{"id":4593,"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-4\/"},"modified":"2016-05-17T10:48:30","modified_gmt":"2016-05-17T05:18:30","slug":"ncert-solutions-class-11-maths-miscellaneous-4","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-miscellaneous-4\/","title":{"rendered":"NCERT Solutions class-11 Maths Miscellaneous"},"content":{"rendered":"

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

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

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

= <\/p>\n

= <\/p>\n

= = = <\/p>\n

= <\/p>\n

= = <\/p>\n

\n

2. For any two complex numbers <\/strong> and <\/strong> prove that <\/strong><\/p>\n

Ans. <\/strong>Let and <\/p>\n

Then and <\/p>\n

Now, <\/p>\n

= <\/p>\n

= <\/p>\n

<\/p>\n

= <\/p>\n

\n

3. Reduce <\/strong> to the standard form.<\/strong><\/p>\n

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

= <\/p>\n

= <\/p>\n

= = <\/p>\n

= <\/p>\n

= <\/p>\n

= = <\/p>\n

= <\/p>\n

\n

4. If <\/strong> prove that <\/strong><\/p>\n

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

Squaring both sides, we get<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Squaring both sides, we get <\/p>\n

\n

5. Convert the following in the polar form:<\/strong><\/p>\n

(i) <\/strong><\/p>\n

(ii) <\/strong><\/p>\n

Ans. (i)<\/strong> Here = <\/p>\n

= <\/p>\n

<\/p>\n

and <\/p>\n

Squaring both sides and adding both the equations, we get<\/p>\n

<\/p>\n

<\/p>\n

and <\/p>\n

and <\/p>\n

[ lies in second quadrant]\n

<\/p>\n

Therefore, Polar form of is <\/p>\n

(ii)<\/strong> Here = <\/p>\n

<\/p>\n

and <\/p>\n

Squaring both sides and adding both the equations, we get<\/p>\n

<\/p>\n

<\/p>\n

and <\/p>\n

and <\/p>\n

[ lies in second quadrant]\n

<\/p>\n

Therefore, Polar form of is <\/p>\n

\n

Solve each of the equations in exercises 6 to 9:<\/strong><\/p>\n

6. <\/strong><\/p>\n

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

Comparing with , and <\/p>\n

<\/p>\n

= <\/p>\n

= = <\/p>\n

Therefore, and <\/p>\n

\n

7. <\/strong><\/p>\n

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

Comparing with , and <\/p>\n

<\/p>\n

= <\/p>\n

= = <\/p>\n

Therefore, and <\/p>\n

\n

8. <\/strong><\/p>\n

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

Comparing with , and <\/p>\n

<\/p>\n

= <\/p>\n

= = <\/p>\n

Therefore, and <\/p>\n

\n

9. <\/strong><\/p>\n

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

Comparing with , and <\/p>\n

<\/p>\n

= <\/p>\n

= = <\/p>\n

Therefore, and <\/p>\n

\n

10. If <\/strong> find <\/strong><\/p>\n

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

= <\/p>\n

= = <\/p>\n

= <\/p>\n

\n

11. If <\/strong> prove that <\/strong><\/p>\n

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

Comparing both sides, we have and <\/p>\n

<\/p>\n

= = <\/p>\n

<\/p>\n

= Proved.<\/p>\n

\n

12. Let <\/strong> find:<\/strong><\/p>\n

(i) <\/strong><\/p>\n

(ii) <\/strong><\/p>\n

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

(i)<\/strong> <\/p>\n

<\/p>\n

<\/p>\n

(ii)<\/strong> <\/p>\n

<\/p>\n

\n

13. Find the modulus and argument of the complex number <\/strong><\/p>\n

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

= <\/p>\n

and <\/p>\n

Squaring both sides and adding both the equations, we get<\/p>\n

<\/p>\n

<\/p>\n

and <\/p>\n

and <\/p>\n

[ lies in second quadrant]\n

<\/p>\n

Therefore, and arg<\/p>\n

\n

14. Find the real numbers <\/strong> and <\/strong> if <\/strong> is the conjugate of <\/strong><\/p>\n

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

Now <\/p>\n

<\/p>\n

<\/p>\n

Comparing both sides, we have and <\/p>\n

Solving both equations, we have and <\/p>\n

\n

15. Find the modulus of <\/strong><\/p>\n

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

= = <\/p>\n

\n

16. If <\/strong> then show that <\/strong><\/p>\n

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

<\/p>\n

<\/p>\n

Comparing both sides, we have and <\/p>\n

Now, <\/p>\n

= <\/p>\n

\n

17. If <\/strong> and <\/strong> are different complex numbers with <\/strong> then find <\/strong><\/p>\n

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

= <\/p>\n

= <\/p>\n

= <\/p>\n

<\/p>\n

\n

18. Find the number of non-zero integral solutions of the equation <\/strong><\/p>\n

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

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

19. If <\/strong> then show that:<\/strong><\/p>\n

<\/strong><\/p>\n

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

Taking modulus on both sides,<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Squaring both sides, we get<\/p>\n

<\/p>\n

\n

20. If <\/strong> then find the least positive integral value of <\/strong><\/p>\n

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

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

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

Miscellaneous Exercise 1. Evaluate: Ans. Given: = = = = = = = = 2. For any two complex numbers and prove that Ans. Let and Then and Now, = = = 3. Reduce to the standard form. Ans. Here: = = = = = = = = = 4. If prove that Ans. Given: … 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-4593","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-4\/\" \/>\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. Evaluate: Ans. Given: = = = = = = = = 2. For any two complex numbers and prove that Ans. Let and Then and Now, = = = 3. Reduce to the standard form. Ans. Here: = = = = = = = = = 4. If prove that Ans. Given: ... 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