{"id":22286,"date":"2020-02-03T17:05:14","date_gmt":"2020-02-03T11:35:14","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=22286"},"modified":"2021-07-02T15:25:53","modified_gmt":"2021-07-02T09:55:53","slug":"1st-puc-basic-maths-question-bank-chapter-3","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/1st-puc-basic-maths-question-bank-chapter-3\/","title":{"rendered":"1st PUC Basic Maths Question Bank Chapter 3 Theory of Indices"},"content":{"rendered":"

Students can Download Basic Maths Chapter 3 Theory of Indices Questions and Answers, Notes Pdf, 1st PUC Basic Maths Question Bank with Answers<\/a>\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 1st PUC Basic Maths Question Bank Chapter 3 Theory of Indices<\/h2>\n

Question 1.
\n3(5-2<\/sup>) + \\(\\left(\\frac{5}{3}\\right)^{-4}\\) + (a + 5)0<\/sup>
\nAnswer:
\n\"1st<\/p>\n

Question 2.
\nShow that \\(\\left(\\frac{x^{b}}{x^{c}}\\right)^{a}-\\left(\\frac{x^{c}}{x^{a}}\\right)^{b} \\cdot\\left(\\frac{x^{a}}{x^{b}}\\right)^{c}=1\\)
\nAnswer:
\nLHS = (xb-c<\/sup>)a<\/sup> (xc-a<\/sup>)3<\/sup> (xa-b<\/sup>)c<\/sup>
\n= xab-bc<\/sup> .xbc-ab<\/sup> .xac-bc<\/sup>
\n= xab-bc+bc+-ab+ac-bc<\/sup>
\n= x0<\/sup>
\n= 1
\n= RHS<\/p>\n

\"1st<\/p>\n

Question 3.
\nIf pqr = 1 Show that \\(\\frac{1}{1+p+q^{-1}}+\\frac{1}{1+q+r^{-1}}+\\frac{1}{1+r+p^{-1}}=1\\)
\nAnswer:
\n\"1st<\/p>\n

Question 4.
\nIf ax<\/sup> = by<\/sup> = and b2<\/sup> = ac. Show that \\(\\frac{1}{x}+\\frac{1}{z}=\\frac{2}{y}\\)
\nAnswer:
\nLet ax<\/sup> = by<\/sup> = cz<\/sup> = k (say)
\n\u21d2 ax<\/sup> = k, by<\/sup> = k, Cz<\/sup> = k
\n\u21d2 a = k1\/x<\/sup>; b = k1\/y<\/sup>; c = k1\/z<\/sup>
\nBy data b2<\/sup> = ac
\n(k1\/y<\/sup>)2<\/sup> = k1\/x<\/sup> .k1\/z<\/sup>
\nk2\/y<\/sup>\u00a0= k1\/x+1\/z<\/sup>
\n\u21d2 \\(\\frac{2}{y}=\\frac{1}{x}+\\frac{1}{z}\\) (\u2235bases are same)<\/p>\n

\"1st<\/p>\n

Question 5.
\nIf 651\/x<\/sup> = 131\/y<\/sup> = 51\/z<\/sup> show that x=y+z.
\nAnswer:
\nLet 651\/x<\/sup> \u21d2 k = 65 k; 131\/y<\/sup> = k \u21d2 13 = k; 51\/z<\/sup> = k \u21d2 5 = k
\nWe know that 65 = 13 \u00d7 5 kx<\/sup> = ky<\/sup>. kz<\/sup> \u21d2 x = y + z<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Basic Maths Chapter 3 Theory of Indices Questions and Answers, Notes Pdf, 1st PUC Basic Maths Question Bank with Answers\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 1st PUC Basic Maths Question Bank Chapter 3 Theory of Indices Question 1. 3(5-2) + …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[81],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/22286"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=22286"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/22286\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=22286"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=22286"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=22286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}