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.You need to login to perform this action.
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