{"id":625887,"date":"2023-09-08T08:57:01","date_gmt":"2023-09-08T08:57:01","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=625887"},"modified":"2023-09-08T08:57:06","modified_gmt":"2023-09-08T08:57:06","slug":"kc-sinha-exercise-12-1-mathematics-solution-class-11-chapter-12-raikhik-asamikaye","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-12-1-mathematics-solution-class-11-chapter-12-raikhik-asamikaye\/","title":{"rendered":"KC Sinha: Exercise 12.1 – Mathematics Solution Class 11 Chapter 12 \u0930\u0948\u0916\u093f\u0915 \u0905\u0938\u092e\u093f\u0915\u093e\u090f\u0901"},"content":{"rendered":"\n\n\n\n\n

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

Exercise 12.1<\/h3>\n\n\n\n

Question 1<\/h4>\n\n\n\n

If x is a non-negative integer then solve
2-3x<5-4x
Sol :<\/p>\n\n\n\n

Adding both sides 4x<\/p>\n\n\n\n

2-3x+4x<5-4x+4x<\/p>\n\n\n\n

2+x<5<\/p>\n\n\n\n

Subtracting both sides 2<\/p>\n\n\n\n

2+x-2<5-2<\/p>\n\n\n\n

x<3<\/p>\n\n\n\n

x={0,1,2}<\/p>\n\n\n\n

[]<\/p>\n\n\n\n

ALTERNATE METHOD<\/p>\n\n\n\n

2-3x<5-4x<\/p>\n\n\n\n

-3x+4x<5-2<\/p>\n\n\n\n

x<2<\/p>\n\n\n\n

Question 2<\/h4>\n\n\n\n

Solve 2(x-2)<3x-2, $x \\in\\{-2,-1,0,1,2,3,4\\}$<\/p>\n\n\n\n

Also show the solution set on the number line<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

2(x-2)<3x-2<\/p>\n\n\n\n

2x-4<3x-2<\/p>\n\n\n\n

Adding both sides 4<\/p>\n\n\n\n

2x<3x+2<\/p>\n\n\n\n

Subtracting both sides 3x<\/p>\n\n\n\n

2x-3x<3x+2-3x<\/p>\n\n\n\n

-x<2<\/p>\n\n\n\n

Multiplying both sides -1<\/p>\n\n\n\n

x>-2<\/p>\n\n\n\n

x={-1,0,1,2,3,4}<\/p>\n\n\n\n

[]<\/p>\n\n\n\n

Question 3<\/h4>\n\n\n\n

Solve (a) 30x<200 (b) 5x-3<3x+1 when<\/p>\n\n\n\n

(i) x is integer<\/p>\n\n\n\n

(ii) x is a natural number<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

30x<200<\/p>\n\n\n\n

Dividing both sides by 30<\/p>\n\n\n\n

$\\dfrac{30 x}{30}<\\dfrac{200}{30}$<\/p>\n\n\n\n

$x<\\dfrac{20}{3}$<\/p>\n\n\n\n

$x<6 \\dfrac{2}{3}$<\/p>\n\n\n\n

(i) <\/p>\n\n\n\n

x={…-3,-2,-1,0,1,2,3,4,5,6.}<\/p>\n\n\n\n

(ii) <\/p>\n\n\n\n

x={1,2,3,4,5,6}<\/p>\n\n\n\n

Question 4<\/h4>\n\n\n\n

Solve <\/p>\n\n\n\n

(a) 3x+5<x-7 (b) 5x-3<3x+1 when<\/p>\n\n\n\n

(i) x is integer<\/p>\n\n\n\n

(ii) x is a real number<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

3x+5<x-7<\/p>\n\n\n\n

Subtracting both sides by 5<\/p>\n\n\n\n

3x+5-5<x-7-5<\/p>\n\n\n\n

3x<x-12<\/p>\n\n\n\n

Subtracting both sides x<\/p>\n\n\n\n

2x<-12<\/p>\n\n\n\n

Dividing both sides by x<\/p>\n\n\n\n

$\\dfrac{2x}{x}<\\dfrac{-12}{2}$<\/p>\n\n\n\n

x<-6<\/p>\n\n\n\n

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

x={…-9,-8,-7}<\/p>\n\n\n\n

(ii) <\/p>\n\n\n\n

x\u03f5(-\u221e,-6)<\/p>\n\n\n\n

Question 7<\/h4>\n\n\n\n

Solve the following inequations :<\/p>\n\n\n\n

(i)<\/strong> 2-3x\u22652(x+6)<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

 2-3x\u22652x+12<\/p>\n\n\n\n

Subtracting both side 2x<\/p>\n\n\n\n

2-5x\u226512<\/p>\n\n\n\n

Subtracting both side 2<\/p>\n\n\n\n

-5x\u226510<\/p>\n\n\n\n

Dividing both sides by -5<\/p>\n\n\n\n

$\\frac{-5 x}{-5} \\leq \\frac{10}{-5}$<\/p>\n\n\n\n

x\u03f5(-\u221e,-2)<\/p>\n\n\n\n

(ii)<\/strong> 2(2x+3)-10<6(x-2)<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

4x+6-10<6x-12<\/p>\n\n\n\n

4x-4<6x-12<\/p>\n\n\n\n

Adding both side 4<\/p>\n\n\n\n

4x-4+4<6x-12+4<\/p>\n\n\n\n

4x<6x-8<\/p>\n\n\n\n

Subtracting 6x both sides<\/p>\n\n\n\n

-2x<-8<\/p>\n\n\n\n

Dividing with -2 both sides<\/p>\n\n\n\n

$\\frac{-2x}{-2}<\\frac{-8}{-2}$<\/p>\n\n\n\n

x>4<\/p>\n\n\n\n

(iii)<\/strong> -(x-3)+4>-2x+5<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

-x+3+4>-2x+5<\/p>\n\n\n\n

-x+7>-2x+5<\/p>\n\n\n\n

-x+7>-2x+5<\/p>\n\n\n\n

Subtracting both sides with 7<\/p>\n\n\n\n

-x>-2x-2<\/p>\n\n\n\n

Adding both sides 2x<\/p>\n\n\n\n

-x+2x>-2x-2+2x<\/p>\n\n\n\n

x>-2<\/p>\n\n\n\n

x\u03f5(-2,\u221e)<\/p>\n\n\n\n

Question 8<\/h4>\n\n\n\n

Solve the following inequations:<\/p>\n\n\n\n

(i)<\/strong> $\\frac{3(x-2)}{5} \\geq \\frac{5(2-x)}{3$<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

$15 \\times \\frac{3(x-2)}{5} \\geq 15 \\times \\frac{5(2-x)}{3}$<\/p>\n\n\n\n

9(x-2)\u226525(2-x)<\/p>\n\n\n\n

9x-18\u226550-25x<\/p>\n\n\n\n

Adding both sides 25x<\/p>\n\n\n\n

9x-18+25x\u226550-25x+25x<\/p>\n\n\n\n

34x-18\u226550<\/p>\n\n\n\n

Adding both sides 18<\/p>\n\n\n\n

34x\u226568<\/p>\n\n\n\n

Dividing both sides by 34<\/p>\n\n\n\n

$\\frac{34 x}{34}\\ge\\frac{68}{34}$<\/p>\n\n\n\n

x\u22652<\/p>\n\n\n\n

x\u03f5(2,\u221e)<\/p>\n\n\n\n

(ii)<\/strong> $\\frac{11-2 x}{5} \\geq \\frac{9-3 x}{8}+\\frac{3}{4}, x \\in \\mathrm{N}$<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

$\\frac{11-2 x}{5} \\geq \\frac{9-3 x+6}{8}$<\/p>\n\n\n\n

$\\frac{11-2 x}{5} \\geq \\frac{15-3 x}{8}$<\/p>\n\n\n\n

Multiplying both sides by 40<\/p>\n\n\n\n

$\\frac{40(11-22)}{5} \\geq 40\\left(\\frac{15-3 x}{8}\\right)$<\/p>\n\n\n\n

88-16x\u226575-15x<\/p>\n\n\n\n

Adding both sides 15x<\/p>\n\n\n\n

88-16x+15x\u226575-15x+15x<\/p>\n\n\n\n

Subtracting 88 both sides<\/p>\n\n\n\n

-x\u2265-13<\/p>\n\n\n\n

Multiplying both sides by -1<\/p>\n\n\n\n

x={1,2,3,4,…..13}<\/p>\n\n\n\n

Question 9<\/h4>\n\n\n\n

Solve the following inequations<\/p>\n\n\n\n

(i)<\/strong> $\\frac{3}{x-2}<0$<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

[]<\/p>\n\n\n\n

\u2234 x-2<0<\/p>\n\n\n\n

Adding both sides 2<\/p>\n\n\n\n

x-2+2<0+2<\/p>\n\n\n\n

x<2<\/p>\n\n\n\n

[]=(-\u221e,2)<\/p>\n\n\n\n

(ii)<\/strong> $-\\frac{1}{x+2}>0$<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

[]<\/p>\n\n\n\n

\u2234 x+2<0<\/p>\n\n\n\n

Subtracting both sides 2<\/p>\n\n\n\n

Question 10<\/h4>\n\n\n\n

Solve the following inequations :<\/p>\n\n\n\n

(i) $\\frac{x-3}{x+5}>0$<\/p>\n\n\n\n

Sol :
=x-3>0 and x+5>0
or
x-3<0 and x+5<0<\/p>\n\n\n\n

=x>3 and x>-5
or
x<3 and x<-5<\/p>\n\n\n\n

=x>3
or
x<-5<\/p>\n\n\n\n

(ii) $\\frac{x-3}{x-5}>0$<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

x-3>0 and x-5>0
or
x-3<0 and x-5<0<\/p>\n\n\n\n

=x>3 and x>5
or
x<3 and x<5<\/p>\n\n\n\n

=x>5
or
x<3<\/p>\n\n\n\n

[]<\/p>\n\n\n\n

Question 11<\/h4>\n\n\n\n

Solve the following inequations
(i) $\\frac{x-1}{x-3}<1$
Sol :
Subtracting both sides with 1<\/p>\n\n\n\n

$\\frac{x-1}{x-3}-1<1-1$<\/p>\n\n\n\n

$\\frac{x-1-(x-3)}{x-3}<0$<\/p>\n\n\n\n

$\\frac{x-1-x +7}{x-3}<0$<\/p>\n\n\n\n

$\\frac{2}{x-3}<0$<\/p>\n\n\n\n

[]<\/p>\n\n\n\n

\u2234 x-3<0<\/p>\n\n\n\n

x<3<\/p>\n\n\n\n

[]=(-\u221e,3)<\/p>\n\n\n\n

(ii) $\\frac{x+1}{x-7} \\geq 2$
Sol :
Subtracting both sides 2<\/p>\n\n\n\n

$\\frac{x+1}{x-7}-2 \\geq 2-2$<\/p>\n\n\n\n

$\\frac{x+1-2(x-7)}{x-7} \\geq 0$<\/p>\n\n\n\n

$\\frac{x+1-2 x+14}{x-7} \\geq 0$<\/p>\n\n\n\n

$\\frac{-x+15}{x-7} \\geq 0$<\/p>\n\n\n\n

=-x+15\u22650 and x-7>0
or
-x+15\u22640 and x-7<0<\/p>\n\n\n\n

=x\u226415 and x>7
or
x\u226515 and x<7<\/p>\n\n\n\n

=7<x\u226415
or
not possible<\/p>\n\n\n\n

[]= (7,15]<\/p>\n\n\n\n

KC Sinha Solutions<\/a><\/div>
KC Sinha Class 11 Solutions<\/a><\/div> <\/div> <\/p>\n","protected":false},"excerpt":{"rendered":"

Exercise 12.1 Question 1 If x is a non-negative integer then solve2-3x<5-4xSol : Adding both sides 4x 2-3x+4x<5-4x+4x 2+x<5 Subtracting both sides 2 2+x-2<5-2 x<3 x={0,1,2} [] ALTERNATE METHOD 2-3x<5-4x -3x+4x<5-2 x<2 Question 2 Solve 2(x-2)<3x-2, $x \\in\\{-2,-1,0,1,2,3,4\\}$ Also show the solution set on the number line Sol : 2(x-2)<3x-2 2x-4<3x-2 Adding both sides 4 2x<3x+2 […]<\/p>\n","protected":false},"author":302,"featured_media":625898,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[919],"tags":[],"boards":[],"class_list":["post-625887","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-11","entry"],"yoast_head":"\nKC Sinha: Exercise 12.1 - Mathematics Solution Class 11 Chapter 12 \u0930\u0948\u0916\u093f\u0915 \u0905\u0938\u092e\u093f\u0915\u093e\u090f\u0901 - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"Exercise 12.1 Question 1 If x is a non-negative integer then solve2-3x<5-4xSol : Adding both sides 4x 2-3x+4x<5-4x+4x 2+x<5 Subtracting both\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-12-1-mathematics-solution-class-11-chapter-12-raikhik-asamikaye\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"KC Sinha: Exercise 12.1 - Mathematics Solution Class 11 Chapter 12 \u0930\u0948\u0916\u093f\u0915 \u0905\u0938\u092e\u093f\u0915\u093e\u090f\u0901\" \/>\n<meta property=\"og:description\" content=\"Exercise 12.1 Question 1 If x is a non-negative integer then solve2-3x<5-4xSol : Adding both sides 4x 2-3x+4x<5-4x+4x 2+x<5 Subtracting both\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-12-1-mathematics-solution-class-11-chapter-12-raikhik-asamikaye\/\" \/>\n<meta property=\"og:site_name\" content=\"IndCareer Schools\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/indcareer\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-08T08:57:01+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-09-08T08:57:06+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2023\/09\/indcareer-schools-2-13-1-scaled.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1600\" \/>\n\t<meta property=\"og:image:height\" content=\"901\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Pooja\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@indcareer\" \/>\n<meta name=\"twitter:site\" content=\"@indcareer\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Pooja\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-12-1-mathematics-solution-class-11-chapter-12-raikhik-asamikaye\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-12-1-mathematics-solution-class-11-chapter-12-raikhik-asamikaye\/\"},\"author\":{\"name\":\"Pooja\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/d6945cf059726f162259ba738092301e\"},\"headline\":\"KC Sinha: Exercise 12.1 – Mathematics Solution Class 11 Chapter 12 \u0930\u0948\u0916\u093f\u0915 \u0905\u0938\u092e\u093f\u0915\u093e\u090f\u0901\",\"datePublished\":\"2023-09-08T08:57:01+00:00\",\"dateModified\":\"2023-09-08T08:57:06+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-12-1-mathematics-solution-class-11-chapter-12-raikhik-asamikaye\/\"},\"wordCount\":668,\"publisher\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-12-1-mathematics-solution-class-11-chapter-12-raikhik-asamikaye\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2023\/09\/indcareer-schools-2-13-1-scaled.jpg\",\"articleSection\":[\"class 11\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-12-1-mathematics-solution-class-11-chapter-12-raikhik-asamikaye\/\",\"url\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-12-1-mathematics-solution-class-11-chapter-12-raikhik-asamikaye\/\",\"name\":\"KC Sinha: Exercise 12.1 - 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