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KVPY Sample Paper KVPY Stream-SX Model Paper-4

  • question_answer
    If min. \[\{{{x}^{2}}(a-b)\,x+1-a-b\}>\] max. \[\{-\,{{x}^{2}}+(a+b)\,x-\text{(1}\,\text{+}\,\text{a}\,\text{+}\,\text{b) }\!\!\}\!\!\text{ }\] then -

    A) \[{{a}^{2}}+{{b}^{2}}<2\]             

    B) \[{{a}^{2}}+{{b}^{2}}<4\]

    C) \[{{a}^{2}}+{{b}^{2}}>4\]             

    D) \[a+b>ab\]

    Correct Answer: B

    Solution :

    [B] Apply\[-\frac{{{(a-b)}^{2}}-\,4\,\,(1-a-b)}{4}>\frac{{{(a+b)}^{2}}-\,4\,\,(1+a+b)}{4}\] \[{{a}^{2}}+{{b}^{2}}<4\]


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