{"id":19287,"date":"2020-01-09T17:40:43","date_gmt":"2020-01-09T12:10:43","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=19287"},"modified":"2021-07-02T15:29:47","modified_gmt":"2021-07-02T09:59:47","slug":"2nd-puc-basic-maths-question-bank-chapter-21-ex-21-2","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-question-bank-chapter-21-ex-21-2\/","title":{"rendered":"2nd PUC Basic Maths Question Bank Chapter 21 Definite Integral and its Applications to Areas Ex 21.2"},"content":{"rendered":"

Students can Download Basic Maths Exercise 21.2 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 2nd PUC Basic Maths Question Bank Chapter 21 Definite Integral and its Applications to Areas Ex 21.2<\/h2>\n

Part-A<\/span><\/p>\n

Applications of Areas <\/span><\/p>\n

2nd PUC Basic Maths Definite Integral and its Applications to Areas Ex 21.2 Two marks Questions and Answers<\/strong><\/p>\n

Question 1.
\nFind the area bounded by the curve y = x2<\/sup>, x – axis and the ordinates x = 0, x = 1
\nAnswer:
\n\"2nd<\/p>\n

Question 2.
\nFind the area bounded by the curve y2<\/sup> = 8x, x – axis and the lines x = 0, x = 2
\nAnswer:
\n\"2nd<\/p>\n

Question 3.
\nFind the area bounded by the curve x2<\/sup> = 8y, y-axis and the abscissas y = 3, y = 6
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 4.
\nFind the area bounded by the curve 3x2<\/sup> = 4y, y-axis and the lines y = 1, y = 2
\nAnswer:
\n\"2nd<\/p>\n

Part- B<\/span><\/p>\n

2nd PUC Basic Maths Definite Integral and its Applications to Areas Ex 21.2 Five Marks Questions and Answers<\/strong><\/p>\n

Question 1.
\nFind the area bounded by the parabola y2<\/sup> = 4ax and its latus rectum.
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

Question 2.
\nFind the area bounded by the parabola y2<\/sup> = 4x and x2<\/sup> = 4y
\nAnswer:
\n\"2nd
\nGiven
\ny2<\/sup> = 4x and x2<\/sup>= 4y
\n\\(\\left(\\frac{x^{2}}{4}\\right)^{2}\\) \u2235y = \\(\\frac{x^{2}}{4}\\)
\n\\(\\frac{x^{4}}{16} = 4 x\\)
\nx4<\/sup> – 43<\/sup>x = 0
\nx(x3<\/sup> – y3<\/sup>) = 0 \u21d2 x = 0, x = 4
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\nFind the area bounded by the curve y2<\/sup> = 5x and the line y = x
\nAnswer:
\ny2<\/sup> = 5x and y = x
\nx2<\/sup> – 5x = 0
\nx(x – 5 ) = 0 \u21d2 x = 0 and x = 5
\n\"2nd<\/p>\n

Question 4.
\nFind the area enclosed between the parabola x2<\/sup> = 4y and the line x = 4y – 2
\n\"2nd
\nAnswer:
\nGiven x2<\/sup> = 4y and line x = 4y – 2
\nx = x2<\/sup> – 2 \u2234 4y = x2<\/sup>
\nx2<\/sup> – x – 2 = 0
\n(x – 2) (x + 1) = 0
\n\u21d2 x = 2, y = -l
\nSo when x = 2, y = 1 \u21d2 (2, 1)
\nWhen x = -1, y = \\(\\frac { 1 }{ 4 }\\) \u21d2 \\(\\left(-1, \\frac{1}{4}\\right)\\)
\nThese two points where line meets parabola as we got these values by solving the 2 equations,
\nSo, required area
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 5.
\nFind the area enclosed between the parabola y2<\/sup> = x and the line x + y = 2
\nAnswer:
\nGiven y = 2 – x and y2<\/sup> = x
\n\u21d2 [2 – x]2<\/sup> = x \u21d2 4 + x2<\/sup> – 4x = x \u21d2 x2<\/sup> – 5x + 4 = 0
\n\u21d2 (x – 4) (x – 1) = 0
\n\u21d2 x = 4 and x = 1
\nwhen x = 1 then y = 2 – 1 = 1 \u21d2 (1,1)
\nwhen x = 4 then y = 2 – 4 = -2 \u21d2 (4, -2)
\n\"2nd<\/p>\n

Question 6.
\nFind the area enclosed between the parabola y2<\/sup> = 4ax and the line y = mx
\nAnswer:
\n\"2nd
\nGiven y2<\/sup> = 4ax and line y = mx.
\nPoints where both meet at a \\(\\left(\\frac{4 a}{m^{2}}, \\frac{4 a}{m}\\right)\\) and (0,0)
\n\u21d2 y2<\/sup> = 4ax
\nm2<\/sup>x2<\/sup> = 4ax \u21d2 x = \\(\\frac{4 \\mathrm{a}}{\\mathrm{m}^{2}}\\) and y = mx = \\(\\mathrm{m} \\cdot \\frac{4 \\mathrm{a}}{\\mathrm{m}^{2}}=\\frac{4 \\mathrm{a}}{\\mathrm{m}}\\)
\nRequired area = Area of y2<\/sup> = 4ax from 0 to \\(\\frac{4 \\mathrm{a}}{\\mathrm{m}^{2}}\\) – Area of the line y = mx from 0 to \\(\\frac{4 \\mathrm{a}}{\\mathrm{m}^{2}}\\)
\n\"2nd<\/p>\n

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

Students can Download Basic Maths Exercise 21.2 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Basic Maths Question Bank Chapter 21 Definite Integral and its Applications to Areas Ex 21.2 …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[82],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/19287"}],"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=19287"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/19287\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=19287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=19287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=19287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}