CAT (QA) PYQs

If $\log (2^a \times 3^b \times 5^c)$ is the arithmetic mean of $\log (2^2 \times 3^3 \times 5)$, $\log (2^6 \times 3 \times 5^7)$, and $\log (2 \times 3^2 \times 5^4)$, then a equals

The real root of the equation $2^{6x} + 2^{3x+2} - 21 = 0$ is

If a, b and c are positive real numbers such that $a > 10 \ge b \ge c$ and $\frac{\log_8(a+b)}{\log_2 c} + \frac{\log_{27}(a - b)}{\log_3 c} = \frac{2}{3}$, then the greatest possible integer value of a is