{"id":39869,"date":"2023-01-19T10:00:05","date_gmt":"2023-01-19T04:30:05","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=39869"},"modified":"2023-01-20T09:40:02","modified_gmt":"2023-01-20T04:10:02","slug":"plus-two-maths-chapter-wise-previous-questions-chapter-4","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/","title":{"rendered":"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants"},"content":{"rendered":"

Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants are part of\u00a0Plus Two Maths Chapter Wise Previous Year Questions and Answers<\/a>. Here we have given Plus Two Maths Chapter Wise Previous Chapter 4 Determinants.<\/p>\n

Kerala\u00a0Plus Two Maths Chapter Wise Previous\u00a0Questions Chapter 4 Determinants<\/h2>\n

Plus Two Maths Determinants 3 Marks Important Questions<\/h3>\n

Question 1.
\nProve that \\(\\begin{array}{|lll|}
\n1 ! & 2 ! & 3 ! \\\\
\n2 ! & 3 ! & 4 ! \\\\
\n3 ! & 4 ! & 5 !
\n\\end{array}\\) (March – 2015)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 2.
\nUsing properties of determinants prove the following. (March – 2010; Christmas -2017)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus
\n\"Plus<\/p>\n

Plus Two Maths Determinants 4 Marks Important Questions<\/h3>\n

Question 1.
\nConsider the matrix \\(A=\\left[\\begin{array}{ll}
\n2 & 5 \\\\
\n3 & 2
\n\\end{array}\\right]\\)<\/p>\n

(i) Find adj (A)
\n(ii) Find A1
\n(iii) Using A-1<\/sup> solve the system of linear equations 2x + 5y = 13x + 2y = 7 (March – 2010)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Plus Two Maths Determinants 6 Marks Important Questions<\/h3>\n

Question 1.
\nConsider the matrix \\(A=\\left[\\begin{array}{lll}
\na & b & c \\\\
\nb & c & a \\\\
\nc & a & b
\n\\end{array}\\right]\\)<\/p>\n

(i) Using the column operat,on
\nC1<\/sub> \u2192 C1<\/sub> + C2<\/sub> + C3<\/sub>,
\nshow that \\(|A|=(a+b+c)\\left|\\begin{array}{ccc}
\n1 & b & c \\\\
\n1 & c & a \\\\
\n1 & a & b
\n\\end{array}\\right|\\)
\n(ii) Show that |A| = – (a3 + b3 + e3 \u2014 3abc)
\n(iii) Find A x adj(A) if a = 1,b = 10,c = 100 (May – 2010)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 2.
\n(i) (a) If \\(A=\\left[\\begin{array}{ccc}
\n1 & 1 & 5 \\\\
\n0 & 1 & 3 \\\\
\n0 & -1 & -2
\n\\end{array}\\right]\\)<\/p>\n

What is the value of |3A|?
\n(b) Find the equation of the line joining the points (1,2) and (-3,-2) using determinants.
\n(ii) Show that \\(\\left|\\begin{array}{lll}
\n1 & a & a^{2} \\\\
\n1 & b & b^{2} \\\\
\n1 & c & c^{2}
\n\\end{array}\\right|=(a-b)(b-c)(c-a)\\)
\nAnswer:
\n\"Plus<\/p>\n

(b) Let (x,y) be the coordinate of any point on The line, then (1,2), (-3, -2) and (x, y) are collinear.<\/p>\n

Hence the area formed will be zero.
\n\"Plus<\/p>\n

Question 3.
\nConsider the following system of linear equations; x + y + z = 6, x – y + z = 2, 2x + y + z = 1
\n(i) Express this system of equations in the Standard form AXB
\n(ii) Prove that A is non-singular.
\n(iii) Find the value of x, y and z satisfying the above equation. (May – 2011)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

\"Plus<\/p>\n

Question 4.
\n(i) lf \\(\\left|\\begin{array}{ll}
\nx & 3 \\\\
\n5 & 2
\n\\end{array}\\right|=5\\), then x = ………..
\n(ii) Prove that
\n\\(\\left|\\begin{array}{ccc}
\ny+k & y & y \\\\
\ny & y+k & y \\\\
\ny & y & y+k
\n\\end{array}\\right|=k^{2}(3 y+k)\\)
\n(iii) Solve the following system of linear Equations, using matrix method; 5x + 2y = 3, 3x + 2y = 5 (March – 2012)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 5.
\n(i) Let B is a square matrix of order 5, then |kB| is equal to ………..
\n(a) |B|
\n(b) k|B|
\n(c) k5<\/sup>|B|
\n(d) 5|B|<\/p>\n

(ii) Prove that \\(\\left|\\begin{array}{lll}
\n1 & x & x^{2} \\\\
\n1 & y & y^{2} \\\\
\n1 & z & z^{2}
\n\\end{array}\\right|=(x-y)(y-z)(z-x)\\)
\n(iii) Check the consistency of the following equations; 2x + 3y + z = 6, x + 2y – z = 2, 7x + y + 2z =10 (May – 2012)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Therefore the system is consistent and has unique solutions.<\/p>\n

Question 6.
\n(i) Find the values of x in which \\(\\left|\\begin{array}{ll}
\n3 & x \\\\
\nx & 1
\n\\end{array}\\right|=\\left|\\begin{array}{ll}
\n3 & 2 \\\\
\n4 & 1
\n\\end{array}\\right|\\)<\/p>\n

(ii) Using the property of determinants, show that the points A(a,b + c), B(b,c + a), C(c,a + b) are collinear.
\n(iii) Examine the consistency of system of following equations: 5x – 6y + 4z = 15, 7x + y – 3z = 19, 2x + y + 6z = 46 (EDUMATE – 2017; March – 2013)<\/span>
\nAnswer:
\n\"Plus
\nSince, the system is consistent and has unique solutions.<\/p>\n

Question 7.
\nConsider a system of linear equations which is given below;
\n\\(\\begin{array}{l}
\n\\frac{2}{x}+\\frac{3}{y}+\\frac{10}{z}=4 ; \\frac{4}{x}-\\frac{6}{y}+\\frac{5}{z}=1 \\\\
\n\\frac{6}{x}+\\frac{9}{y}-\\frac{20}{z}=2
\n\\end{array}\\)<\/p>\n

(i) Express the above equation in the matrix form AX = B.
\n(ii) Find A-1<\/sup>, the inverse of A.
\n(iii) Find x,y and z. (May – 2013)
\nAnswer:
\n\"Plus<\/p>\n

Question 8.
\nConsider the matrices \\(A=\\left[\\begin{array}{ll}
\n2 & 3 \\\\
\n4 & 5
\n\\end{array}\\right]\\)<\/p>\n

(i) Find A2<\/sup> – 7A – 21 = 0
\n(ii) Hence find A-1
\n(iii) Solve the following system of equations using matrix method 2x + 3y = 4; 4x + 5y = 6 (March – 2014)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

(iii) The given system of equations can be converted into matrix form AX = B
\n\"Plus<\/p>\n

Question 9.
\n(i) Let A be a square matrix of order 2 x 2 then |KA| is equal to
\n(a) K|A|
\n(b) K2<\/sup>|A|
\n(c) K3<\/sup>|A|
\n(d) 2K|A|<\/p>\n

(ii) Prove that
\n\\(\\left|\\begin{array}{ccc}
\n\\mathbf{a}-\\mathbf{b}-\\mathbf{c} & \\mathbf{2 a} & 2 \\mathbf{a} \\\\
\n2 \\mathrm{~b} & \\mathrm{~b}-\\mathrm{c}-\\mathrm{a} & 2 \\mathrm{~b} \\\\
\n2 \\mathrm{c} & 2 \\mathrm{c} & \\mathrm{c}-\\mathrm{a}-\\mathrm{b}
\n\\end{array}\\right|=(\\mathrm{a}+\\mathrm{b}+\\mathrm{c})^{3}\\)<\/p>\n

(iii) Examine the consistency of the system of Equations. 5x + 3y = 5; 2x + 6y = 8 (May- 2014)<\/span>
\nAnswer:
\n\"Plus
\n(iii) The given system of equation can be written in matrix form as
\n\"Plus
\nsolution exist and hence it is consistent.<\/p>\n

Question 10.
\n(a) Choose the correct statement related to the matnces \\(A=\\left[\\begin{array}{ll}
\n1 & 0 \\\\
\n0 & 1
\n\\end{array}\\right], B=\\left[\\begin{array}{ll}
\n0 & 1 \\\\
\n1 & 0
\n\\end{array}\\right]\\)
\n\\(\\begin{array}{l}
\n\\text { (i) } A^{3}=A, B^{3} \\neq B \\\\
\n\\text { (ii) } A^{3} \\neq A, B^{3}=B \\\\
\n\\text { (iii) } A^{3}=A, B^{3}=B \\\\
\n\\text { (iv) } A^{3} \\neq A, B^{3} \\neq B
\n\\end{array}\\)<\/p>\n

(b) lf \\(M=\\left[\\begin{array}{ll}
\n7 & 5 \\\\
\n2 & 3
\n\\end{array}\\right]\\) then verity the equation M2<\/sup> – 10M + 11 I2<\/sub> = O<\/p>\n

(c) Inverse of the matrix \\(\\left[\\begin{array}{lll}
\n0 & 1 & 2 \\\\
\n0 & 1 & 1 \\\\
\n1 & 0 & 2
\n\\end{array}\\right]\\) (March – 2015)
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 11.
\nSolve the system of Linear equations x + 2y + z = 8; 2x + y – z = 1; x – y + z = 2 (March – 2015)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 12.
\n(a) If \\(\\left|\\begin{array}{ll}
\nx & 1 \\\\
\n1 & x
\n\\end{array}\\right|=15\\) then find the value of X.<\/p>\n

(b)Solve the following system of equations 3x – 2y + 3z = ?, 2x + y – z = 1 4x – 3y + 2z = 4 (May – 2015)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 13.
\n(i)The value of the determinant \\(\\left|\\begin{array}{ccc}
\n1 & 1 & 1 \\\\
\n1 & -1 & -1 \\\\
\n1 & 1 & -1
\n\\end{array}\\right|\\) is
\n(a) -4
\n(b) 0
\n(c) 1
\n(d) 4<\/p>\n

(ii) Using matrix method, solve the system of linear equations x + y + 2z = 4; 2x – y + 3z = 9; 3x – y – z = 2 (May – 2016)<\/span>
\nAnswer:
\n(i) (d) 4
\n(ii) Express the given equation in the matrix form as AX = B
\n\"Plus<\/p>\n

Question 14.
\n(i) If \\(A=\\left[\\begin{array}{ll}
\na & 1 \\\\
\n1 & 0
\n\\end{array}\\right]\\) is such that A2<\/sup> = I then a equals
\n(a) 1
\n(b) -1
\n(c) 0
\n(d) 2<\/p>\n

(ii)Solve the system of equations x – y + z = 4; 2x + y – 3z = 0; x + y + z = 2 Using matrix method. (March – 2017)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 15.
\n(i) IfA is a 2 x 2 matrix with |A| = 5, then |adjA| is
\n(a) 5
\n(b) 25
\n(c) 1\/5
\n(d) 1\/25<\/p>\n

(ii) Solve the system of equations using matrix method.
\nx + y + z = 1; 2x + 3y – z = 6; x – y + z = -1 (May – 2017)<\/span>
\nAnswer:
\n(i) (a) 5
\n(ii) LetA X=B,
\n\"Plus
\n\"Plus<\/p>\n

We hope the Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants help you. If you have any query regarding Kerala Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"

Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants are part of\u00a0Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 4 Determinants. Kerala\u00a0Plus Two Maths Chapter Wise Previous\u00a0Questions Chapter 4 Determinants Plus Two Maths Determinants 3 Marks Important Questions Question 1. Prove […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[42728],"tags":[],"yoast_head":"\nPlus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants - A Plus Topper<\/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:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants\" \/>\n<meta property=\"og:description\" content=\"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants are part of\u00a0Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 4 Determinants. Kerala\u00a0Plus Two Maths Chapter Wise Previous\u00a0Questions Chapter 4 Determinants Plus Two Maths Determinants 3 Marks Important Questions Question 1. Prove […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/\" \/>\n<meta property=\"og:site_name\" content=\"A Plus Topper\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/aplustopper\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-01-19T04:30:05+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-01-20T04:10:02+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/Plus-Two-Maths-Chapter-Wise-Previous-Questions-Chapter-4-Determinants-1.png\" \/>\n<meta name=\"twitter:card\" content=\"summary\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Kalyan\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/www.aplustopper.com\/#organization\",\"name\":\"Aplus Topper\",\"url\":\"https:\/\/www.aplustopper.com\/\",\"sameAs\":[\"https:\/\/www.facebook.com\/aplustopper\/\"],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"contentUrl\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"width\":1585,\"height\":375,\"caption\":\"Aplus Topper\"},\"image\":{\"@id\":\"https:\/\/www.aplustopper.com\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.aplustopper.com\/#website\",\"url\":\"https:\/\/www.aplustopper.com\/\",\"name\":\"A Plus Topper\",\"description\":\"Improve your Grades\",\"publisher\":{\"@id\":\"https:\/\/www.aplustopper.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.aplustopper.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/Plus-Two-Maths-Chapter-Wise-Previous-Questions-Chapter-4-Determinants-1.png\",\"contentUrl\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/Plus-Two-Maths-Chapter-Wise-Previous-Questions-Chapter-4-Determinants-1.png\",\"width\":341,\"height\":111,\"caption\":\"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 1\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#webpage\",\"url\":\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/\",\"name\":\"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants - A Plus Topper\",\"isPartOf\":{\"@id\":\"https:\/\/www.aplustopper.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#primaryimage\"},\"datePublished\":\"2023-01-19T04:30:05+00:00\",\"dateModified\":\"2023-01-20T04:10:02+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.aplustopper.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants\"}]},{\"@type\":\"Article\",\"@id\":\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#webpage\"},\"author\":{\"@id\":\"https:\/\/www.aplustopper.com\/#\/schema\/person\/b82e489789d83ccf01d664235804eb43\"},\"headline\":\"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants\",\"datePublished\":\"2023-01-19T04:30:05+00:00\",\"dateModified\":\"2023-01-20T04:10:02+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#webpage\"},\"wordCount\":1257,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/www.aplustopper.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/Plus-Two-Maths-Chapter-Wise-Previous-Questions-Chapter-4-Determinants-1.png\",\"articleSection\":[\"HSSLiVE\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#respond\"]}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.aplustopper.com\/#\/schema\/person\/b82e489789d83ccf01d664235804eb43\",\"name\":\"Kalyan\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/a08b17f948aaea19c0551b8ee4b91ca0?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/a08b17f948aaea19c0551b8ee4b91ca0?s=96&d=mm&r=g\",\"caption\":\"Kalyan\"},\"url\":\"https:\/\/www.aplustopper.com\/author\/kalyan\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants - A Plus Topper","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:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/","og_locale":"en_US","og_type":"article","og_title":"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants","og_description":"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants are part of\u00a0Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 4 Determinants. Kerala\u00a0Plus Two Maths Chapter Wise Previous\u00a0Questions Chapter 4 Determinants Plus Two Maths Determinants 3 Marks Important Questions Question 1. Prove […]","og_url":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/","og_site_name":"A Plus Topper","article_publisher":"https:\/\/www.facebook.com\/aplustopper\/","article_published_time":"2023-01-19T04:30:05+00:00","article_modified_time":"2023-01-20T04:10:02+00:00","og_image":[{"url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/Plus-Two-Maths-Chapter-Wise-Previous-Questions-Chapter-4-Determinants-1.png"}],"twitter_card":"summary","twitter_misc":{"Written by":"Kalyan","Est. reading time":"6 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/www.aplustopper.com\/#organization","name":"Aplus Topper","url":"https:\/\/www.aplustopper.com\/","sameAs":["https:\/\/www.facebook.com\/aplustopper\/"],"logo":{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/#logo","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","width":1585,"height":375,"caption":"Aplus Topper"},"image":{"@id":"https:\/\/www.aplustopper.com\/#logo"}},{"@type":"WebSite","@id":"https:\/\/www.aplustopper.com\/#website","url":"https:\/\/www.aplustopper.com\/","name":"A Plus Topper","description":"Improve your Grades","publisher":{"@id":"https:\/\/www.aplustopper.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.aplustopper.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#primaryimage","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/Plus-Two-Maths-Chapter-Wise-Previous-Questions-Chapter-4-Determinants-1.png","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/Plus-Two-Maths-Chapter-Wise-Previous-Questions-Chapter-4-Determinants-1.png","width":341,"height":111,"caption":"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 1"},{"@type":"WebPage","@id":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#webpage","url":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/","name":"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants - A Plus Topper","isPartOf":{"@id":"https:\/\/www.aplustopper.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#primaryimage"},"datePublished":"2023-01-19T04:30:05+00:00","dateModified":"2023-01-20T04:10:02+00:00","breadcrumb":{"@id":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.aplustopper.com\/"},{"@type":"ListItem","position":2,"name":"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants"}]},{"@type":"Article","@id":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#article","isPartOf":{"@id":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#webpage"},"author":{"@id":"https:\/\/www.aplustopper.com\/#\/schema\/person\/b82e489789d83ccf01d664235804eb43"},"headline":"Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants","datePublished":"2023-01-19T04:30:05+00:00","dateModified":"2023-01-20T04:10:02+00:00","mainEntityOfPage":{"@id":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#webpage"},"wordCount":1257,"commentCount":0,"publisher":{"@id":"https:\/\/www.aplustopper.com\/#organization"},"image":{"@id":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#primaryimage"},"thumbnailUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/Plus-Two-Maths-Chapter-Wise-Previous-Questions-Chapter-4-Determinants-1.png","articleSection":["HSSLiVE"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-4\/#respond"]}]},{"@type":"Person","@id":"https:\/\/www.aplustopper.com\/#\/schema\/person\/b82e489789d83ccf01d664235804eb43","name":"Kalyan","image":{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/a08b17f948aaea19c0551b8ee4b91ca0?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/a08b17f948aaea19c0551b8ee4b91ca0?s=96&d=mm&r=g","caption":"Kalyan"},"url":"https:\/\/www.aplustopper.com\/author\/kalyan\/"}]}},"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/posts\/39869"}],"collection":[{"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/comments?post=39869"}],"version-history":[{"count":1,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/posts\/39869\/revisions"}],"predecessor-version":[{"id":155080,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/posts\/39869\/revisions\/155080"}],"wp:attachment":[{"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/media?parent=39869"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/categories?post=39869"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/tags?post=39869"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}