Means — CAT Previous-Year Questions

For some positive and distinct real numbers x, y and z if $\frac{1}{\sqrt{\mathrm{y}}+\sqrt{\mathrm{z}}}$ is the arithmetic mean of $\frac{1}{\sqrt{\mathrm{x}}+\sqrt{\mathrm{z}}}$ and $\frac{1}{\sqrt{\mathrm{x}}+\sqrt{y}}$, then the relationship which will always hold true, is?

The arithmetic mean of x, y and z is 80, and that of x, y, z, u and v is 75, where u = (x + y)/2 and v = (y + z)/2. If x ≥ z, then the minimum possible value of x is

Suppose, log₃x = log₁₂y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log₆G is equal to:

If log (2^a × 3^b × 5^c) is the arithmetic mean of log (2² × 3³ × 5), log (2⁶ × 3 × 5⁷), and log (2 × 3² × 5⁴), then a equals

If the product of n positive real numbers is unity, then their sum is necessarily