{"id":14167,"date":"2019-12-23T10:48:35","date_gmt":"2019-12-23T05:18:35","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=14167"},"modified":"2021-07-02T15:35:11","modified_gmt":"2021-07-02T10:05:11","slug":"1st-puc-maths-question-bank-chapter-8","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/1st-puc-maths-question-bank-chapter-8\/","title":{"rendered":"1st PUC Maths Question Bank Chapter 8 Binomial Theorem"},"content":{"rendered":"<p>Students can Download Maths Chapter 8 Binomial Theorem\u00a0Questions and Answers, Notes Pdf, <a href=\"https:\/\/kseebsolutions.guru\/1st-puc-maths-question-bank\/\">1st PUC Maths Question Bank with Answers<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n<h2>Karnataka 1st PUC Maths Question Bank Chapter 8 Binomial Theorem<\/h2>\n<p>Question 1.<br \/>\nState and prove Binomial theorem.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71213\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-1.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 1\" width=\"387\" height=\"633\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-1.png 387w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-1-183x300.png 183w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71214\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-2.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 2\" width=\"359\" height=\"287\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-2.png 359w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-2-300x240.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/p>\n<p>Some observations in a binomial theorem:<br \/>\n(1) The expansion of {a + b)<sup>n<\/sup> has (n + 1) terms<br \/>\n(2) The coefficients <sup>n<\/sup>C<sub>r<\/sub>\u00a0occurring in the binomial theorem are known as binomial coefficients.<br \/>\n(3) The indices of V go on decreasing and that of &#8216;a&#8217; go on increasing by 1 at each stage.<br \/>\ni.e., for each term: index of a + index of b-n.<br \/>\n(4) Since <sup>n<\/sup>C<sub>r<\/sub>=<sup>n<\/sup>C<sub>n<\/sub>_<sub>r <\/sub>we have<br \/>\n<sup>n<\/sup>C<sub>0<\/sub> =<sup>n<\/sup>C<sub>n<\/sub>, <sup>n<\/sup>C<sub>x<\/sub> =<sup>n<\/sup>C<sub>n<\/sub>_<sub>r <\/sub>and so on.<br \/>\nThus the coefficients of the terms equidistant from the beginning and the end in a binomial theorem are equal.<br \/>\n(5) General term in (a + b)<sup>n<\/sup>: T<sub>r+1<\/sub>\u00a0&#8211; <sup>n<\/sup>C<sub>r <\/sub>a<sup>n<span style=\"font-size: 16px;\">&#8211;<\/span><\/sup><sup>r<\/sup>b<sup>r<br \/>\n<\/sup>(6) Middle terms in (a + b)<sup>n<\/sup><\/p>\n<ul>\n<li>When &#8216;n&#8217; is even, the middle term<br \/>\n\\(=\\left(\\frac{n}{2}+1\\right)^{t h} \\text { term }\\)<\/li>\n<li>When &#8216;n&#8217; is odd ,the middle term are<br \/>\n\\(\\frac{1}{2}(n+1)^{n} \\text { term an } \\frac{1}{2}(n+3)^{n} \\text { term }\\)<\/li>\n<\/ul>\n<p>(7) Taking a = x and b = -y in the expansion, we get (x-y)<sup>n<\/sup> =[x + (-y)]<sup>n<\/sup><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71215\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-3.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 3\" width=\"370\" height=\"467\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-3.png 370w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-3-238x300.png 238w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions-300x28.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 2.<br \/>\nExpand each of the expression<br \/>\n(i)\\(\\left(x^{2}+\\frac{3}{x}\\right)^{4}\\)<br \/>\n(ii)\\((1-2 x)^{5}\\)<br \/>\n(iii)\\(\\left(\\frac{2}{x}-\\frac{x}{2}\\right)^{5}\\)<br \/>\n(iv)\\((2 x-3)^{6}\\)<br \/>\n(v)\\(\\left(\\frac{x}{3}+\\frac{1}{x}\\right)^{5}\\)<br \/>\n(vi)\\(\\left(x+\\frac{1}{x}\\right)^{6}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71216\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-4.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 4\" width=\"332\" height=\"395\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-4.png 332w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-4-252x300.png 252w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71217\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-5.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 5\" width=\"368\" height=\"539\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-5.png 368w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-5-205x300.png 205w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71218\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-6.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 6\" width=\"359\" height=\"493\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-6.png 359w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-6-218x300.png 218w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/p>\n<p>Question 3.<br \/>\nUsing binomial theorem, evaluate each of the following:<br \/>\n(i) (98)<sup>5<\/sup><br \/>\n(ii) (96)<sup>3<\/sup><br \/>\n(iii) (102)<sup>5<\/sup><br \/>\n(iv) (101)<sup>4<\/sup><br \/>\n(v) (99)<sup>5<br \/>\n<\/sup>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71219\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-7.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 7\" width=\"387\" height=\"371\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-7.png 387w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-7-300x288.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71220\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-8.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 8\" width=\"380\" height=\"554\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-8.png 380w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-8-206x300.png 206w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions-300x28.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 4.<br \/>\nWhich is longer \\((1.01)^{1000000} \\text { or } 10,000 ?\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71221\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-9.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 9\" width=\"393\" height=\"215\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-9.png 393w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-9-300x164.png 300w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/><\/p>\n<p>Question 5.<br \/>\nUsing Binomial theorem, indicate which number is larger \\( (1.1)^{10000} \\text { or } 1000 ?\\)<br \/>\nAnswer:<br \/>\nSpilitting 1.01 and using Binomial theorem write the first few terms, we have.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71222\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-10.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 10\" width=\"381\" height=\"162\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-10.png 381w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-10-300x128.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><\/p>\n<p>Question 6.<br \/>\nFind (a + b)<sup>4<\/sup> &#8211; (a -b)<sup>4<\/sup>. Hence evaluate<br \/>\n\\((\\sqrt{3}+\\sqrt{2})^{4}-(\\sqrt{3}-\\sqrt{2})^{4}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71223\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-11.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 11\" width=\"378\" height=\"336\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-11.png 378w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-11-300x267.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p>Question 7.<br \/>\nFind (x +1)<sup>6<\/sup> +(x -1)<sup>6<\/sup>. Hence or otherwise evaluate<br \/>\n\\((\\sqrt{2}+1)^{6}+(\\sqrt{2}-1)^{6}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71224\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-12.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 12\" width=\"374\" height=\"59\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-12.png 374w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-12-300x47.png 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71225\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-13.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 13\" width=\"380\" height=\"385\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-13.png 380w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-13-296x300.png 296w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<p>Question 8.<br \/>\nEvaluate:<br \/>\n\\((\\sqrt{3}+\\sqrt{2})^{6}+(\\sqrt{3}-\\sqrt{2})^{6}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71226\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-14.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 14\" width=\"387\" height=\"542\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-14.png 387w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-14-214x300.png 214w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/p>\n<p>Question 9.<br \/>\nFind the value of<br \/>\n\\(\\left(a^{2}+\\sqrt{a^{2}-1}\\right)^{4}+\\left(a^{2}-\\sqrt{a^{2}-1}\\right)^{4}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71227\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-15.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 15\" width=\"203\" height=\"42\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71228\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-16.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 16\" width=\"376\" height=\"341\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-16.png 376w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-16-300x272.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions-300x28.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 10.<br \/>\nShow that 9<sup>n+1<\/sup> &#8211; 8n &#8211; 9 is divisible by 64, whenever &#8216;n&#8217; is a positive integer.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71229\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-17.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 17\" width=\"361\" height=\"282\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-17.png 361w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-17-300x234.png 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><\/p>\n<p>Question 11.<br \/>\nUsing binomial theorem, prove that 6<sup>n <\/sup>-5n always leaves remainder 1 when<br \/>\ndivided by 25.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71230\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-18.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 18\" width=\"390\" height=\"195\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-18.png 390w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-18-300x150.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><\/p>\n<p>Question 12.<br \/>\nProve that<br \/>\n\\(\\sum_{n=0}^{n} y \\cdot c_{n}=4\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71231\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-19.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 19\" width=\"298\" height=\"82\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71232\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-20.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 20\" width=\"72\" height=\"94\" \/><\/p>\n<p>Question 13.<br \/>\nFind the 4<sup>th<\/sup> term in the expansion of (x-2 y)<sup>12<\/sup>.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71233\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-21.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 21\" width=\"333\" height=\"167\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-21.png 333w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-21-300x150.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p>Question 14.<br \/>\nFind the 13<sup>th<\/sup> term in the expansion of<br \/>\n\\(\\left(9 x-\\frac{1}{3 \\sqrt{x}}\\right)^{18}, x \\neq 0 \\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71234\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-22.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 22\" width=\"237\" height=\"264\" \/><\/p>\n<p>Question 15.<br \/>\nWrite the general term in the expression of<br \/>\n(i) (x<sup>2<\/sup> -y)<sup>6<\/sup><br \/>\n(ii)\u00a0(x<sup>2<\/sup>-yx)<sup>12<\/sup>,x\u22600<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71235\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-23.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 23\" width=\"290\" height=\"234\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions-300x28.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 16.<br \/>\nFind the coefficient of<br \/>\n(i) x<sup>5<\/sup> in (x + 3)<sup>8<\/sup><br \/>\n(ii) a<sup>5<\/sup>b<sup>7 <\/sup>in (a &#8211; 2b)<sup>12<br \/>\n<\/sup>(iii) x<sup>6<\/sup>y<sup>3<\/sup> in (x + 2y)<sup>9<br \/>\n<\/sup>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71236\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-24.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 24\" width=\"342\" height=\"252\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-24.png 342w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-24-300x221.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/p>\n<p>Question 17.<br \/>\nFind a, if the 17<sup>th<\/sup> and 18<sup>th<\/sup> terms of the expansion (2 +a)<sup>50<\/sup> are equal.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71237\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-25.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 25\" width=\"281\" height=\"353\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-25.png 281w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-25-239x300.png 239w\" sizes=\"(max-width: 281px) 100vw, 281px\" \/><\/p>\n<p>Question 18.<br \/>\nIn the expansion of (1+ a)<sup>m+n<\/sup>, prove that coefficients of a<sup>m<\/sup> and a<sup>n<\/sup> are equal.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71238\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-26.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 26\" width=\"299\" height=\"228\" \/><\/p>\n<p>Question 19.<br \/>\nProve that the coefficient of x<sup>n<\/sup> in the expansion of (1 + x)<sup>2n<\/sup> is twice the coefficient of x<sup>n<\/sup> in the expansion of (1+x)<sup>2n-1<br \/>\n<\/sup>Answer:<br \/>\nIn (1+x)<sup>2n <\/sup>we have<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71239\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-27.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 27\" width=\"374\" height=\"522\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-27.png 374w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-27-215x300.png 215w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><br \/>\nFrom (1) and (2) we get, the coefficient of x<sup>n<\/sup> in (1 + x)<sup>2n<\/sup> is twice the coefficient of x<sup>n<\/sup> in (1 + x)<sup>2n-<\/sup><sup>1<\/sup>.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions-300x28.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 20.<br \/>\nFind a positive value of m for which the coefficient of x<sup>2<\/sup> in the expansion (1 + x)<sup>m<\/sup> is 6.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71240\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-28.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 28\" width=\"328\" height=\"172\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-28.png 328w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-28-300x157.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><sup><br \/>\n<\/sup><\/p>\n<p>Question 21.<br \/>\nFind the middle terms in the expansions of<br \/>\n(i) \\(\\left(3-\\frac{x^{3}}{6}\\right)^{7}\\)<br \/>\n(ii)\\(\\left(\\frac{x}{3}+9 y\\right)^{10}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71241\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-29.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 29\" width=\"331\" height=\"183\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-29.png 331w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-29-300x166.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71242\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-30.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 30\" width=\"305\" height=\"288\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-30.png 305w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-30-300x283.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 22.<br \/>\nShow that the middle term in the expansion of \\((1+x)^{2 n} \\text { is } \\frac{1 \\cdot 3 \\cdot 5 \\ldots(2 n-1)}{\\lfloor n} 2^{n} x^{n} \\)where &#8216;n&#8217; is a positive integer.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71243\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-31.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 31\" width=\"388\" height=\"400\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-31.png 388w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-31-291x300.png 291w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/p>\n<p>Question 23.<br \/>\nThe second, third and fourth terms in the binomial expansion (x + a)<sup>n<\/sup> are 240, 720 and 1080, respectively. Find x, a and n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71244\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-32.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 32\" width=\"325\" height=\"210\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-32.png 325w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-32-300x194.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71245\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-33.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 33\" width=\"327\" height=\"622\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-33.png 327w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-33-158x300.png 158w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><\/p>\n<p>Question 24.<br \/>\nThe coefficients of three consecutive terms in the expansion of (1 + a)<sup>n<\/sup> are in the ratio 1:7: 42. Find n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71246\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-34.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 34\" width=\"387\" height=\"399\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-34.png 387w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-34-291x300.png 291w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71247\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-35.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 35\" width=\"332\" height=\"389\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-35.png 332w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-35-256x300.png 256w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions-300x28.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 25.<br \/>\nThe coefficients (r-1)<sup>th<\/sup>, r<sup>th<\/sup>,and (r + 1)<sup>th<\/sup>, terms in the expansion of (x + 1)<sup>th<\/sup>, are in the ratio 1:3:5. Find n and r.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71248\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-36.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 36\" width=\"392\" height=\"609\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-36.png 392w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-36-193x300.png 193w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71249\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-37.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 37\" width=\"230\" height=\"116\" \/><\/p>\n<p>Question 26.<br \/>\nFind the term independent of x in the expansion of \\(\\left(\\frac{3}{2} x^{2}-\\frac{1}{3 x}\\right)^{6}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71250\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-38.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 38\" width=\"361\" height=\"367\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-38.png 361w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-38-295x300.png 295w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><\/p>\n<p>Question 27.<br \/>\nFind the term independent of x in the expansion of \\(\\left(\\sqrt[3]{x}+\\frac{1}{2 \\sqrt[3]{x}}\\right)^{18}, x&gt;0\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71251\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-39.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 39\" width=\"332\" height=\"316\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-39.png 332w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-39-300x286.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><\/p>\n<p>Question 28.<br \/>\nFind a, 6 and n in the expansion of (a + b)<sup>n<\/sup> if the first three terms of the expansion are 729,7290 and 30375, respectively.<br \/>\nAnswer:<br \/>\nGiven: T<sub>x<\/sub> = 729, T<sub>2<\/sub> = 7290 and T<sub>3<\/sub> = 30375<br \/>\n\u2234 a<sup>n<\/sup>=729&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;.(1)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71252\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-40.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 40\" width=\"328\" height=\"615\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-40.png 328w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-40-160x300.png 160w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions-300x28.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 29.<br \/>\nFind a if the coefficients of x<sup>2<\/sup> and x<sup>3<\/sup> in the expansion of (3 +ax)<sup>9<\/sup> are equal.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71253\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-41.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 41\" width=\"274\" height=\"249\" \/><\/p>\n<p>Question 30.<br \/>\nIf the coefficients of (r &#8211; 5)<sup>th<\/sup> and (2r -1)<sup>th <\/sup>terms in the expansion of (1 + x)<sup>34<\/sup> are equal, find r.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71254\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-42.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 42\" width=\"388\" height=\"118\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-42.png 388w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-42-300x91.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71255\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-43.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 43\" width=\"207\" height=\"113\" \/><\/p>\n<p>Question 31.<br \/>\nIf the coefficients of a<sup>r-1<\/sup>, a<sup>r<\/sup> and a<sup>r+1<\/sup> in the expansion of (1 + a)<sup>n<\/sup> are in arithmetic progression, prove that n<sup>2<\/sup> &#8211; n(4r +1) + 4r<sup>2<\/sup> -2 = 0.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71256\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-44.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 44\" width=\"354\" height=\"531\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-44.png 354w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-44-200x300.png 200w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/p>\n<p>Question 32.<br \/>\nShow that the coefficient of the middle term in the expansion of (1 + x)<sup>2n<\/sup>\u00a0is equal to the sum of the coefficients of two middle terms in the expansion of (1 + x)<sup>2<span style=\"font-size: 16px;\">n<\/span><\/sup><sup>-1<\/sup>.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71257\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-45.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 45\" width=\"387\" height=\"248\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-45.png 387w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-45-300x192.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71258\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-46.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 46\" width=\"364\" height=\"157\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-46.png 364w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-46-300x129.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/p>\n<p>Question 33.<br \/>\nFind n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of<br \/>\n\\(\\left(\\sqrt[4]{2}+\\frac{1}{\\sqrt[4]{3}}\\right)^{n} \\text { is } \\sqrt{6}: 1\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71259\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-47.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 47\" width=\"391\" height=\"757\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-47.png 391w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-47-155x300.png 155w\" sizes=\"(max-width: 391px) 100vw, 391px\" \/><\/p>\n<p>Question 34.<br \/>\nFind the r<sup>th <\/sup>term from the end in the expansion of (x + a)<sup>n<\/sup>.<br \/>\nAnswer:<br \/>\nr<sup>th <\/sup> term from the end in (x + a)<sup>n<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71260\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-48.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 48\" width=\"176\" height=\"105\" \/><br \/>\n<\/sup><\/p>\n<p>Question 35.<br \/>\nIf a and b are distinct integers, prove that a-b is a factor of a<sup>n<\/sup> -b<sup>n<\/sup>, whenever n is a positive integer.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71261\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-49.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 49\" width=\"358\" height=\"251\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-49.png 358w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-49-300x210.png 300w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><\/p>\n<p>Question 36.<br \/>\nThe sum of the coefficients of the first three terms in the expansion of<br \/>\n\\(\\left(x-\\frac{3}{x^{2}}\\right)^{m}, x \\neq 0, m \\)being a natural numbers, is 559. Find the term of the expansion containing x<sup>3<\/sup>.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71262\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-50.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 50\" width=\"389\" height=\"520\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-50.png 389w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-50-224x300.png 224w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 37.<br \/>\nFind the coefficient of x<sup>5<\/sup> in the product (1 + 2x)<sup>6<\/sup>(1 &#8211; x)<sup>7<\/sup> using binomial theorem.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71263\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-51.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 51\" width=\"364\" height=\"390\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-51.png 364w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-51-280x300.png 280w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/p>\n<p>Question 38.<br \/>\nFind the coefficient of a<sup>4<\/sup> in the product (1 + 2a)<sup>4<\/sup>(2-a)<sup>s<\/sup> using binomial theorem.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71264\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-52.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 52\" width=\"363\" height=\"551\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-52.png 363w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-52-198x300.png 198w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 39.<br \/>\nExpand using Binomial theorem<br \/>\n\\(\\left(1+\\frac{x}{2}-\\frac{2}{x}\\right)^{4}, x \\neq 0\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71265\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-53.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 53\" width=\"380\" height=\"684\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-53.png 380w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-53-167x300.png 167w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions-300x28.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 40.<br \/>\nFind the expansion of (3x<sup>2<\/sup> &#8211; 1ax + 3a<sup>2<\/sup>)<sup>3<\/sup> using binomial theorem.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71266\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-54.png\" alt=\"1st PUC Maths Question Bank Chapter 8 Binomial Theorem 54\" width=\"372\" height=\"410\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-54.png 372w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/12\/1st-PUC-Maths-Question-Bank-Chapter-8-Binomial-Theorem-54-272x300.png 272w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students can Download Maths Chapter 8 Binomial Theorem\u00a0Questions and Answers, Notes Pdf, 1st PUC Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 1st PUC Maths Question Bank Chapter 8 Binomial Theorem Question 1. State and prove Binomial theorem. Answer: Some &hellip;<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[81],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/14167"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=14167"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/14167\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=14167"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=14167"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=14167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}