Prove that from Mathematics Determinants
    • Zigya Logo

    Previous Year Papers

    Download Solved Question Papers Free for Offline Practice and view Solutions Online.

    Test Series

    Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

    Test Yourself

    Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
    Advertisement

    Determinants

    Multiple Choice QuestionsLong Answer Type

    111.

    Prove that:
    open vertical bar table row 1 cell space straight a end cell cell space space bc end cell row 1 cell space straight b end cell cell space space ca end cell row 1 cell space straight c end cell cell space ab end cell end table close vertical bar space equals space left parenthesis straight a minus straight b right parenthesis thin space left parenthesis straight b minus straight c right parenthesis thin space left parenthesis straight c minus straight a right parenthesis



    70 Views
    Answer
    112.

    Prove that:
    open vertical bar table row 1 cell space space straight x end cell cell space space yz end cell row 1 cell space space straight y end cell cell space space zx end cell row 1 cell space straight z end cell cell space space xy end cell end table close vertical bar space equals space left parenthesis straight x minus straight y right parenthesis thin space left parenthesis straight y minus straight z right parenthesis thin space left parenthesis straight z minus straight x right parenthesis




    93 Views
    Answer
    113.

    Prove that:
    open vertical bar table row straight a straight b straight c row cell straight a squared end cell cell straight b squared end cell cell straight c squared end cell row bc ca ab end table close vertical bar space equals space left parenthesis ab plus bc plus ca right parenthesis thin space left parenthesis straight a minus straight b right parenthesis thin space left parenthesis straight b minus straight c right parenthesis thin space left parenthesis straight c minus straight a right parenthesis





    73 Views
    Answer

    Multiple Choice QuestionsShort Answer Type

    114.

    Prove that:
    open vertical bar table row straight a cell space space straight a squared end cell cell space space straight b plus straight c end cell row straight b cell space space straight b squared end cell cell space space straight c plus straight a end cell row straight c cell space straight c squared end cell cell space space straight a plus straight b end cell end table close vertical bar space equals space left parenthesis straight a plus straight b plus straight c right parenthesis thin space left parenthesis straight a minus straight b right parenthesis thin space left parenthesis straight b minus straight c right parenthesis thin space left parenthesis straight c minus straight a right parenthesis

    69 Views
    Answer
    Advertisement

    Multiple Choice QuestionsLong Answer Type

    115.

    Prove that:
    open vertical bar table row straight alpha cell space space straight beta end cell cell space space space space straight gamma end cell row cell straight alpha squared end cell cell space space straight beta squared end cell cell space space space straight gamma squared end cell row cell straight beta plus straight gamma end cell cell space space space straight gamma plus straight alpha end cell cell space space space space straight alpha plus straight beta end cell end table close vertical bar space equals space left parenthesis straight beta minus straight gamma right parenthesis space left parenthesis straight gamma minus straight alpha right parenthesis thin space left parenthesis straight alpha minus straight beta right parenthesis thin space left parenthesis straight alpha plus straight beta plus straight gamma right parenthesis

    62 Views
    Answer

    Multiple Choice QuestionsShort Answer Type

    116.

    Show that:
    open vertical bar table row 1 cell space space straight x end cell cell space space yz end cell row 1 cell space straight y end cell cell space space zx end cell row 1 cell space straight z end cell cell space space xy end cell end table close vertical bar space equals space open vertical bar table row 1 cell space space space straight x end cell cell space space straight x squared end cell row 1 cell space space straight y end cell cell space space straight y squared end cell row 1 cell space straight z end cell cell space space straight z squared end cell end table close vertical bar
    and hence factorise.

    77 Views
    Answer
    117.

    Using the properties of determinants, show that:
    open vertical bar table row 1 cell space space space straight x plus straight y end cell cell space space space straight x squared plus straight y squared end cell row 1 cell space straight y plus straight z end cell cell space space straight y squared plus straight z squared end cell row 1 cell space straight z plus straight x end cell cell space space straight z squared plus straight x squared end cell end table close vertical bar space equals space left parenthesis straight x minus straight y right parenthesis thin space left parenthesis straight y minus straight z right parenthesis thin space left parenthesis straight z minus straight x right parenthesis

    89 Views
    Answer

    Multiple Choice QuestionsLong Answer Type

    118. Using properties of determinants, prove that
    open vertical bar table row straight x cell space straight x squared end cell cell space yz end cell row straight y cell space straight y squared end cell cell space zx end cell row straight z cell space straight z squared end cell cell space xy end cell end table close vertical bar space equals space left parenthesis straight x minus straight y right parenthesis thin space left parenthesis straight y minus straight z right parenthesis thin space left parenthesis straight z minus straight x right parenthesis thin space left parenthesis xy plus yz plus zx right parenthesis
    139 Views
    Answer
    Advertisement
    Advertisement
    Zigya App

    119.

    Prove that
    open vertical bar table row cell straight a cubed plus 1 end cell cell space space space straight a squared end cell cell space space straight a end cell row cell straight b cubed plus 1 end cell cell space straight b squared end cell cell space space straight b end cell row cell straight c cubed plus 1 end cell cell straight c squared end cell cell space straight c end cell end table close vertical bar space equals space minus left parenthesis straight a minus straight b right parenthesis thin space left parenthesis straight b minus straight c right parenthesis thin space left parenthesis straight c minus straight a right parenthesis thin space left parenthesis straight a space straight b space straight c space plus space 1 right parenthesis.

    Let space increment space equals space open vertical bar table row cell straight a cubed plus 1 end cell cell space space straight a squared end cell cell space space straight a end cell row cell straight b cubed plus 1 end cell cell space space straight b squared end cell cell space straight b end cell row cell straight c cubed plus 1 end cell cell space straight c squared end cell cell space space straight c end cell end table to the power of blank close vertical bar space equals space open vertical bar table row cell straight a cubed end cell cell space space straight a squared end cell cell space straight a end cell row cell straight b cubed end cell cell space straight b squared end cell straight b row cell straight c cubed end cell cell space straight c squared end cell straight c end table close vertical bar space plus space open vertical bar table row 1 cell space space straight a squared end cell cell space space straight a end cell row 1 cell space straight b squared end cell cell space space straight b end cell row 1 cell space straight c squared end cell cell space space straight c end cell end table close vertical bar space space space space space equals negative open vertical bar table row straight a cell space space straight a squared end cell cell space straight a cubed end cell row straight b cell space straight b squared end cell cell space straight b cubed end cell row straight c cell space straight c squared end cell cell space straight c cubed end cell end table close vertical bar minus 1 open vertical bar table row 1 cell space space straight a end cell cell space space straight a squared end cell row 1 cell space straight b end cell cell space space straight b squared end cell row 1 cell space space straight c end cell cell space space straight c squared end cell end table close vertical bar space space space space equals negative abc space open vertical bar table row 1 cell space straight a end cell cell space straight a squared end cell row 1 cell space straight b end cell cell space straight b squared end cell row 1 cell space straight c end cell cell space straight c squared end cell end table close vertical bar minus open vertical bar table row 1 cell space straight a end cell cell space straight a squared end cell row 1 cell space straight b end cell cell space straight b squared end cell row 1 cell space straight c end cell cell space straight c squared end cell end table close vertical bar space equals space minus left parenthesis abc plus 1 right parenthesis space open vertical bar table row 1 cell space straight a end cell cell space straight a squared end cell row 1 cell space straight b end cell cell space straight b squared end cell row 1 cell space straight c end cell cell space straight c squared end cell end table close vertical bar equals negative left parenthesis abc plus 1 right parenthesis space open vertical bar table row 1 cell space space straight a end cell cell space space space straight a squared end cell row 0 cell space space straight b minus straight a end cell cell space space space space straight b squared minus straight a squared end cell row 0 cell space space straight c minus straight a end cell cell space space space straight c squared minus straight a squared end cell end table close vertical bar comma space by space straight R subscript 2 minus straight R subscript 1 comma space straight R subscript 3 minus straight R subscript 1 equals space minus left parenthesis abc plus 1 right parenthesis thin space open vertical bar table row cell straight b minus straight a end cell cell space space space space space straight b squared minus straight a squared end cell row cell straight c minus straight a end cell cell straight c squared minus straight a squared end cell end table close vertical bar equals space minus left parenthesis abc plus 1 right parenthesis thin space left parenthesis straight b minus straight a right parenthesis thin space left parenthesis straight c minus straight a right parenthesis thin space open vertical bar table row 1 cell space space space space space space straight b plus straight a end cell row 1 cell space space space space space space straight c plus straight a end cell end table close vertical bar equals space minus left parenthesis abc plus 1 right parenthesis thin space left parenthesis straight b minus straight a right parenthesis thin space left parenthesis straight c minus straight a right parenthesis thin space left parenthesis straight c plus straight a minus straight b minus straight a right parenthesis equals negative left parenthesis abc plus 1 right parenthesis thin space left parenthesis straight b minus straight a right parenthesis thin space left parenthesis straight c minus straight a right parenthesis thin space left parenthesis straight c minus straight b right parenthesis equals negative left parenthesis straight a minus straight b right parenthesis thin space left parenthesis straight b minus straight c right parenthesis thin space left parenthesis straight c minus straight a right parenthesis thin space left parenthesis abc plus 1 right parenthesis therefore space space space space space space open vertical bar table row cell straight a cubed plus 1 end cell cell space space space straight a squared end cell cell space space straight a end cell row cell straight b cubed plus 1 end cell cell space straight b squared end cell cell space straight b end cell row cell straight c cubed plus 1 end cell cell space straight c squared end cell cell space straight c end cell end table close vertical bar space equals space minus left parenthesis straight a minus straight b right parenthesis thin space left parenthesis straight b minus straight c right parenthesis thin space left parenthesis straight c minus straight a right parenthesis thin space left parenthesis abc plus 1 right parenthesis
    72 Views
  • Switch Icon Switch
    • Advertisement

    Multiple Choice QuestionsShort Answer Type

    120. If x = – 9 is a root of
    open vertical bar table row straight x cell space space 3 end cell cell space space 7 end cell row 2 cell space space straight x end cell cell space space 2 end cell row 7 cell space 6 end cell cell space straight x end cell end table close vertical bar space equals 0 comma
    find the other roots.
    71 Views
    Answer
    Advertisement
    Flag Popup Icon
    Flag it
    Submit
    Flag Popup Icon
    Switch to
    flexipad
    Share It Icon
    Share it
    Share It
    Share it