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JEE Main & Advanced Sample Paper JEE Main Sample Paper-46

  • question_answer
    The coefficient of \[{{x}^{2}}{{y}^{2}}yz{{t}^{2}}\] and \[xyzt\] in the expansion of \[{{(x+y+z+t)}^{4}}\] are in the ratio

    A)  4 : 2 : 1                      

    B)  1 : 2 : 4           

    C)  2 : 4 : 1                      

    D)  1 : 4 : 2

    Correct Answer: B

    Solution :

     Coefficient of \[{{x}^{2}}{{y}^{2}}\] in \[{{(x+y+z+t)}^{4}}\] \[=\frac{4!}{2!\,2!}=6\] Coefficient of \[yz{{t}^{2}}\] in \[{{(x+y+z+t)}^{4}}\] \[=\frac{4!}{1!\,\,1!\,\,2!}=12\] and coefficient of \[xyzt\] in \[{{(x+y+z+t)}^{4}}\] \[=\frac{4!}{1!\,\,1!\,\,1!}=24\] \[\therefore \] Required ratio is 6 : 12 : 24, i.e., 1 : 2 : 4.


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