{"id":4634,"date":"2016-05-17T11:49:00","date_gmt":"2016-05-17T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-miscellaneous-12\/"},"modified":"2016-05-17T13:36:31","modified_gmt":"2016-05-17T08:06:31","slug":"ncert-solutions-class-11-maths-miscellaneous-12","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-miscellaneous-12\/","title":{"rendered":"NCERT Solutions class-11 Maths Miscellaneous"},"content":{"rendered":"

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

1. Write the negation of the following statements:<\/strong><\/p>\n

(i) <\/strong> For every positive real number <\/strong>, the number <\/strong> is also positive.<\/strong><\/p>\n

(ii) <\/strong> All cats scratch.<\/strong><\/p>\n

(iii) <\/strong> For every real number <\/strong>, either <\/strong> or <\/strong><\/p>\n

(iv) <\/strong> There exists a number <\/strong> such that <\/strong><\/p>\n

Ans. (i) <\/strong> There exists a positive real number such that is not positive.<\/p>\n

(ii) <\/strong> There exists a cat which does not scratch.<\/p>\n

(iii) <\/strong> There exists a real number such that or <\/p>\n

(iv) <\/strong> There does not exist a number such that <\/p>\n

\n

2. State the converse and contrapositive of each of the following statements:<\/strong><\/p>\n

(i) <\/strong> A positive integer is prime only if it has no divisors other than 1 and itself.<\/strong><\/p>\n

(ii) <\/strong> I go to a beach whenever it is a sunny day.<\/strong><\/p>\n

(iii) <\/strong> If it is not outside, then you feel thirsty.<\/strong><\/p>\n

Ans. (i) <\/strong>Contrapositive: If a positive integer has divisors other than 1 and itself then it is not prime.<\/p>\n

Converse: If a positive integer has no divisors other than 1 and itself then it is a prime.<\/p>\n

(ii) <\/strong>Contrapositive: If I do not go to a beach then it is not a sunny day.<\/p>\n

Converse: If I go to a beach then it is a sunny day.<\/p>\n

(iii) <\/strong>Contrapositive: If you do not feel thirsty then it is not hot outside.<\/p>\n

Converse: If you feel thirsty then it is hot outside.<\/p>\n

\n

3. Rewrite each of the following statements in the form \u201c<\/strong> it and only if <\/strong>\u201d.<\/strong><\/p>\n

(i) It is necessary to have a password to log on to the server.<\/strong><\/p>\n

(ii) There is traffic Jam whenever it rains.<\/strong><\/p>\n

(iii) You can access the website only if you pay a subscription fee.<\/strong><\/p>\n

Ans. (i) <\/strong>If you log on to the server then you have a password.<\/p>\n

(ii) <\/strong>If it rains, then there is traffic jam.<\/p>\n

(iii) <\/strong>If you can access the website, then you pay a subscription fee.<\/p>\n

\n

4. Rewrite each of the following statements in the form \u201c<\/strong> it and only if <\/strong>\u201d.<\/strong><\/p>\n

(i) <\/strong> If you watch television, then your mind is free and if your mind is free, then you watch television.<\/strong><\/p>\n

(ii) <\/strong> For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.<\/strong><\/p>\n

(iii) <\/strong> If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.<\/strong><\/p>\n

Ans. (i) <\/strong>You watch television if and only if your mind is free.<\/p>\n

(ii) <\/strong>You get an A grade if and only if you do all the homework regularly.<\/p>\n

(iii) <\/strong>A quadrilateral is equiangular if and only if it is a rectangle.<\/p>\n

\n

5. Given below are two statements:<\/strong><\/p>\n

25 is a multiple of 5.<\/strong><\/p>\n

25 is a multiple of 8.<\/strong><\/p>\n

Write the compound statements connecting these two statements with \u201cand\u201d and \u201cor\u201d. In both cases check the validity of the compound statement.<\/strong><\/p>\n

Ans. <\/strong>The compound statement with \u201cand\u201d is: 25 is a multiple of 5 and 8.<\/p>\n

Since, is true and is false therefore the compound statement with \u201cand\u201d is not true.<\/p>\n

Therefore, the statement \u201c and \u201d is not valid.<\/p>\n

Now the compound statement with \u201cor\u201d is: 25 is a multiple of 5 or 8.<\/p>\n

Since, is true and is false therefore the compound statement with \u201cor\u201d is true.<\/p>\n

Therefore, the statement \u201c and \u201d is valid.<\/p>\n

\n

6. Check the validity of the statements given below by the method given against it:<\/strong><\/p>\n

(i) <\/strong> The sum of an irrational number and a rational number is irrational (by contradiction method)<\/strong><\/p>\n

(ii) <\/strong> If <\/strong> is a real number with <\/strong> then <\/strong> (by contradiction method)<\/strong><\/p>\n

Ans. (i) <\/strong>Let us assume that is not true.<\/p>\n

Sum of an irrational and a rational number is not irrational.<\/p>\n

There exists an irrational number and a rational number such that is not irrational.<\/p>\n

(say) is a rational number.<\/p>\n

<\/p>\n

is rational.<\/p>\n

But is irrational, which is contradiction, therefore our supposition is wrong.<\/p>\n

Therefore, is true.<\/p>\n

(ii) <\/strong>Let and be the statements given by<\/p>\n

is a real number with <\/p>\n

<\/p>\n

If possible let is not true, then is true.<\/p>\n

and is true.<\/p>\n

is a real number with and which is contradiction, therefore our supposition is wrong.<\/p>\n

Therefore, is true.<\/p>\n

\n

7. Write the following statement in five different ways, conveying the same meaning:<\/strong><\/p>\n

If a triangle is equiangular, then it is an obtuse angled triangle.<\/strong><\/p>\n

Ans. (i) <\/strong>A triangle is equiangular implies that it is an obtuse angled triangle.<\/p>\n

(ii) <\/strong>A triangle is equiangular only if it an obtuse angled triangle.<\/p>\n

(iii) <\/strong>For a triangle to be equiangular it is necessary it is an obtuse angled triangle.<\/p>\n

(iv) <\/strong>For a triangle to be obtuse angled triangle it is sufficient that the triangle is equiangular.<\/p>\n

(v) <\/strong>Is a triangle is not equiangular then it is not an obtuse angled triangle.<\/p>\n","protected":false},"excerpt":{"rendered":"

Miscellaneous Exercise 1. Write the negation of the following statements: (i) For every positive real number , the number is also positive. (ii) All cats scratch. (iii) For every real number , either or (iv) There exists a number such that Ans. (i) There exists a positive real number such that is not positive. (ii) … 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-4634","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-12\/\" \/>\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. Write the negation of the following statements: (i) For every positive real number , the number is also positive. (ii) All cats scratch. (iii) For every real number , either or (iv) There exists a number such that Ans. (i) There exists a positive real number such that is not positive. (ii) ... 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