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Directions : In these questions, two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answer.                [NICL (AO) 2014]

I. \[40{{x}^{2}}-47x+12=0\]

II. \[5{{y}^{2}}-51y+54=0\]

A) If \[x\le y\]

B) lf \[x<y\]

C) If \[x>y\]

D) If relationship between x and y cannot be established

E) lf \[x\ge y\]

Correct Answer: B

Solution :

I. \[40{{x}^{2}}-47x+12=0\]

By splitting the middle term,

\[40{{x}^{2}}-32x+15x+12=0\]

\[8x\,(5x-4)-3\,(5x-4)=0\]

\[(8x-3)(5x-4)=0\,\,\Rightarrow \,\,x=\frac{3}{8},\]\[\frac{4}{5}\]

II. \[5{{y}^{2}}-51y+54=0\]

By splitting the middle term,

\[5{{y}^{2}}-45y-6y+54=0\]

\[5y\,(y-9)-6\,(y-9)=0\]

\[(5y-6)(y-9)=0\,\,\Rightarrow \,\,y=\frac{6}{5},\]9

Hence, \[y>x\]