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SSC Sample Paper SSC CGL - Sample Paper-15

  • question_answer
    If \[{{a}^{2}}+{{b}^{2}}=2\] and \[{{c}^{2}}+{{d}^{2}}=1,\] then the value of \[{{(ad-bc)}^{2}}+{{(ac+bd)}^{2}}\] is

    A) \[\frac{4}{9}\]                          

    B) \[\frac{1}{2}\]

    C) 1                                 

    D) 2

    Correct Answer: D

    Solution :

    \[{{(ad-bc)}^{2}}+{{(ac+bd)}^{2}}\] \[={{a}^{2}}{{d}^{2}}+{{b}^{2}}{{c}^{2}}-2abcd+{{a}^{2}}{{c}^{2}}+{{b}^{2}}{{d}^{2}}-2abcd\] \[={{a}^{2}}{{b}^{2}}+{{b}^{2}}{{c}^{2}}+{{a}^{2}}{{c}^{2}}+{{b}^{2}}{{d}^{2}}\] \[={{a}^{2}}{{d}^{2}}+{{b}^{2}}{{d}^{2}}+{{b}^{2}}{{c}^{2}}+{{a}^{2}}{{c}^{2}}\] \[={{d}^{2}}({{a}^{2}}+{{b}^{2}})+{{c}^{2}}({{b}^{2}}+{{a}^{2}})\] \[=({{a}^{2}}+{{b}^{2}})({{c}^{2}}+{{d}^{2}})\] \[=2\times 1=2\]


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