1.

There are three teams x,x+1 and y childrens and total number of childrens in the teams is 24. if two childrens of the same team do not fight, thenA. maximum number of fights is 190B. maximum number of fights is 191C. maximum number of fights occur when x=7D. maximum number of fights occur when x=8

Answer» Correct Answer - B::C::D
`becausex+x+1+y=24`
`impliesy=23-2x`
Let N=Total number of fights subject to the condition that any two children of one tem do not fight.
`thereforeN=2.^(24)C_(2)-(.^(x)C_(2)+.^(x+1)C_(2)+.^(y)C_(2))`
`=.^(24)C_(2)-(.^(x)C_(2)+.^(x+1)C_(2)+.^(23-2x)C_(2))`
`=23-3x^(2)+45x`
`therefore(dN)/(dx)=0-6x+45`
for maximum or minimum, put `(dN)/(dx)=0impliex=7.5`
`impliesx=7" "[because x in I]`
Now, `(d^(2)N)/(dx^(2)) lt0`
`therefore` N will be maximum when x=7
and N=23-`3(7)^(2)+45xx7=191`


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