If ⊗ is an operation such that a ⊗ b = 2a when a > b, a + b when a < b, a² when a = b, then $$\left[ {\frac{{\left( {5 \otimes 7} \right) + \left( {4 \otimes 4} \right)}}{{3\left( {5 \otimes 5} \right) - \left( {15 \otimes 11} \right) - 3}}} \right]$$     is equal to?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Given, }}a \otimes b = 2a{\text{ }} \cr & {\text{Where }}a > b \cr & a \otimes b = a + b \cr & {\text{Where }}a < b \cr & a \otimes b = {a^2} \cr & {\text{Where }}a = b \cr & \frac{{\left( {5 \otimes 7} \right) + \left( {4 \otimes 4} \right)}}{{3\left( {5 \otimes 5} \right) - \left( {15 \otimes 11} \right) - 3}}{\text{ }} \cr & {\text{ = }}\frac{{\left( {5 + 7} \right) + {{\left( 4 \right)}^2}}}{{3{{\left( 5 \right)}^2} - \left( {2 \times 15} \right) - 3}} \cr & {\text{ = }}\frac{{12 + 16}}{{75 - 30 - 3}} \cr & {\text{ = }}\frac{{28}}{{42}} \cr & {\text{ = }}\frac{2}{3} \cr} $$