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Number of positive unequal integral solutions of the equation `x+y+z=12` isA. 21B. 42C. 63D. 84 |
Answer» Correct Answer - B We have, x+y+z=12 Assume `x lt y lt z`. Here, `x,y,z ge1` `therefore`Solutions of Eq. (i) are `(1,2,9),(1,3,8),(1,4,7),(1,5,6),(2,3,7),(2,4,6) and (3,4,5)`. Number of positive integral solutions of Eq. (i)=7 but x,y,z can be arranged in 3!=6 Hence, required number of solutions`=7xx6=42`. |
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