{"id":18574,"date":"2020-01-07T17:12:13","date_gmt":"2020-01-07T11:42:13","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=18574"},"modified":"2021-07-02T15:30:42","modified_gmt":"2021-07-02T10:00:42","slug":"2nd-puc-maths-question-bank-chapter-4-ex-4-1","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-maths-question-bank-chapter-4-ex-4-1\/","title":{"rendered":"2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.1"},"content":{"rendered":"

Students can Download Maths Chapter 4 Determinants Ex 4.1 Questions and Answers, Notes Pdf, 2nd PUC 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 2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.1<\/h2>\n

2nd PUC Maths Determinants NCERT Text Book Questions and Answers Ex 4.1<\/h3>\n

Evaluate the determinations<\/p>\n

Question 1.
\n\\(\\left|\\begin{array}{rr}{2} & {4} \\\\{-5} & {-1}\\end{array}\\right|\\)
\nAnswer:
\n2 x (-1) -4x (-5)
\n<\/span>= -2 + 20 = 18<\/span><\/p>\n

Question 2.
\n(i)
\n\\(\\left|\\begin{array}{rr}{\\cos \\theta} & {-\\sin \\theta} \\\\{\\sin \\theta} & {\\cos \\theta}\\end{array}\\right|\\)
\nAnswer:
\nCos \u03b8 x Cos \u03b8 – sin \u03b8 x sin \u03b8
\n= cos2<\/sup> \u03b8 + sin2<\/sup> \u03b8 = 1<\/p>\n

(ii)
\n\\(\\left|\\begin{array}{cc}{\\mathbf{x}^{2}-\\mathbf{x}+\\mathbf{1}} & {\\mathbf{x}-\\mathbf{1}} \\\\{\\mathbf{x}+\\mathbf{1}} & {\\mathbf{x}+\\mathbf{1}}\\end{array}\\right|\\)
\nAnswer:
\n(x2<\/sup> – x + 1) (x + 1) – (x – 1) (x + 1)
\n= x3<\/sup> + 1 – (x2<\/sup> – 1)
\n= x3<\/sup> – x2<\/sup> + 2<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\n\\(\\text { If } \\mathbf{A}=\\left[\\begin{array}{ll}{1} & {2} \\\\{4} & {2}\\end{array}\\right]\\),then show that |2A| = 4 |A|
\nAnswer:
\n\"2nd<\/p>\n

Question 4.
\n\\(\\text { If } \\mathbf{A}=\\left[\\begin{array}{lll}{\\mathbf{1}} & {\\mathbf{0}} & {\\mathbf{1}} \\\\{\\mathbf{0}} & {\\mathbf{1}} & {\\mathbf{2}} \\\\{\\mathbf{0}} & {\\mathbf{0}} & {\\mathbf{4}}\\end{array}\\right]\\) then show that |3A| = 27 |A|
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

Question 5.
\nEvaluate the determinant
\n(i)
\n\\(\\left|\\begin{array}{rrr}{3} & {-4} & {5} \\\\{1} & {1} & {-2} \\\\{2} & {3} &{1}\\end{array}\\right|\\)
\nAnswer:
\nExpanding along R2<\/sub> (Second Row where two elements are zeroes)
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

(ii)
\n\\(\\left|\\begin{array}{rrr}{3} & {-4} & {5} \\\\{1} & {1} & {-2} \\\\{2} & {3} & {1}\\end{array}\\right|\\)
\nAnswer:
\nExpanding along R1
\n\"2nd<\/sub><\/p>\n

(iii)
\n\\(\\left|\\begin{array}{ccc}{0} & {1} & {2} \\\\{-1} & {0} & {-3} \\\\{-2} & {3} & {0}\\end{array}\\right|\\)
\nAnswer:
\nExpanding along R1
\n\"2nd<\/sub><\/p>\n

(iv)
\n\\(\\left|\\begin{array}{ccc}{2} & {-1} & {-2} \\\\{0} & {2} & {-1} \\\\{3} & {-5} &{0}\\end{array}\\right|\\)
\nAnswer:
\nExpanding along R3
\n\"2nd<\/sub><\/p>\n

Question 6.
\n\\(\\text { If } A=\\left[\\begin{array}{ccc}{1} & {1} & {-2} \\\\{2} & {1} & {-3} \\\\{5} & {4} & {-9}\\end{array}\\right] \\text { find }|A|\\)
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 7.
\nfind X if
\n(i)
\n\\(\\left|\\begin{array}{cc}{2} & {4} \\\\{5} & {1}\\end{array}\\right|=\\left|\\begin{array}{cc}{2 x} & {4} \\\\{6} & {x}\\end{array}\\right|\\)
\nAnswer:
\n2 x 1 -4 x 5 = 2 \u00d7 x \u00d7 -4 \u00d7 6
\n2 – 20 = 2x2<\/sup> – 24 – 18
\n= 2x2 <\/sup>– 24
\n2x2<\/sup> = 6,
\nx2<\/sup> = 3
\n\\(x=\\pm \\sqrt{3}\\)<\/p>\n

(ii)
\n\\(\\left|\\begin{array}{cc}{2} & {3} \\\\{4} & {5}\\end{array}\\right|=\\left|\\begin{array}{cc}{x} & {3} \\\\{2 x} & {5}\\end{array}\\right|\\)
\n2 x 5 -3 x 4=5 x x – 6x
\n10 – 12\u00a0 = 5x – 6x
\n-2\u00a0 \u00a0 \u00a0 \u00a0=-x
\nx = 2<\/p>\n

\"KSEEB<\/p>\n

Question 8.
\n\\(\\text { If }\\left|\\begin{array}{cc}{x} & {2} \\\\{18} {x}\\end{array}\\right|=\\left|\\begin{array}{cc}{6} & {2} \\\\{18} & {6}\\end{array}\\right|\\)
\n(A) 6
\n(B) \u00b1 6
\n(C) -6
\n(D) 0
\nAnswer:
\n2 x 18 = 6 x 6-18 x 2
\nx2 <\/sup>– 36 = 36 – 36
\nx2<\/sup> – 36 = 0
\nx2<\/sup> = 36
\nx= \u00b16
\nhence B is the correct answer.
\nNote: Two determinants ms equal does not mean corresponding elements are equal so do not equate the elements like we are doing in matrix.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Maths Chapter 4 Determinants Ex 4.1 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.1 2nd PUC Maths Determinants NCERT Text Book …<\/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\/18574"}],"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=18574"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/18574\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=18574"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=18574"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=18574"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}