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NTSE Sample Paper NTSE SAT Practice Test-11

  • question_answer
    It is given that px - qy = a; qx + py = b and \[{{x}^{2}}+{{y}^{2}}=1\] The value of\[({{p}^{2}}+{{q}^{2}})\]is

    A) ab(,a+b)          

    B)        \[{{a}^{2}}+{{b}^{2}}\]

    C) \[\frac{{{a}^{3}}+{{b}^{3}}}{ab}\]                         

    D) none of these

    Correct Answer: B

    Solution :

    [b] \[{{(px-qy)}^{2}}+{{\left( qx+py \right)}^{2}}=\text{ }{{a}^{2}}+{{b}^{2}}\] \[\Rightarrow \left( {{p}^{2}}+{{q}^{2}} \right)\left( {{x}^{2}}+{{y}^{2}} \right)={{a}^{2}}+{{b}^{2}}\] \[\Rightarrow {{p}^{2}}+{{q}^{2}}={{a}^{2}}+{{b}^{2}}.\]


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