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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
If $x,y$ are real numbers such that
$2^{x+\frac{1}{2}}\times 4^{y-\frac{5}{6}}=3^{x-\frac{1}{2}}\times 9^{y-\frac{1}{3}}$ then which of the following is true?
Solution
$2^{x+\frac{1}{2}}\times 4^{y-\frac{5}{6}}=3^{x-\frac{1}{2}}\times 9^{y-\frac{1}{3}}$Convert powers:
$4=2^2,\quad 9=3^2$
$2^{x+\frac{1}{2}}\times 2^{2y-\frac{5}{3}}=3^{x-\frac{1}{2}}\times 3^{2y-\frac{2}{3}}$
$2^{x+2y-\frac{7}{6}}=3^{x+2y-\frac{7}{6}}$
Since bases are different,
$x+2y-\frac{7}{6}=0$
$6x+12y-7=0$
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