{"id":625672,"date":"2023-09-07T12:22:02","date_gmt":"2023-09-07T12:22:02","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=625672"},"modified":"2023-09-07T12:22:06","modified_gmt":"2023-09-07T12:22:06","slug":"kc-sinha-exercise-5-1-mathematics-solution-class-10-chapter-5-samantar-shredhi","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-5-1-mathematics-solution-class-10-chapter-5-samantar-shredhi\/","title":{"rendered":"KC Sinha: Exercise 5.1 – Mathematics Solution Class 10 Chapter 5 \u0938\u092e\u093e\u0902\u0924\u0930 \u0936\u094d\u0930\u0947\u0922\u0940"},"content":{"rendered":"\n

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

TYPE-I \u0905\u0928\u0941\u0915\u094d\u0930\u092e \u091c\u093f\u0938\u0915\u0947 n \u0935\u093e\u0901 \u092a\u0926 \u0926\u093f\u092f\u0947 \u0939\u094b\u0902 , \u0915\u0947 \u092a\u0926\u094b\u0902 \u0915\u094b \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928:<\/p>\n\n\n\n

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

\u0928\u093f\u092e\u094d\u0928 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0905\u0928\u0941\u0915\u094d\u0930\u092e\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0925\u092e \u0924\u0940\u0928 \u092a\u0926\u094b\u0902 \u0915\u094b \u0932\u093f\u0916\u0947?<\/strong><\/p>\n\n\n\n

(i) tn<\/sub> = 3n + 1<\/strong><\/p>\n\n\n\n

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

n = 1,2,3 \u0930\u0916\u0928\u0947 \u092a\u0930,
t1<\/sub> = 3(1) + 1 = 3 + 1 = 4
t2<\/sub> = 3(2) + 1 = 6 + 1 = 7
t3<\/sub> = 3(3) + 1 = 9 + 1 = 10<\/p>\n\n\n\n

\u2234 \u092a\u094d\u0930\u0925\u092e \u0924\u0940\u0928 \u092a\u0926 4, 7, 10 <\/p>\n\n\n\n

(ii) tn<\/sub> = 2n<\/sup><\/strong><\/p>\n\n\n\n

Sol :
n = 1,2,3 \u0930\u0916\u0928\u0947 \u092a\u0930,
t1<\/sub> = 21<\/sup> = 2
t2<\/sub> = 22<\/sup> = 2 \u00d7 2 = 4
t3<\/sub> = 23<\/sup> = 2 \u00d7 2 \u00d7 2 = 8<\/p>\n\n\n\n

\u2234 \u092a\u094d\u0930\u0925\u092e \u0924\u0940\u0928 \u092a\u0926 2 , 4 , 8<\/p>\n\n\n\n

(iii) tn<\/sub> = n2<\/sup> + 1<\/strong><\/p>\n\n\n\n

Sol :
n = 1,2,3 \u0930\u0916\u0928\u0947 \u092a\u0930,
t1<\/sub> = (1)2<\/sup> + 1 = 1 + 1 = 2
t2<\/sub> = (2)2<\/sup> + 1 = 4 + 1 = 5
t3<\/sub> = (3)2<\/sup> + 1 = 9 + 1 = 10<\/p>\n\n\n\n

\u2234 \u092a\u094d\u0930\u0925\u092e \u0924\u0940\u0928 \u092a\u0926 2 , 5 , 10<\/p>\n\n\n\n

(iv) tn<\/sub> = n(n + 2)<\/strong><\/p>\n\n\n\n

Sol :
n = 1,2,3 \u0930\u0916\u0928\u0947 \u092a\u0930,
t1<\/sub> = (1)(1+2) = (1)(3) = 3
t2<\/sub> = (2)(2+2) = (2)(4) = 8
t3<\/sub> = (3)(3+2) = (3)(5) = 15<\/p>\n\n\n\n

\u2234 \u092a\u094d\u0930\u0925\u092e \u0924\u0940\u0928 \u092a\u0926 3 , 8 , 15<\/p>\n\n\n\n

(v) tn<\/sub> = 2n+5
<\/strong>Sol :<\/p>\n\n\n\n

n = 1,2,3 \u0930\u0916\u0928\u0947 \u092a\u0930,
t1<\/sub> = 2(1) + 5 = 2 + 5 = 7
t2<\/sub> = 2(2) + 5 = 4 + 5 = 9
t3<\/sub> = 2(3) + 5 = 6 + 5 = 11<\/p>\n\n\n\n

\u2234 \u092a\u094d\u0930\u0925\u092e \u0924\u0940\u0928 \u092a\u0926 7 , 9 , 11<\/p>\n\n\n\n

(vi) $\\mathrm{t}_{\\mathrm{n}}=\\frac{\\mathrm{n}-3}{4}$<\/strong><\/p>\n\n\n\n

Sol :
n = 1,2,3 \u0930\u0916\u0928\u0947 \u092a\u0930,
$\\mathrm{t}_{1}=\\frac{1-3}{4}=\\frac{-2}{4}=\\frac{-1}{2}$
<\/p>\n\n\n\n

$\\mathrm{t}_{2}=\\frac{2-3}{4}=\\frac{-1}{4}$<\/p>\n\n\n\n

$\\mathrm{t}_{3}=\\frac{3-3}{4}=0$<\/p>\n\n\n\n

\u2234 \u092a\u094d\u0930\u0925\u092e \u0924\u0940\u0928 \u092a\u0926 $=\\frac{-1}{2}, \\frac{-1}{4} ,0$<\/p>\n\n\n\n

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

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0905\u0928\u0941\u0915\u094d\u0930\u092e\u094b\u0902 , \u091c\u093f\u0928\u0915\u0947 n \u0935\u093e\u0901 \u092a\u0926 \u0926\u093f\u090f \u0917\u092f\u0947 \u0939\u0948 , \u0915\u0947 \u092a\u0942\u091b\u0947 \u0917\u092f\u0947 (indicated) \u092a\u0926\u094b \u0915\u094b \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0964<\/strong><\/p>\n\n\n\n

(i) $t_n=\\frac{n^2(n+1)}{3}; t_1,t_2$<\/strong><\/p>\n\n\n\n

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

n=1 \u0930\u0916\u0928\u0947 \u092a\u0930,<\/p>\n\n\n\n

$t_1=\\frac{(1)^2(1+1)}{3}=\\frac{1(2)}{3}=\\frac{2}{3}$<\/p>\n\n\n\n

n=2 \u0930\u0916\u0928\u0947 \u092a\u0930,<\/p>\n\n\n\n

$t_2=\\frac{2^2(2+1)}{3}=\\frac{4(3)}{3}=4$<\/p>\n\n\n\n

(ii) $t_n=\\frac{n(n-2)}{n+3}; t_20$<\/strong><\/p>\n\n\n\n

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

t20<\/sub> \u092e\u0947\u0902 n=20 \u0930\u0916\u0928\u0947 \u092a\u0930  <\/p>\n\n\n\n

$\\mathrm{t}_{20}=\\frac{20(20-2)}{20+3}$<\/p>\n\n\n\n

$=\\frac{20 \\times 18}{23}=\\frac{360}{23}$<\/p>\n\n\n\n

(iii) tn<\/sub>= (n – 1)(2 – n)(3 + n) ; t20<\/sub><\/strong><\/p>\n\n\n\n

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

t20<\/sub> \u092e\u0947 n=20 \u0930\u0916\u0928\u0947 \u092a\u0930
t20<\/sub> = (20 \u2013 1)(2 \u2013 20)(3+20)
= (19)(-18)(23)
= -7866<\/p>\n\n\n\n

(iv) $\\mathrm{t}_{\\mathrm{n}}=\\frac{\\mathrm{t}_{\\mathrm{n}-1}}{\\mathrm{n}^{2}}, \\mathrm{t}_{1}=3$;<\/strong><\/p>\n\n\n\n

$\\mathrm{t}_{2}, \\mathrm{t}_{3},(\\mathrm{n} \\geq 2)$<\/strong><\/p>\n\n\n\n

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

$\\mathrm{t}_{2}=\\frac{\\mathrm{t}_{2-1}}{(2)^{2}}=\\frac{\\mathrm{t}_{1}}{4}=\\frac{3}{4}$ [given : t1<\/sub> = 3]
and $\\mathrm{t}_{3}=\\frac{\\mathrm{t}_{3-1}}{(3)^{2}}=\\frac{\\mathrm{t}_{2}}{9}$<\/p>\n\n\n\n

$=\\frac{\\frac{3}{4}}{9}=\\frac{3}{4 \\times 9}=\\frac{1}{12}$ $\\left[\\because \\mathrm{t}_{2}=\\frac{3}{4}\\right]$<\/p>\n\n\n\n

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

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0909\u092a\u0915\u094d\u0930\u092e\u094b\u0902 \u0915\u0947 \u0906\u0917\u093e\u092e\u0940 \u0924\u0940\u0928 \u092a\u0926\u094b\u0902 \u0915\u094b \u0932\u093f\u0916\u0947:-<\/strong><\/p>\n\n\n\n

(i) t2<\/sub>=2 , tn-1<\/sub>+1, (n\u22653)<\/strong><\/p>\n\n\n\n

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

\u0928\u093f\u0915\u093e\u0932\u0947 t3 <\/sub>, t4<\/sub>, t5<\/sub> <\/p>\n\n\n\n

t3<\/sub>= t3-1<\/sub>+1 =t2<\/sub>+1 [\u0926\u093f\u092f\u093e \u0939\u0948 : t2<\/sub>=2 ]<\/p>\n\n\n\n

=2+1=3<\/p>\n\n\n\n

 t4<\/sub>=t4-1<\/sub>+1= t3<\/sub>+1 [t3<\/sub>=3]<\/p>\n\n\n\n

= 3+1=4<\/p>\n\n\n\n

 t5<\/sub>=t5-1<\/sub>+1= t4<\/sub>+1 [t4<\/sub>=4]<\/p>\n\n\n\n

= 3+1=4<\/p>\n\n\n\n

\u2234\u0906\u0917\u093e\u092e\u0940 \u0924\u0940\u0928 \u092a\u0926 3 , 4 , 5<\/p>\n\n\n\n

(ii) t1<\/sub>=3 , tn<\/sub>=3tn-1<\/sub>+2 \u0938\u092d\u0940 n>1 \u0915\u0947 \u0932\u093f\u090f<\/strong><\/p>\n\n\n\n

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

Given : <\/p>\n\n\n\n

t1<\/sub>=3 \u0914\u0930 \u0928\u093f\u0915\u093e\u0932\u0947 t2 <\/sub>, t3<\/sub>, t4<\/sub> <\/p>\n\n\n\n

t2<\/sub>=3t2-1<\/sub>+2 =3t1<\/sub>+2 [t1<\/sub>=3] <\/p>\n\n\n\n

=3(3)+2=11<\/p>\n\n\n\n

t3<\/sub>=3t3-1<\/sub>+2 =3t2<\/sub>+2 [t2<\/sub>=11] <\/p>\n\n\n\n

=3(11)+2=35<\/p>\n\n\n\n

t4<\/sub>=3t4-1<\/sub>+2 =3t3<\/sub>+2 [t3<\/sub>=35] <\/p>\n\n\n\n

=3(35)+2=107<\/p>\n\n\n\n

\n
KC Sinha Solutions<\/a><\/div>\n\n\n\n
KC Sinha Class 10 Solutions<\/a><\/div>\n<\/div>\n\n\n\n

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

TYPE-I \u0905\u0928\u0941\u0915\u094d\u0930\u092e \u091c\u093f\u0938\u0915\u0947 n \u0935\u093e\u0901 \u092a\u0926 \u0926\u093f\u092f\u0947 \u0939\u094b\u0902 , \u0915\u0947 \u092a\u0926\u094b\u0902 \u0915\u094b \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928: Question 1 \u0928\u093f\u092e\u094d\u0928 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0905\u0928\u0941\u0915\u094d\u0930\u092e\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0925\u092e \u0924\u0940\u0928 \u092a\u0926\u094b\u0902 \u0915\u094b \u0932\u093f\u0916\u0947? (i) tn = 3n + 1 Sol : n = 1,2,3 \u0930\u0916\u0928\u0947 \u092a\u0930,t1 = 3(1) + 1 = 3 + 1 = 4t2 = 3(2) + 1 = 6 […]<\/p>\n","protected":false},"author":302,"featured_media":625674,"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":[24],"tags":[],"boards":[],"class_list":["post-625672","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-10","entry"],"yoast_head":"\nKC Sinha: Exercise 5.1 - Mathematics Solution Class 10 Chapter 5 \u0938\u092e\u093e\u0902\u0924\u0930 \u0936\u094d\u0930\u0947\u0922\u0940 - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"TYPE-I \u0905\u0928\u0941\u0915\u094d\u0930\u092e \u091c\u093f\u0938\u0915\u0947 n \u0935\u093e\u0901 \u092a\u0926 \u0926\u093f\u092f\u0947 \u0939\u094b\u0902 , \u0915\u0947 \u092a\u0926\u094b\u0902 \u0915\u094b \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928: Question 1 \u0928\u093f\u092e\u094d\u0928 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0905\u0928\u0941\u0915\u094d\u0930\u092e\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0925\u092e \u0924\u0940\u0928 \u092a\u0926\u094b\u0902 \u0915\u094b \u0932\u093f\u0916\u0947?\" \/>\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-5-1-mathematics-solution-class-10-chapter-5-samantar-shredhi\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"KC Sinha: Exercise 5.1 - Mathematics Solution Class 10 Chapter 5 \u0938\u092e\u093e\u0902\u0924\u0930 \u0936\u094d\u0930\u0947\u0922\u0940\" \/>\n<meta property=\"og:description\" content=\"TYPE-I \u0905\u0928\u0941\u0915\u094d\u0930\u092e \u091c\u093f\u0938\u0915\u0947 n \u0935\u093e\u0901 \u092a\u0926 \u0926\u093f\u092f\u0947 \u0939\u094b\u0902 , \u0915\u0947 \u092a\u0926\u094b\u0902 \u0915\u094b \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928: Question 1 \u0928\u093f\u092e\u094d\u0928 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0905\u0928\u0941\u0915\u094d\u0930\u092e\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0925\u092e \u0924\u0940\u0928 \u092a\u0926\u094b\u0902 \u0915\u094b \u0932\u093f\u0916\u0947?\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-5-1-mathematics-solution-class-10-chapter-5-samantar-shredhi\/\" \/>\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=\"2023-09-07T12:22:02+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-09-07T12:22:06+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2023\/09\/indcareer-schools-2-6-1-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=\"3 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-5-1-mathematics-solution-class-10-chapter-5-samantar-shredhi\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-5-1-mathematics-solution-class-10-chapter-5-samantar-shredhi\/\"},\"author\":{\"name\":\"Pooja\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/d6945cf059726f162259ba738092301e\"},\"headline\":\"KC Sinha: Exercise 5.1 – Mathematics Solution Class 10 Chapter 5 \u0938\u092e\u093e\u0902\u0924\u0930 \u0936\u094d\u0930\u0947\u0922\u0940\",\"datePublished\":\"2023-09-07T12:22:02+00:00\",\"dateModified\":\"2023-09-07T12:22:06+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-5-1-mathematics-solution-class-10-chapter-5-samantar-shredhi\/\"},\"wordCount\":312,\"publisher\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-5-1-mathematics-solution-class-10-chapter-5-samantar-shredhi\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2023\/09\/indcareer-schools-2-6-1-scaled.jpg\",\"articleSection\":[\"Class 10\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-5-1-mathematics-solution-class-10-chapter-5-samantar-shredhi\/\",\"url\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-5-1-mathematics-solution-class-10-chapter-5-samantar-shredhi\/\",\"name\":\"KC Sinha: Exercise 5.1 - 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