{"id":29695,"date":"2022-03-29T11:00:19","date_gmt":"2022-03-29T05:30:19","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=29695"},"modified":"2022-03-29T11:09:10","modified_gmt":"2022-03-29T05:39:10","slug":"ncert-solutions-for-class-12-maths-chapter-4-ex-4-2","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-2\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 4 Determinants Ex 4.2 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-2\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2<\/h2>\n

\"NCERT<\/p>\n

Class 12 Maths Ex 4.2 Solutions NCERT Solutions Question 1.<\/strong>
\n\\(\\left| \\begin{matrix} x & a & x+a \\\\ y & b & y+b \\\\ z & c & z+c \\end{matrix} \\right|\\) = 0
\nSolution:
\nL.H.S = \\(\\left| \\begin{matrix} x & a & x \\\\ y & b & y \\\\ z & c & z \\end{matrix} \\right| +\\left| \\begin{matrix} x & a & a \\\\ y & b & b \\\\ z & c & c \\end{matrix} \\right| \\)
\n(C1<\/sub> = C3<\/sub> and C2<\/sub> = C3<\/sub>)
\n= 0 + 0
\n= 0
\n= R.H.S<\/p>\n

Ncert Solutions Class 12 Maths Chapter 4 Exercise 4.2 Question 2.<\/strong>
\n\\(\\left| \\begin{matrix} a-b & b-c & c-a \\\\ b-c & c-a & a-b \\\\ c-a & a-b & b-c \\end{matrix} \\right| =0\\)
\nSolution:
\n\"Class<\/p>\n

Exercise 4.2 Class 12 NCERT Solutions Question 3.<\/strong>
\n\\(\\left| \\begin{matrix} 2 & 7 & 65 \\\\ 3 & 8 & 75 \\\\ 5 & 9 & 86 \\end{matrix} \\right| =0\\)
\nSolution:
\n\\(\\left| \\begin{matrix} 2 & 7 & 65 \\\\ 3 & 8 & 75 \\\\ 5 & 9 & 86 \\end{matrix} \\right| =\\left| \\begin{matrix} 2 & 7 & 0 \\\\ 3 & 8 & 0 \\\\ 5 & 9 & 0 \\end{matrix} \\right| \\)
\n\\({ C }_{ 3 }\\rightarrow { C }_{ 3 }-{ C }_{ 1 }-{ 9C }_{ 2 }=0\\)<\/p>\n

Ex 4.2 Class 12 Maths NCERT Solutions\u00a0 Question 4.<\/strong>
\n\\(\\left| \\begin{matrix} 1 & bc & a(b+c) \\\\ 1 & ca & b(c+a) \\\\ 1 & ab & c(a+b) \\end{matrix} \\right| =0\\)
\nSolution:
\n\"Ncert<\/p>\n

\"NCERT<\/p>\n

Ex 4.2 Class 12 NCERT Solutions Question 5.<\/strong>
\n\\(\\left| \\begin{matrix} b+c & q+r & y+z \\\\ c+a & r+p & z+x \\\\ a+b & p+q & x+y \\end{matrix} \\right| =2\\left| \\begin{matrix} a & p & x \\\\ b & q & y \\\\ c & r & z \\end{matrix} \\right| \\)
\nSolution:
\n\"Exercise<\/p>\n

By using properties of determinants in Exercise 6 to 14, show that:<\/p>\n

Question 6.
\n\\(\\left| \\begin{matrix} 0 & a & -b \\\\ -a & 0 & -c \\\\ b & c & 0 \\end{matrix} \\right| =0\\)
\nSolution:
\n\"Ex<\/p>\n

Question 7.
\n\\(\\left| \\begin{matrix} { -a }^{ 2 } & ab & ac \\\\ ba & { -b }^{ 2 } & bc \\\\ ac & cb & { -c }^{ 2 } \\end{matrix} \\right| ={ 4a }^{ 2 }{ b }^{ 2 }{ c }^{ 2 }\\)
\nSolution:
\n\"Ex<\/p>\n

\"NCERT<\/p>\n

Question 8.
\n(a) \\(\\left| \\begin{matrix} 1 & a & { a }^{ 2 } \\\\ 1 & b & { b }^{ 2 } \\\\ 1 & c & { c }^{ 2 } \\end{matrix} \\right| =(a-b)(b-c)(c-a)\\)
\n(b) \\(\\left| \\begin{matrix} 1 & 1 & 1 \\\\ a & b & c \\\\ { a }^{ 3 } & { b }^{ 3 } & { c }^{ 3 } \\end{matrix} \\right| =(a-b)(b-c)(c-a)(a+b+c)\\)
\nSolution:
\n(a) \\(\\left|\\begin{array}{lll}
\n1 & a & a^{2} \\\\
\n1 & b & b^{2} \\\\
\n1 & c & c^{2}
\n\\end{array}\\right|\\)
\n\"NCERT
\nTaking out (b – a) from R2<\/sub> and (c – a) from R3<\/sub>.
\nExpanding along C1<\/sub>
\n= (b – a)(c – a)\\(\\left|\\begin{array}{ll}
\n1 & b+a \\\\
\n1 & c+a
\n\\end{array}\\right|\\)
\n= (b – a) (c – a) (c + a – b – a) = (b – a) (c – a) (c – b)
\n= (-1 )(a – b)(c – a)(-1)(b – c)
\n= (a- b) (b – c) (c – a)<\/p>\n

(b) \\(\\left|\\begin{array}{ccc}
\n1 & 1 & 1 \\\\
\na & b & c \\\\
\na^{3} & b^{3} & c^{3}
\n\\end{array}\\right|\\)
\n\"NCERT<\/p>\n

Question 9.
\n\\(\\left| \\begin{matrix} x & x^{ 2 } & yx \\\\ y & { y }^{ 2 } & zx \\\\ z & { z }^{ 2 } & xy \\end{matrix} \\right| =(x-y)(y-z)(z-x)(xy+yz+zx)\\)
\nSolution:
\nLet \u2206 = \\(\\left| \\begin{matrix} x & x^{ 2 } & yx \\\\ y & { y }^{ 2 } & zx \\\\ z & { z }^{ 2 } & xy \\end{matrix} \\right|\\)
\nApplying R1<\/sub> \u2192 R1<\/sub> – R2<\/sub>, R2<\/sub> \u2192 R2<\/sub> – R3<\/sub>
\n\"NCERT<\/p>\n

Question 10.
\n(a) \\(\\left| \\begin{matrix} x+4 & 2x & 2x \\\\ 2x & x+4 & 2x \\\\ 2x & 2x & x+4 \\end{matrix} \\right| =(5x+4){ (4-x) }^{ 2 }\\)
\n(b) \\(\\left| \\begin{matrix} y+x & y & y \\\\ y & y+k & y \\\\ y & y & y+k \\end{matrix} \\right| ={ k }^{ 2 }(3y+k) \\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 11.
\n(a) \\(\\left| \\begin{matrix} a-b-c & \\quad 2a & \\quad 2a \\\\ 2b & \\quad b-c-a & \\quad 2b \\\\ 2c & 2c & \\quad c-a-b \\end{matrix} \\right| ={ (a+b+c) }^{ 3 } \\)
\n(b) \\(\\left| \\begin{matrix} x+y+2z & \\quad z & \\quad z \\\\ x & \\quad y+z+2x & \\quad x \\\\ y & y & \\quad z+x+2y \\end{matrix} \\right| ={ 2(x+y+z) }^{ 3 } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 12.
\n\\(\\left| \\begin{matrix} 1 & \\quad x & { \\quad x }^{ 2 } \\\\ { x }^{ 2 } & \\quad 1 & x \\\\ x & { \\quad x }^{ 2 } & 1 \\end{matrix} \\right| ={ { (1-x }^{ 3 }) }^{ 2 } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 13.
\n\\(\\left| \\begin{matrix} 1+{ a }^{ 2 }-{ b }^{ 2 } & \\quad 2ab & \\quad -2b \\\\ 2ab & \\quad 1-{ a }^{ 2 }+{ b }^{ 2 } & \\quad 2a \\\\ 2b & \\quad -2a & \\quad 1-{ a }^{ 2 }+{ b }^{ 2 } \\end{matrix} \\right| ={ (1+{ a }^{ 2 }+{ b }^{ 2 }) }^{ 3 } \\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 14.
\n\\(\\left| \\begin{matrix} { a }^{ 2 }+1 & \\quad ab & \\quad ac \\\\ ab\\quad & \\quad b^{ 2 }+1 & \\quad bc \\\\ ca\\quad & \\quad cb & \\quad { c }^{ 2 }+1 \\end{matrix} \\right| =1+{ a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 } \\)
\nSolution:
\nLet
\n\u2206 = \\(\\left| \\begin{matrix} { a }^{ 2 }+1 & \\quad ab & \\quad ac \\\\ ab\\quad & \\quad b^{ 2 }+1 & \\quad bc \\\\ ca\\quad & \\quad cb & \\quad { c }^{ 2 }+1 \\end{matrix} \\right| \\)
\n\\(\\left| \\begin{matrix} { a }^{ 2 }+1 & \\quad ab+0 & \\quad ac+0 \\\\ ab+0\\quad & \\quad b^{ 2 }+1 & \\quad bc+0 \\\\ ca+0\\quad & \\quad cb+0 & \\quad { c }^{ 2 }+1 \\end{matrix} \\right| \\)
\nThis may be expressed as the sum of 8 determinants
\n\"NCERT<\/p>\n

Question 15.
\nIf A be a square matrix of order 3×3, then | kA | is equal to
\n(a) k|A|
\n(b) k\u00b2 |A|
\n(c) k\u00b3 |A|
\n(d) 3k|A|
\nSolution:
\nOption (c) is correct.<\/p>\n

\"NCERT<\/p>\n

Question 16.
\nWhich of the following is correct:
\n(a) Determinant is a square matrix
\n(b) Determinant is a number associated to a matrix
\n(c) Determinant is a number associated to a square matrix
\n(d) None of these
\nSolution:
\nOption (c) is correct.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-2\/ NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2 Class 12 Maths Ex 4.2 Solutions NCERT Solutions Question 1. = 0 Solution: L.H.S = (C1 = C3 and C2 …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2<\/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 4 Determinants Ex 4.2 - 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-4-ex-4-2\/\" \/>\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 4 Determinants Ex 4.2 - 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