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Question

The number of integral solutions of x+y+z=0 with x5,y5,z5 is

A
134
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B
136
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C
138
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D
140
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Solution

The correct option is C 136
Let x=p5,y=q5 and z=r5, where p,q,r0.
Then the given equation reduces to p+q+r=15(1)
Now, we have to find non-negative integral solution of Eq. (1).
The total number of such solutions is 15+31C31= 17C2=136.

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