Class XI Chapter 8 – Binomial Theorem Maths ______________________________________________________________________________ Question 6: Find the 13 th term in the expansion of Solution 6: It is known . r 1 th term, Tr 1 Thus, the 13 th term in the expansion of 18 1812 1 T13 T12 1 C12 9x 3 x 12 18! 6 6 1 1 1 9 x 12!6! 3 x 12 18 1 9 x , x0 3 x , in the binomial expansion of n 12 12 1 9x 3 x 18 is a b 18 17 16 15 14 13.12! 6 1 12 1 6 2 12 x .3 9 3 3 6 12 12!.65432 x 3 18564 6 is given by T C a b r1 n nr r r Question 7: Find the middle terms in the expansions of Solution 7: It is known that in the expansion of a b n 3 x 3 6 7 , in n is odd, then there are two middle terms, Namely n 1 2 th term and n 1 1 2 th term. 3 x Therefore, the middle terms in the expansion 3 6 term 3 3 9 7 73 x 3 7! 4 x 4 31 3 3 1 3 3 T T C 6 3!4! 6 7 65.4! 1 105 3 x x 32.4! 2 3 8 4 9 9 3 3 7 are 71 2 th 4 th and th 71 1 5 2 th Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 8 – Binomial Theorem Maths ______________________________________________________________________________ 3 4 12 7 74 x 4 7! 3 x 5 41 4 3 1 3 4 T T C 3 765.4! 3 12 35 12 x x 4 4 4!.32 2 3 48 6 4!3! 6 3 x Thus, the middle terms in the expansion of 3 6 7 are 105 8 x 9 and 35 48 x 12 . Question 8: Find the middle terms in the expansion of Solution 8: It is known that in the expansion of n n 1 2 th term. a b Therefore, the middle term in the expansion of 105 5 10 x 5 10! x 5 5 4 51 5 9 9 5 T T C y y 3 5!5! 3 10 x 9y 3 , in n is even, then the middle term is 10 x 9y 3 10 9 8 7 6.5! 1 3 9 3 3 5432.5! 3 10 5 5 5 2 5 10 xy 5 2523 x y 6123 x y 5 5 5 5 5 Thus, the middle term in the expansion of 10 x 9y 3 is is th 10 1 6 2 5 5 61236 xy . th Question 9: In the expansion of Solution 9: It is known that T C a b n nr r r1 r m n 1 a 1 th , prove that coefficients of Tr 1 m a and n a are equal. r term, , in the binomial expansion of a b n is given by Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

- Page 1 and 2:
Class XI Chapter 1 - Sets Maths ___

- Page 3 and 4:
Class XI Chapter 1 - Sets Maths ___

- Page 5 and 6:
Class XI Chapter 1 - Sets Maths ___

- Page 7 and 8:
Class XI Chapter 1 - Sets Maths ___

- Page 9 and 10:
Class XI Chapter 1 - Sets Maths ___

- Page 11 and 12:
Class XI Chapter 1 - Sets Maths ___

- Page 13 and 14:
Class XI Chapter 1 - Sets Maths ___

- Page 15 and 16:
Class XI Chapter 1 - Sets Maths ___

- Page 17 and 18:
Class XI Chapter 1 - Sets Maths ___

- Page 19 and 20:
Class XI Chapter 1 - Sets Maths ___

- Page 21 and 22:
Class XI Chapter 1 - Sets Maths ___

- Page 23 and 24:
Class XI Chapter 1 - Sets Maths ___

- Page 25 and 26:
Class XI Chapter 1 - Sets Maths ___

- Page 27 and 28:
Class XI Chapter 1 - Sets Maths ___

- Page 29 and 30:
Class XI Chapter 1 - Sets Maths ___

- Page 31 and 32:
Class XI Chapter 1 - Sets Maths ___

- Page 33 and 34:
Class XI Chapter 1 - Sets Maths ___

- Page 35 and 36:
Class XI Chapter 1 - Sets Maths ___

- Page 37 and 38:
Class XI Chapter 1 - Sets Maths ___

- Page 39 and 40:
Class XI Chapter 1 - Sets Maths ___

- Page 41 and 42:
Class XI Chapter 1 - Sets Maths ___

- Page 43 and 44:
Class XI Chapter 2 - Relations and

- Page 45 and 46:
Class XI Chapter 2 - Relations and

- Page 47 and 48:
Class XI Chapter 2 - Relations and

- Page 49 and 50:
Class XI Chapter 2 - Relations and

- Page 51 and 52:
Class XI Chapter 2 - Relations and

- Page 53 and 54:
Class XI Chapter 2 - Relations and

- Page 55 and 56:
Class XI Chapter 2 - Relations and

- Page 57 and 58:
Class XI Chapter 2 - Relations and

- Page 59 and 60:
Class XI Chapter 2 - Relations and

- Page 61 and 62:
Class XI Chapter 3 - Trigonometric

- Page 63 and 64:
Class XI Chapter 3 - Trigonometric

- Page 65 and 66:
Class XI Chapter 3 - Trigonometric

- Page 67 and 68:
Class XI Chapter 3 - Trigonometric

- Page 69 and 70:
Class XI Chapter 3 - Trigonometric

- Page 71 and 72:
Class XI Chapter 3 - Trigonometric

- Page 73 and 74:
Class XI Chapter 3 - Trigonometric

- Page 75 and 76:
Class XI Chapter 3 - Trigonometric

- Page 77 and 78:
Class XI Chapter 3 - Trigonometric

- Page 79 and 80:
Class XI Chapter 3 - Trigonometric

- Page 81 and 82:
Class XI Chapter 3 - Trigonometric

- Page 83 and 84:
Class XI Chapter 3 - Trigonometric

- Page 85 and 86:
Class XI Chapter 3 - Trigonometric

- Page 87 and 88:
Class XI Chapter 3 - Trigonometric

- Page 89 and 90:
Class XI Chapter 3 - Trigonometric

- Page 91 and 92:
Class XI Chapter 3 - Trigonometric

- Page 93 and 94:
Class XI Chapter 3 - Trigonometric

- Page 95 and 96:
Class XI Chapter 3 - Trigonometric

- Page 97 and 98:
Class XI Chapter 3 - Trigonometric

- Page 99 and 100:
Class XI Chapter 4 - Principle of M

- Page 101 and 102:
Class XI Chapter 4 - Principle of M

- Page 103 and 104:
Class XI Chapter 4 - Principle of M

- Page 105 and 106:
Class XI Chapter 4 - Principle of M

- Page 107 and 108:
Class XI Chapter 4 - Principle of M

- Page 109 and 110:
Class XI Chapter 4 - Principle of M

- Page 111 and 112:
Class XI Chapter 4 - Principle of M

- Page 113 and 114:
Class XI Chapter 4 - Principle of M

- Page 115 and 116:
Class XI Chapter 4 - Principle of M

- Page 117 and 118:
Class XI Chapter 4 - Principle of M

- Page 119 and 120:
Class XI Chapter 4 - Principle of M

- Page 121 and 122:
Class XI Chapter 4 - Principle of M

- Page 123 and 124:
Class XI Chapter 4 - Principle of M

- Page 125 and 126:
Class XI Chapter 5 - Complex Number

- Page 127 and 128:
Class XI Chapter 5 - Complex Number

- Page 129 and 130:
Class XI Chapter 5 - Complex Number

- Page 131 and 132:
Class XI Chapter 5 - Complex Number

- Page 133 and 134:
Class XI Chapter 5 - Complex Number

- Page 135 and 136:
Class XI Chapter 5 - Complex Number

- Page 137 and 138:
Class XI Chapter 5 - Complex Number

- Page 139 and 140:
Class XI Chapter 5 - Complex Number

- Page 141 and 142:
Class XI Chapter 5 - Complex Number

- Page 143 and 144:
Class XI Chapter 5 - Complex Number

- Page 145 and 146:
Class XI Chapter 5 - Complex Number

- Page 147 and 148:
Class XI Chapter 5 - Complex Number

- Page 149 and 150:
Class XI Chapter 5 - Complex Number

- Page 151 and 152:
Class XI Chapter 5 - Complex Number

- Page 153 and 154:
Class XI Chapter 5 - Complex Number

- Page 155 and 156:
Class XI Chapter 6 - Linear Inequal

- Page 157 and 158:
Class XI Chapter 6 - Linear Inequal

- Page 159 and 160:
Class XI Chapter 6 - Linear Inequal

- Page 161 and 162:
Class XI Chapter 6 - Linear Inequal

- Page 163 and 164:
Class XI Chapter 6 - Linear Inequal

- Page 165 and 166:
Class XI Chapter 6 - Linear Inequal

- Page 167 and 168:
Class XI Chapter 6 - Linear Inequal

- Page 169 and 170:
Class XI Chapter 6 - Linear Inequal

- Page 171 and 172:
Class XI Chapter 6 - Linear Inequal

- Page 173 and 174:
Class XI Chapter 6 - Linear Inequal

- Page 175 and 176: Class XI Chapter 6 - Linear Inequal
- Page 177 and 178: Class XI Chapter 6 - Linear Inequal
- Page 179 and 180: Class XI Chapter 6 - Linear Inequal
- Page 181 and 182: Class XI Chapter 6 - Linear Inequal
- Page 183 and 184: Class XI Chapter 6 - Linear Inequal
- Page 185 and 186: Class XI Chapter 6 - Linear Inequal
- Page 187 and 188: Class XI Chapter 6 - Linear Inequal
- Page 189 and 190: Class XI Chapter 6 - Linear Inequal
- Page 191 and 192: Class XI Chapter 6 - Linear Inequal
- Page 193 and 194: Class XI Chapter 6 - Linear Inequal
- Page 195 and 196: Class XI Chapter 6 - Linear Inequal
- Page 197 and 198: Class XI Chapter 7 - Permutation an
- Page 199 and 200: Class XI Chapter 7 - Permutation an
- Page 201 and 202: Class XI Chapter 7 - Permutation an
- Page 203 and 204: Class XI Chapter 7 - Permutation an
- Page 205 and 206: Class XI Chapter 7 - Permutation an
- Page 207 and 208: Class XI Chapter 7 - Permutation an
- Page 209 and 210: Class XI Chapter 7 - Permutation an
- Page 211 and 212: Class XI Chapter 7 - Permutation an
- Page 213 and 214: Class XI Chapter 7 - Permutation an
- Page 215 and 216: Class XI Chapter 7 - Permutation an
- Page 217 and 218: Class XI Chapter 7 - Permutation an
- Page 219 and 220: Class XI Chapter 8 - Binomial Theor
- Page 221 and 222: Class XI Chapter 8 - Binomial Theor
- Page 223 and 224: Class XI Chapter 8 - Binomial Theor
- Page 225: Class XI Chapter 8 - Binomial Theor
- Page 229 and 230: Class XI Chapter 8 - Binomial Theor
- Page 231 and 232: Class XI Chapter 8 - Binomial Theor
- Page 233 and 234: Class XI Chapter 8 - Binomial Theor
- Page 235 and 236: Class XI Chapter 8 - Binomial Theor
- Page 237 and 238: Class XI Chapter 8 - Binomial Theor
- Page 239 and 240: Class XI Chapter 8 - Binomial Theor
- Page 241 and 242: Class XI Chapter 9 - Sequences and
- Page 243 and 244: Class XI Chapter 9 - Sequences and
- Page 245 and 246: Class XI Chapter 9 - Sequences and
- Page 247 and 248: Class XI Chapter 9 - Sequences and
- Page 249 and 250: Class XI Chapter 9 - Sequences and
- Page 251 and 252: Class XI Chapter 9 - Sequences and
- Page 253 and 254: Class XI Chapter 9 - Sequences and
- Page 255 and 256: Class XI Chapter 9 - Sequences and
- Page 257 and 258: Class XI Chapter 9 - Sequences and
- Page 259 and 260: Class XI Chapter 9 - Sequences and
- Page 261 and 262: Class XI Chapter 9 - Sequences and
- Page 263 and 264: Class XI Chapter 9 - Sequences and
- Page 265 and 266: Class XI Chapter 9 - Sequences and
- Page 267 and 268: Class XI Chapter 9 - Sequences and
- Page 269 and 270: Class XI Chapter 9 - Sequences and
- Page 271 and 272: Class XI Chapter 9 - Sequences and
- Page 273 and 274: Class XI Chapter 9 - Sequences and
- Page 275 and 276: Class XI Chapter 9 - Sequences and
- Page 277 and 278:
Class XI Chapter 9 - Sequences and

- Page 279 and 280:
Class XI Chapter 9 - Sequences and

- Page 281 and 282:
Class XI Chapter 9 - Sequences and

- Page 283 and 284:
Class XI Chapter 9 - Sequences and

- Page 285 and 286:
Class XI Chapter 9 - Sequences and

- Page 287 and 288:
Class XI Chapter 9 - Sequences and

- Page 289 and 290:
Class XI Chapter 9 - Sequences and

- Page 291 and 292:
Class XI Chapter 9 - Sequences and

- Page 293 and 294:
Class XI Chapter 9 - Sequences and

- Page 295 and 296:
Class XI Chapter 9 - Sequences and

- Page 297 and 298:
Class XI Chapter 9 - Sequences and

- Page 299 and 300:
Class XI Chapter 9 - Sequences and

- Page 301 and 302:
Class XI Chapter 9 - Sequences and

- Page 303 and 304:
Class XI Chapter 9 - Sequences and

- Page 305 and 306:
Class XI Chapter 9 - Sequences and

- Page 307 and 308:
Class XI Chapter 9 - Sequences and

- Page 309 and 310:
Class XI Chapter 9 - Sequences and

- Page 311 and 312:
Class XI Chapter 9 - Sequences and

- Page 313 and 314:
Class XI Chapter 10 - Straight Line

- Page 315 and 316:
Class XI Chapter 10 - Straight Line

- Page 317 and 318:
Class XI Chapter 10 - Straight Line

- Page 319 and 320:
Class XI Chapter 10 - Straight Line

- Page 321 and 322:
Class XI Chapter 10 - Straight Line

- Page 323 and 324:
Class XI Chapter 10 - Straight Line

- Page 325 and 326:
Class XI Chapter 10 - Straight Line

- Page 327 and 328:
Class XI Chapter 10 - Straight Line

- Page 329 and 330:
Class XI Chapter 10 - Straight Line

- Page 331 and 332:
Class XI Chapter 10 - Straight Line

- Page 333 and 334:
Class XI Chapter 10 - Straight Line

- Page 335 and 336:
Class XI Chapter 10 - Straight Line

- Page 337 and 338:
Class XI Chapter 10 - Straight Line

- Page 339 and 340:
Class XI Chapter 10 - Straight Line

- Page 341 and 342:
Class XI Chapter 10 - Straight Line

- Page 343 and 344:
Class XI Chapter 10 - Straight Line

- Page 345 and 346:
Class XI Chapter 10 - Straight Line

- Page 347 and 348:
Class XI Chapter 10 - Straight Line

- Page 349 and 350:
Class XI Chapter 10 - Straight Line

- Page 351 and 352:
Class XI Chapter 10 - Straight Line

- Page 353 and 354:
Class XI Chapter 10 - Straight Line

- Page 355 and 356:
Class XI Chapter 10 - Straight Line

- Page 357 and 358:
Class XI Chapter 10 - Straight Line

- Page 359 and 360:
Class XI Chapter 10 - Straight Line

- Page 361 and 362:
Class XI Chapter 10 - Straight Line

- Page 363 and 364:
Class XI Chapter 10 - Straight Line

- Page 365 and 366:
Class XI Chapter 10 - Straight Line

- Page 367 and 368:
Class XI Chapter 10 - Straight Line

- Page 369 and 370:
Class XI Chapter 10 - Straight Line

- Page 371 and 372:
Class XI Chapter 10 - Straight Line

- Page 373 and 374:
Class XI Chapter 11 - Conic Section

- Page 375 and 376:
Class XI Chapter 11 - Conic Section

- Page 377 and 378:
Class XI Chapter 11 - Conic Section

- Page 379 and 380:
Class XI Chapter 11 - Conic Section

- Page 381 and 382:
Class XI Chapter 11 - Conic Section

- Page 383 and 384:
Class XI Chapter 11 - Conic Section

- Page 385 and 386:
Class XI Chapter 11 - Conic Section

- Page 387 and 388:
Class XI Chapter 11 - Conic Section

- Page 389 and 390:
Class XI Chapter 11 - Conic Section

- Page 391 and 392:
Class XI Chapter 11 - Conic Section

- Page 393 and 394:
Class XI Chapter 11 - Conic Section

- Page 395 and 396:
Class XI Chapter 11 - Conic Section

- Page 397 and 398:
Class XI Chapter 11 - Conic Section

- Page 399 and 400:
Class XI Chapter 11 - Conic Section

- Page 401 and 402:
Class XI Chapter 11 - Conic Section

- Page 403 and 404:
Class XI Chapter 11 - Conic Section

- Page 405 and 406:
Class XI Chapter 11 - Conic Section

- Page 407 and 408:
Class XI Chapter 11 - Conic Section

- Page 409 and 410:
Class XI Chapter 11 - Conic Section

- Page 411 and 412:
Class XI Chapter 11 - Conic Section

- Page 413 and 414:
Class XI Chapter 11 - Conic Section

- Page 415 and 416:
Class XI Chapter 11 - Conic Section

- Page 417 and 418:
Class XI Chapter 12 - Introduction

- Page 419 and 420:
Class XI Chapter 12 - Introduction

- Page 421 and 422:
Class XI Chapter 12 - Introduction

- Page 423 and 424:
Class XI Chapter 12 - Introduction

- Page 425 and 426:
Class XI Chapter 12 - Introduction

- Page 427 and 428:
Class XI Chapter 12 - Introduction

- Page 429 and 430:
Class XI Chapter 12 - Introduction

- Page 431 and 432:
Class XI Chapter 13 - Limits and De

- Page 433 and 434:
Class XI Chapter 13 - Limits and De

- Page 435 and 436:
Class XI Chapter 13 - Limits and De

- Page 437 and 438:
Class XI Chapter 13 - Limits and De

- Page 439 and 440:
Class XI Chapter 13 - Limits and De

- Page 441 and 442:
Class XI Chapter 13 - Limits and De

- Page 443 and 444:
Class XI Chapter 13 - Limits and De

- Page 445 and 446:
Class XI Chapter 13 - Limits and De

- Page 447 and 448:
Class XI Chapter 13 - Limits and De

- Page 449 and 450:
Class XI Chapter 13 - Limits and De

- Page 451 and 452:
Class XI Chapter 13 - Limits and De

- Page 453 and 454:
Class XI Chapter 13 - Limits and De

- Page 455 and 456:
Class XI Chapter 13 - Limits and De

- Page 457 and 458:
Class XI Chapter 13 - Limits and De

- Page 459 and 460:
Class XI Chapter 13 - Limits and De

- Page 461 and 462:
Class XI Chapter 13 - Limits and De

- Page 463 and 464:
Class XI Chapter 13 - Limits and De

- Page 465 and 466:
Class XI Chapter 13 - Limits and De

- Page 467 and 468:
Class XI Chapter 13 - Limits and De

- Page 469 and 470:
Class XI Chapter 13 - Limits and De

- Page 471 and 472:
Class XI Chapter 13 - Limits and De

- Page 473 and 474:
Class XI Chapter 13 - Limits and De

- Page 475 and 476:
Class XI Chapter 13 - Limits and De

- Page 477 and 478:
Class XI Chapter 13 - Limits and De

- Page 479 and 480:
Class XI Chapter 13 - Limits and De

- Page 481 and 482:
Class XI Chapter 13 - Limits and De

- Page 483 and 484:
Class XI Chapter 13 - Limits and De

- Page 485 and 486:
Class XI Chapter 13 - Limits and De

- Page 487 and 488:
Class XI Chapter 13 - Limits and De

- Page 489 and 490:
Class XI Chapter 13 - Limits and De

- Page 491 and 492:
Class XI Chapter 14 - Mathematical

- Page 493 and 494:
Class XI Chapter 14 - Mathematical

- Page 495 and 496:
Class XI Chapter 14 - Mathematical

- Page 497 and 498:
Class XI Chapter 14 - Mathematical

- Page 499 and 500:
Class XI Chapter 14 - Mathematical

- Page 501 and 502:
Class XI Chapter 14 - Mathematical

- Page 503 and 504:
Class XI Chapter 14 - Mathematical

- Page 505 and 506:
Class XI Chapter 14 - Mathematical

- Page 507 and 508:
Class XI Chapter 15 - Statistics Ma

- Page 509 and 510:
Class XI Chapter 15 - Statistics Ma

- Page 511 and 512:
Class XI Chapter 15 - Statistics Ma

- Page 513 and 514:
Class XI Chapter 15 - Statistics Ma

- Page 515 and 516:
Class XI Chapter 15 - Statistics Ma

- Page 517 and 518:
Class XI Chapter 15 - Statistics Ma

- Page 519 and 520:
Class XI Chapter 15 - Statistics Ma

- Page 521 and 522:
Class XI Chapter 15 - Statistics Ma

- Page 523 and 524:
Class XI Chapter 15 - Statistics Ma

- Page 525 and 526:
Class XI Chapter 15 - Statistics Ma

- Page 527 and 528:
Class XI Chapter 15 - Statistics Ma

- Page 529 and 530:
Class XI Chapter 15 - Statistics Ma

- Page 531 and 532:
Class XI Chapter 15 - Statistics Ma

- Page 533 and 534:
Class XI Chapter 15 - Statistics Ma

- Page 535:
Class XI Chapter 15 - Statistics Ma