{"id":4605,"date":"2016-05-17T09:49:00","date_gmt":"2016-05-17T04:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-miscellaneous-7\/"},"modified":"2016-05-17T11:05:05","modified_gmt":"2016-05-17T05:35:05","slug":"ncert-solutions-class-11-maths-miscellaneous-7","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-miscellaneous-7\/","title":{"rendered":"NCERT Solutions class-11 Maths Miscellaneous"},"content":{"rendered":"

Miscellaneous Exercise<\/strong><\/p>\n

1. Find <\/strong> and <\/strong> in the expansion of <\/strong> if the first three terms of the expansion are 729, 7290 and 30375 respectively.<\/strong><\/p>\n

Ans. <\/strong>Given: <\/p>\n

\u2026..(i)<\/p>\n

<\/p>\n

\u2026..(ii)<\/p>\n

And <\/p>\n

\u2026..(iii)<\/p>\n

Multiplying eq. (i) and eq. (iii),<\/p>\n

\u2026..(iv)<\/p>\n

Squaring both sides in eq. (ii),<\/p>\n

\u2026..(v)<\/p>\n

Dividing eq. (iv) by eq. (v),<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

From eq. (i), <\/p>\n

<\/p>\n

<\/p>\n

And From eq. (ii), <\/p>\n

<\/p>\n

Therefore, , and <\/p>\n

\n

2. Find <\/strong> if the coefficient of <\/strong> and <\/strong> in the expansion of <\/strong> are equal.<\/strong><\/p>\n

Ans. <\/strong>Here <\/p>\n

<\/p>\n

Coefficient of = and Coefficient of = <\/p>\n

According to question, <\/p>\n

<\/p>\n

= <\/p>\n

\n

3. Find the coefficient of <\/strong> in the product <\/strong> using binomial theorem.<\/strong><\/p>\n

Ans. <\/strong>Using Binomial Theorem,<\/p>\n

<\/p>\n

<\/p>\n

= <\/p>\n

<\/p>\n

Coefficient of in the product<\/p>\n

= <\/p>\n

= <\/p>\n

\n

4. If <\/strong> and <\/strong> are distinct integers, prove that <\/strong> is a factor of <\/strong> whenever <\/strong> is a positive integer.<\/strong><\/p>\n

Ans. <\/strong>We have, <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

which shows that is a factor of <\/p>\n

\n

5. Evaluate: <\/strong><\/p>\n

Ans. <\/strong>Given: <\/p>\n

Using Binomial Theorem,<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

= <\/p>\n

<\/p>\n

<\/p>\n

= <\/p>\n

= <\/p>\n

= <\/p>\n

\n

6. Find the value of <\/strong><\/p>\n

Ans. <\/strong>Putting and we have<\/p>\n

= <\/p>\n

= <\/p>\n

= = <\/p>\n

= = <\/p>\n

= = <\/p>\n

\n

7. Find an approximation of <\/strong> using the first three terms of its expansion.<\/strong><\/p>\n

Ans. <\/strong>Here = <\/p>\n

= = = 0.951<\/p>\n

\n

8. Find <\/strong> if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of <\/strong> is <\/strong><\/p>\n

Ans. <\/strong>Here <\/p>\n

5th<\/sup> term from the beginning = <\/p>\n

5th<\/sup> term from the end = term from beginning = term from the beginning<\/p>\n

= <\/p>\n

Now, <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

9. Expand using binomial theorem <\/strong><\/p>\n

Ans. <\/strong>We have <\/p>\n

= <\/p>\n

= <\/p>\n

<\/p>\n

= <\/p>\n

= <\/p>\n

\n

10. Find the expansion of <\/strong> using binomial theorem.<\/strong><\/p>\n

Ans. <\/strong>Here <\/p>\n

= <\/p>\n

= <\/p>\n

= <\/p>\n

= <\/p>\n

= <\/p>\n","protected":false},"excerpt":{"rendered":"

Miscellaneous Exercise 1. Find and in the expansion of if the first three terms of the expansion are 729, 7290 and 30375 respectively. Ans. Given: \u2026..(i) \u2026..(ii) And \u2026..(iii) Multiplying eq. (i) and eq. (iii), \u2026..(iv) Squaring both sides in eq. (ii), \u2026..(v) Dividing eq. (iv) by eq. (v), From eq. (i), And From eq. … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,281],"tags":[],"class_list":["post-4605","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"\nNCERT Solutions class-11 Maths Miscellaneous | myCBSEguide<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-miscellaneous-7\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions class-11 Maths Miscellaneous | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Miscellaneous Exercise 1. Find and in the expansion of if the first three terms of the expansion are 729, 7290 and 30375 respectively. Ans. Given: \u2026..(i) \u2026..(ii) And \u2026..(iii) Multiplying eq. (i) and eq. (iii), \u2026..(iv) Squaring both sides in eq. (ii), \u2026..(v) Dividing eq. (iv) by eq. (v), From eq. (i), And From eq. ... 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