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JEE Main & Advanced Sample Paper JEE Main Sample Paper-22

  • question_answer
    If the equation \[co{{t}^{4}}x-2\,cos\,e{{c}^{2}}x+{{a}^{2}}\text{ }=0\]has at least one solution then, sum of all possible integral values of 'a' is equal to

    A)  4                                

    B)  3

    C)  2                                

    D)  0

    Correct Answer: D

    Solution :

    \[{{\cot }^{4}}x-2(1+{{\cot }^{2}}x)\,+{{a}^{2}}=0\] \[\Rightarrow \,\,{{\cot }^{4}}x-2{{\cot }^{2}}\,x+{{a}^{2}}-2=0\] \[\Rightarrow \,\,{{({{\cot }^{2}}x-1)}^{2}}=3-a\]to have atleast one solution \[3-{{a}^{2}}\ge 0\] \[\Rightarrow \,\,\,{{a}^{2}}-3\le 0\] \[a\in [-\sqrt{3},\,\,\sqrt{3}]\] Integral value -1, 0, 1 \[\therefore \] sum = 0


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