2 2 2 2 1 2 n 2 3 n n = ◊ C + ◊ C + ◊ C2 + + n◊ Cn ) 2 n 2 n 2 n 2 n 2 n 2 + ( C1 + C2 + C2 + C3 + Cn )] 1 ( 2n-1 2n = n◊ Cn-1 + Cn ) 2 38. We have, (1 + x + x 2 ) n = a 0 + a 1 x + a 2 x 2 + … + a 2n x 2n …(i) Replace x by –x, we get, (1 – x + x 2 ) n = a 0 – a 1 x + a 2 x 2 + … + a 2n x 2n …(ii) Replace x by 1 x in Eq. (i), we get n Ê 1 1 ˆ a1 a2 a2 Á1 + + = a 2 0 + + + + Ë ˜ 2 2 x x ¯ x x x Multiplying Eqs (ii) and (i), we get, 2 2 2 2 2 0 1 2 3 n n n …(iii) 2 n Ê 1 1 ˆ (1 - x + x ) Á1 + + Ë 2 ˜ x x ¯ = ( a - a + a - a + + a ) + (…) x + Comparing the co-efficients of the constant terms from both the sides, we get 2 2 2 2 2 ( a0 - a1 + a2 - a3 + + a n ) = Co-efficient of constant term in 2 n 2 n 1 (1 - x + x ) (1 + x + x ) ¥ 2n x = Co-efficient of x 2n in (1 – x + x 2 ) n (1 + x + x 2 ) n = [(1 + x 2 ) 2 – x 2 ] n = (1 + x 2 + x 2 ) n = Co-efficient of t n in (1 + t + t 2 ) n = a n 39. We have, (x + 1)(x + 2)(x + 3)…(x + (n – 1))(x + n) = A 0 + A 1 x + A 2 x 2 + A 3 x 3 + … + A n x n log{(x + 1)(x + 2)…(x + (n – 1))(x + n)} = log(A 0 + A 1 x + A 2 x 2 + … + A n x n ) (i) Differentiating both sides w.r.t x and put x = 1, we get Ê1 1 1 1 ˆ Á + + + + Ë2 3 4 ( n + 1) ˜ ¯ A1+ 2A2 + 3A3+ + nAn = A0 + A1+ A2 + A3+ + An A1+ 2A2 + 3A3+ + nAn = ( n + 1)! Thus, A 1 + 2A 2 + 3A 3 + … + nA n Ê1 1 1 1 ˆ = ( n + 1)! ¥ + + + + Ë Á2 3 4 n + 1˜ ¯ (ii) Differentiating both sides w.r.t x and put x = 0, we get n
6.46 Algebra <strong>Booster</strong> A1 Ê 1 1 1 1 ˆ = 1 A Á + + + + + 0 Ë 2 3 4 n + 1˜ ¯ Ê 1 1 1 1 ˆ A1= A0Á1 + + + + + Ë 2 3 4 n + 1˜ ¯ Ê 1 1 1 1 ˆ A1 = n! ¥ Á1+ + + + + Ë 2 3 4 n + 1˜ ¯ 40. Clearly, A r = C r fi n A r = n C r Also, B r = C r fi n+1 B r = n+1 C r Now, A r + A r–1 = n A r + n A r+1 = n C r + n C r+1 = n+1 C r = n+1 B r = B r Hence, the result. Ê 1 1 ˆ 41. Let S = Â Â + Á n n 0£< £ C C ˜ Ë ¯ fi fi fi fi na fi S = 2 42. We have, i j n i j Ê Ê n -i n- j ˆˆ = Á Â Â + Á n n 0£< i j£ n Cn-i C ˜˜ Ë Ë n- j¯¯ È Ê 1 1 ˆ = Ín Â Â + Á n n 0 i j n Ci C ˜ ÍÎ £< £ Ë j¯ Ê i j ˆ˘ - Â Â + Á n n 0£< i j£ n Cn-i C ˜˙ Ë n- j¯˙˚ Ê 1 1 ˆ = n Â Â + - S Á ˜ ¯ n n 0£< i j£ n Ë Ci Cj Ê 1 1 ˆ 2S = n Â Â + Á ˜ ¯ n n 0£< i j£ n Ë Ci Cj Ê n n Ên - rˆ Ê r ˆˆ 2S = nÁÂÁ ˜ + ÂÁ n ˜ Ë ¯ Ë C ˜ Ë ¯¯ n r= 0 Cr r= 0 Ê n Ê n ˆˆ 2S = nÁÂ Á n ˜˜ Ër = 0Ë Cr ¯¯ 2Ê n Ê 1 ˆˆ 2 2S = n ÁÂ Á n a n ˜ = r = 0Ë C ˜ Ë ¯¯ n n ÂÂ 2 i= 0 j= 0 ( C + C ) i j r r n n n n ÂÂ Ci ÂÂ Cj i= 0 j= 0 i= 0 j= 0 n n n n ÂÂ Ci ÂÂ j= 0 i= 0 i= 0 j= 0 n n n n = ( ) + ( ) Ê ˆ Ê ˆ = Á ( ) ˜ + Á ( Cj) ˜ Ë ¯ Ë ¯ Â Â = (2 ) + (2 ) j= 0 i= 0 n n n n Â Â = 2 (1) + 2 (1) j= 0 i= 0 = 2 n (n + 1) + 2 n (n + 1) = (n + 1)2 n–1 43. We know that fi fi fi fi n n n ÂÂ Â ( C + C ) = ( C + C ) i j i j i= 0 j= 0 i= 0 n n + 1 n n Â Â + 2 ( C + C ) 0£< i j£ n ( n + 1)2 = 2 + 2 + 2 ( C + C ) n + 1 n n i Â Â 0£< i j£ n n Â Â ( n + 1)2 = 2.2 + 2 ( C + C )` n n 0£< i j£ n 0£< i j£ n ( n + 1)2 = 2 + ( C + C ) n Â Â 0£< i j£ n 44. We have, n n ÂÂ ( CC i j) = i= 0 j= 0 45. We know that fi fi fi fi 46. We have, n Â Â ( C + C ) = n◊2 i j n Â n Â n ( C ) ( C ) i i= 0 j= 0 = (2 n ) ¥ (2 n ) = (2 2n ) Ê ÂÂ n n n n 2 ( CC i j) = Á Â Ci ˜ + 2 Â Â ( CC i j) i= 0 j= 0 Ëi= 0 ¯ 0£ i< j£ n Â n n n n 2 C Â Ê ˆ i Cj = Á Â Ci ˜ + Â Â CC i j i= 0 j= 0 Ëi= 0 ¯ 0£ i< j£ n n n n 2n 2 ◊ 2 = Cn + 2 ◊ Â Â( CC i j) 0£< i j£ n n 2n 2n 2 = Cn + 2 ◊ Â Â( CC i j) 0£< i j£ n n 1 2n 2n Â Â( CC i j) = (2 - Cn) 0£< i j£ n 2 ˆ ( ) ( ) 2 ( ) n Â Â 0£< i j£ n (( i ¥ j) CC ) i j i j i j j i j j
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: Permutations and Combinations 5.49
Page 352 and 353: Permutations and Combinations 5.51
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 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: 6.44 Algebra Booster n n Â Ck k =
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 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:
7.44 Algebra Booster 77. We have, 2
Page 473 and 474:
7.46 Algebra Booster 90. We know th
Page 475 and 476:
Page 477 and 478:
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
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?