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In a ` A B C ,A-=(alpha,beta),B-=(1,2),C-=(2,3),`point `A`lies on the line `y=2x+3,`where `alpha,beta`are integers, and the area of the triangle is `S`such that `[S]=2`where `[`.`]`denotes the greatest integer function. Then the possible coordinates of `A`can be`(-7,-11)`(b) `(-6,-9)``(2,7)`(d) `(3,9)`A. `(alpha)/(beta)=3/7`B. `3alpha beta=14`C. `2alpha+3beta=18`D. `alpha+6beta=30` |
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Answer» Correct Answer - A::C::D Clearly `R(alpha,beta)` is centroid of `DeltaABC`s `:.R(alpha,beta)=((3+1+2)/3,(9+2+3)/3)=(2,14/3)` `impliesalpha=2` and `beta=14/3` Hence `2alpha+3beta=18` |
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