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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 32

  • question_answer
    Let h(x) be differentiable for all x and let\[f\left( x \right)=\left( kx+{{e}^{x}} \right)h\left( x \right)\], where k is some constant. If \[h\left( 0 \right)=5,\text{ }h'\left( 0 \right)=-2\] and\[f'\left( 0 \right)=18\], then the value of k is -

    A) 5                     

    B)        4

    C) 3         

    D)        2.2

    Correct Answer: C

    Solution :

    [c] \[f(x)=(kx+{{e}^{x}})h(x)\] Diff. \[f'\left( x \right)=\left( kx+{{e}^{x}} \right)h'\left( x \right)+h\left( x \right)\left( k+{{e}^{x}} \right)\] put \[x=0\] \[18=-2+5\left( k+1 \right)\] \[k=3\]             


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