{"id":32132,"date":"2022-03-29T16:30:44","date_gmt":"2022-03-29T11:00:44","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=32132"},"modified":"2022-03-29T16:47:31","modified_gmt":"2022-03-29T11:17:31","slug":"ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 7 Integrals Miscellaneous Exercise Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise<\/h2>\n

\"NCERT<\/p>\n

Class 12 Maths Chapter 7 Miscellaneous Exercise Solutions Question 1.<\/strong>
\n\\(\\frac{1}{x-x^{3}}\\)
\nSolution:
\n\\(\\int \\frac{1}{x-x^{3}} d x=\\int \\frac{1}{x\\left(1-x^{2}\\right)} d x=\\int \\frac{1}{x(1-x)(1+x)} d x\\)
\nLet\\(\\frac{1}{x(1-x)(1+x)}=\\frac{\\mathrm{A}}{x}+\\frac{\\mathrm{B}}{1-x}+\\frac{\\mathrm{C}}{1+x}\\)
\n1 = A(1 – x)(l + x) + Bx(l + x) + Cx(l – x) Put x = 0 in (1), we get A = 1
\nPut x = 1 in (1), we get 1 = 2B \u2234 B = \\(\\frac { 1 }{ 2 }\\)
\nPut x = – 1 in (1), we get 1 = – 2C \u2234 C = \\(\\frac { – 1 }{ 2 }\\)
\n\"Class<\/p>\n

Miscellaneous Exercise Chapter 7 Class 12 Question 2.<\/strong>
\n\\(\\frac{1}{\\sqrt{x+a}+\\sqrt{x+b}}\\)
\nSolution:
\n\"Miscellaneous<\/p>\n

Miscellaneous Chapter 7 Class 12 Question 3.<\/strong>
\n\\(\\frac{1}{x \\sqrt{a x-x^{2}}}\\)
\nSolution:
\n\"Miscellaneous<\/p>\n

Ncert Solutions For Class 12 Maths Chapter 7 Miscellaneous Exercise Question 4.<\/strong>
\n\\(\\frac{1}{x^{2}\\left(x^{4}+1\\right)^{\\frac{3}{4}}}\\)
\nSolution:
\n\"Ncert<\/p>\n

Miscellaneous Ch 7 Class 12 Question 5.<\/strong>
\n\\(\\frac{1}{x^{\\frac{1}{2}}+x^{\\frac{1}{3}}}\\)
\nSolution:
\n\"Miscellaneous<\/p>\n

\"NCERT<\/p>\n

Miscellaneous Exercise Class 12 Chapter 7 Question 6.<\/strong>
\n\\(\\frac{5 x}{(x+1)\\left(x^{2}+9\\right)}\\)
\nSolution:
\nLet \\(\\frac{5 x}{(x+1)\\left(x^{2}+9\\right)}\\) = \\(\\frac{A}{x+1}+\\frac{B x+C}{x^{2}+9}\\)
\n\u21d2 5x = A(x\u00b2 + 9) + (Bx + C)(x + 1) … (1)
\nPut x = – 1 in (1), we get
\n– 5 = – 10
\n\u2234 A = \\(\\frac { -5 }{ 10 }\\) = \\(\\frac { – 1 }{ 2 }\\)
\nEquating the coefficients of x\u00b2 and constant
\nterm, we get A + B = 0, 9 A + C = 0
\n\"Miscellaneous<\/p>\n

Ch 7 Miscellaneous Class 12 Question 7.<\/strong>
\n\\(\\frac{\\sin x}{\\sin (x-a)}\\)
\nSolution:
\n\"Ch
\n= sin a \u222bcot dt + cos a \u222bdt
\n= sin a log |sin t| + cos a (t) + C1<\/sub>
\n= sin a log |sin(x – a)| + cos a[x – 1] + C1<\/sub>
\n= sin a.logsin (x – a) + x cosa + C, where C = C1<\/sub> – a cos a<\/p>\n

Ncert Solutions Class 12 Maths Chapter 7 Miscellaneous Exercise Question 8.<\/strong>
\n\\(\\frac{e^{5 \\log x}-e^{4 \\log x}}{e^{3 \\log x}-e^{2 \\log x}}\\)
\nSolution:
\n\"Ncert<\/p>\n

\"NCERT<\/p>\n

Miscellaneous Exercise On Chapter 7 Class 12 Question 9.<\/strong>
\n\\(\\frac{\\cos x}{\\sqrt{4-\\sin ^{2} x}}\\)
\nSolution:
\n\"Miscellaneous<\/p>\n

Integration Miscellaneous Class 12 Question 10.<\/strong>
\n\\(\\frac{\\sin ^{8} x-\\cos ^{8} x}{1-2 \\sin ^{2} x \\cos ^{2} x}\\)
\nSolution:
\nLet I = \\(\\frac{\\sin ^{8} x-\\cos ^{8} x}{1-2 \\sin ^{2} x \\cos ^{2} x}\\)dx
\nsin8<\/sup>x – cos8<\/sup>x (sin4<\/sup>x – cos4<\/sup>x)(sin4<\/sup>x + cos4<\/sup>x)
\n= (sin\u00b2x – cos\u00b2x)(sin\u00b2x + cos\u00b2x)(sin4<\/sup>x + cos4<\/sup>x)
\n= (sn\u00b2x – cos\u00b2x(1)[(sin\u00b2x + cos\u00b2x) – 2sin\u00b2x cos\u00b2x]
\n= (sin\u00b2x – cos\u00b2x)( 1 – 2sin\u00b2x cos\u00b2x)
\n\"Integration<\/p>\n

Question 11.
\n\\(\\frac{1}{\\cos (x+a) \\cos (x+b)}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 12.
\n\\(\\frac{x^{3}}{\\sqrt{1-x^{8}}}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 13.
\n\\(\\frac{e^{x}}{\\left(1+e^{x}\\right)\\left(2+e^{x}\\right)}\\)
\nSolution:
\nLet I = \\(\\frac{e^{x}}{\\left(1+e^{x}\\right)\\left(2+e^{x}\\right)}\\) dx
\nPut t = ex<\/sup>
\n\\(\\frac { dt }{ dx }\\) = ex<\/sup>
\ndt = ex<\/sup> dx
\n= \\(\\int \\frac{d t}{(1+t)(2+t)}\\)
\nLet \\(\\frac{1}{(1+t)(2+t)}=\\frac{\\mathrm{A}}{(1+t)}+\\frac{\\mathrm{B}}{(2+t)}\\)
\n\u2234 1 = A(2 + t) + B(1 + t) … (1)
\nPut t = – 2 in (1), we get A = 1
\nPut t = – 2 in (1), we get 1 = – B \u2234B = – 1
\n\\(\\frac{1}{(1+t)(2+t)}=\\frac{1}{(1+t)}-\\frac{1}{(2+t)}\\)
\nI = \\(\\int \\frac{1}{1+t} d t-\\int \\frac{1}{2+t} d t\\)
\n= \\(\\log |1+t|-\\log |2+t|+C\\)
\n= \\(\\log \\left|\\frac{1+t}{2+t}\\right|+\\mathrm{C}=\\log \\left(\\frac{1+e^{x}}{2+e^{x}}\\right)+\\mathrm{C}\\)<\/p>\n

\"NCERT<\/p>\n

Question 14.
\n\\(\\frac{1}{\\left(x^{2}+1\\right)\\left(x^{2}+4\\right)}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 15.
\n\\(\\cos ^{3} x e^{\\log \\sin x}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 16.
\n\\(e^{3 \\log x}\\left(x^{4}+1\\right)^{-1}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 17.
\n\\(f^{\\prime}(a x+b)[f(a x+b)]^{n}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 18.
\n\\(\\frac{1}{\\sqrt{\\sin ^{3} x \\sin (x+\\alpha)}}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 19.
\n\\(\\frac{\\sin ^{-1} \\sqrt{x}-\\cos ^{-1} \\sqrt{x}}{\\sin ^{-1} \\sqrt{x}+\\cos ^{-1} \\sqrt{x}}, x \\in[0,1]\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 20.
\n\\(\\sqrt{\\frac{1-\\sqrt{x}}{1+\\sqrt{x}}}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 21.
\n\\(\\frac{2+\\sin 2 x}{1+\\cos 2 x} e^{x}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 22.
\n\\(\\frac{x^{2}+x+1}{(x+1)^{2}(x+2)}\\)
\nSolution:
\nLet \\(\\frac{x^{2}+x+1}{(x+1)^{2}(x+2)}=\\frac{\\mathrm{A}}{(x+1)}+\\frac{\\mathrm{B}}{(x+1)^{2}}+\\frac{\\mathrm{C}}{(x+2)}\\)
\n\u21d2 x\u00b2 + x + 1 = A(x + 1)(x + 2) + B(x + 2) + C(x + 1)\u00b2 … (1)
\nPut x = – 1 in (1), we get B = 1
\nPut x = – 2 in (1), we get C = 3
\nEquating the coefficients of x2, we get
\nA + C = 1 \u2234 A = – 2
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 23.
\n\\(\\tan ^{-1} \\sqrt{\\frac{1-x}{1+x}}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 24.
\n\\(\\frac{\\sqrt{x^{2}+1}\\left[\\log \\left(x^{2}+1\\right)-2 \\log x\\right]}{x^{4}}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 25.
\n\\(\\int_{\\frac{\\pi}{2}}^{\\pi} e^{x}\\left(\\frac{1-\\sin x}{1-\\cos x}\\right) d x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 26.
\n\\(\\int_{0}^{\\frac{\\pi}{4}} \\frac{\\sin x \\cos x}{\\cos ^{4} x+\\sin ^{4} x} d x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 27.
\n\\(\\int_{0}^{\\frac{\\pi}{2}} \\frac{\\cos ^{2} x d x}{\\cos ^{2} x+4 \\sin ^{2} x}\\)
\nSolution:
\nLet I = \\(\\int_{0}^{\\frac{\\pi}{2}} \\frac{\\cos ^{2} x d x}{\\cos ^{2} x+4 \\sin ^{2} x}\\)
\nDividing the Nr. and Dr. by cos\u00b2x, we get
\n\"NCERT
\nwhere t\u00b2 = y
\n\u21d2 1 = A(1 + 4y) + B(1 + y) … (1)
\nPut y = – 1 in (1), we get 1 = – 3A \u2234 A = \\(\\frac { – 1 }{ 3 }\\)
\nEquating the coefficients of y, we get
\n4A + B = 0
\n\u2234 B = \\(\\frac { 4 }{ 3 }\\)
\n\"NCERT<\/p>\n

Question 28.
\n\\(\\int_{\\frac{\\pi}{6}}^{\\frac{\\pi}{3}} \\frac{\\sin x+\\cos x}{\\sqrt{\\sin 2 x}} d x\\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 29.
\n\\(\\int_{0}^{1} \\frac{d x}{\\sqrt{1+x}-\\sqrt{x}}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 30.
\n\\(\\int_{0}^{\\frac{\\pi}{4}} \\frac{\\sin x+\\cos x}{9+16 \\sin 2 x} d x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 31.
\n\\(\\int_{0}^{\\frac{\\pi}{2}} \\sin 2 x \\tan ^{-1}(\\sin x) d x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 32.
\n\\(\\int_{0}^{\\pi} \\frac{x \\tan x}{\\sec x+\\tan x} d x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 33.
\n\\(\\left.\\int_{1}^{4}|| x-1|+| x-2|+| x-3 \\mid\\right] d x\\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 34.
\n\\(\\int_{1}^{3} \\frac{d x}{x^{2}(x+1)}=\\frac{2}{3}+\\log \\frac{2}{3}\\)
\nSolution:
\nLet \\(\\frac{1}{x^{2}(x+1)}=\\frac{A}{x}+\\frac{B}{x^{2}}+\\frac{C}{x+1}\\)
\n1 = Ax(x + 1) + B(x + 1) + C(x\u00b2) … (1)
\nPut x = 0 in (1), we get B = 1
\nPut x = – 1 in (1), we get C = 1
\nEquating the coefficients of x\u00b2, we get
\nA + C = 0 \u2234 A = – 1
\n\"NCERT<\/p>\n

Question 35.
\n\\(\\int_{0}^{1} x e^{x} d x=1\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 36.
\n\\(\\int_{-1}^{1} x^{17} \\cos ^{4} x d x=0\\)
\nSolution:
\nLet f(x) = x17<\/sup>cos4<\/sup>x
\nf(- x) = (- x)17<\/sup>cos< sup>4(-x)
\n\u2234 f(x) is an odd function.
\n\u2234 \\(\\int_{-1}^{1} x^{17} \\cos ^{4} x \\cdot d x=0\\)
\n\\(\\int_{-a}^{a} f(x) d x=0, \\text { if } f(x) \\text { is odd }\\)<\/p>\n

Question 37.
\n\\(\\int_{0}^{\\frac{\\pi}{2}} \\sin ^{3} x d x=\\frac{2}{3}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 38.
\n\\(\\int_{0}^{\\frac{\\pi}{4}} 2 \\tan ^{3} x d x=1-\\log 2\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 39.
\n\\(\\int_{0}^{1} \\sin ^{-1} x d x=\\frac{\\pi}{2}-1\\)
\nSolution
\n\u222bsin-1<\/sup> x dx = x sin-1<\/sup> x + \\(\\sqrt{1-x^{2}}\\)
\n(Refer in-tegrals of inverse trigonometric functions)
\n\u2234 \\(\\int_{0}^{1} \\sin ^{-1} x d x=\\left[x \\sin ^{-1} x+\\sqrt{1-x^{2}}\\right]_{0}^{1}\\)
\n= \\(\\left(\\frac{\\pi}{2}+0\\right)-(0+1)=\\frac{\\pi}{2}-1\\)<\/p>\n

Question 40.
\nEvaluate \\(\\int_{0}^{1} e^{2-3 x} d x\\) as a limit of a sum.
\nSolution:
\nLet I = \\(\\int_{0}^{1} e^{2-3 x} d x\\)
\nHere f(x) = e2-3x<\/sup>, a = 0, b = 1
\nnh = b – a = 1 – 0 = 1
\nf(0 + h) = f(h) = e2-3h<\/sup>
\nf(0 + 2h) = f(2h) = e2-6h<\/sup>
\n……………………………….
\nf(0 + (n – 1)h = f((n – 1)h) = e2-3(n-1)h<\/sup>
\n\"NCERT<\/p>\n

Question 41.
\n\\(\\int \\frac{d x}{e^{x}+e^{-x}}\\) is equal to
\na. tan-1<\/sup>(ex<\/sup>) + C
\nb. tan-1<\/sup>(e-x<\/sup>) + C
\nc. log(ex<\/sup> – e-x<\/sup>) + C
\nd. log(ex<\/sup> + x-x<\/sup>) + C
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 42.
\n\\(\\int \\frac{\\cos 2 x}{(\\sin x+\\cos x)^{2}} d x\\) is equal to
\na. \\(\\frac{-1}{\\sin x+\\cos x}+\\mathrm{C}\\)
\nb. log|sin x + cos x| + C
\nc. log|sin x – cos x| + C
\nd. \\(\\frac{1}{(\\sin x+\\cos x)^{2}}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 43.
\nIf \\(f(a+b-x)=f(x), \\text { then } \\int_{a}^{b} x f(x) d x\\) is equal to
\na. \\(\\frac{a+b}{2} \\int_{a}^{b} f(b-x) d x\\)
\nb. \\(\\frac{a+b}{2} \\int_{a}^{b} f(b+x) d x\\)
\nc. \\(\\frac{b-a}{2} \\int_{a}^{b} f(x) d x\\)
\nd. \\(\\frac{a+b}{2} \\int_{a}^{b} f(x) d x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 44.
\nThe value of \\(\\int_{0}^{1} \\tan ^{-1}\\left(\\frac{2 x-1}{1+x-x^{2}}\\right) d x\\) is
\na. 1
\nb. 0
\nc. – 1
\nd. \\(\\frac{\\pi}{4}\\)
\nSolution:
\n\"NCERT<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise Class 12 Maths Chapter 7 Miscellaneous Exercise Solutions Question 1. Solution: Let 1 = A(1 – x)(l + x) + Bx(l …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise - MCQ Questions<\/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:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise Class 12 Maths Chapter 7 Miscellaneous Exercise Solutions Question 1. Solution: Let 1 = A(1 – x)(l + x) + Bx(l … NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ Questions\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-29T11:00:44+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-03-29T11:17:31+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:site\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"15 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mcq-questions.com\/#website\",\"url\":\"https:\/\/mcq-questions.com\/\",\"name\":\"MCQ Questions\",\"description\":\"MCQ Questions for Class 1 to 12\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mcq-questions.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1\",\"contentUrl\":\"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1\",\"width\":170,\"height\":17,\"caption\":\"NCERT Solutions\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/#webpage\",\"url\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/\",\"name\":\"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise - MCQ Questions\",\"isPartOf\":{\"@id\":\"https:\/\/mcq-questions.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/#primaryimage\"},\"datePublished\":\"2022-03-29T11:00:44+00:00\",\"dateModified\":\"2022-03-29T11:17:31+00:00\",\"author\":{\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\"},\"breadcrumb\":{\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mcq-questions.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise\"}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\",\"name\":\"Prasanna\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"caption\":\"Prasanna\"},\"url\":\"https:\/\/mcq-questions.com\/author\/prasanna\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise - MCQ Questions","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise - MCQ Questions","og_description":"These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise Class 12 Maths Chapter 7 Miscellaneous Exercise Solutions Question 1. Solution: Let 1 = A(1 – x)(l + x) + Bx(l … NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise Read More »","og_url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/","og_site_name":"MCQ Questions","article_publisher":"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","article_published_time":"2022-03-29T11:00:44+00:00","article_modified_time":"2022-03-29T11:17:31+00:00","og_image":[{"url":"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png"}],"twitter_card":"summary_large_image","twitter_creator":"@ncertsolguru","twitter_site":"@ncertsolguru","twitter_misc":{"Written by":"Prasanna","Est. reading time":"15 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebSite","@id":"https:\/\/mcq-questions.com\/#website","url":"https:\/\/mcq-questions.com\/","name":"MCQ Questions","description":"MCQ Questions for Class 1 to 12","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mcq-questions.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/#primaryimage","inLanguage":"en-US","url":"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1","contentUrl":"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1","width":170,"height":17,"caption":"NCERT Solutions"},{"@type":"WebPage","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/#webpage","url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/","name":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise - MCQ Questions","isPartOf":{"@id":"https:\/\/mcq-questions.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/#primaryimage"},"datePublished":"2022-03-29T11:00:44+00:00","dateModified":"2022-03-29T11:17:31+00:00","author":{"@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3"},"breadcrumb":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-miscellaneous-exercise\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mcq-questions.com\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise"}]},{"@type":"Person","@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3","name":"Prasanna","image":{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","caption":"Prasanna"},"url":"https:\/\/mcq-questions.com\/author\/prasanna\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/32132"}],"collection":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/comments?post=32132"}],"version-history":[{"count":3,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/32132\/revisions"}],"predecessor-version":[{"id":37765,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/32132\/revisions\/37765"}],"wp:attachment":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/media?parent=32132"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/categories?post=32132"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/tags?post=32132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}