For positive non-zero real variables $x$ and $y$, if

$\ln \left( \frac{x + y}{2} \right) = \frac{1}{2} [ \ln (x) + \ln (y) ]$

then, the value of $\frac{x}{y} + \frac{y}{x}$ is

In the sequence 6, 9, 14, $x$, 30, 41, a possible value of $x$ is

Sequence the following sentences in a coherent passage.

P: This fortuitous geological event generated a colossal amount of energy and heat that resulted in the rocks rising to an average height of 4 km across the contact zone.

Q: Thus, the geophysicists tend to think of the Himalayas as an active geological event rather than as a static geological feature.

R: The natural process of the cooling of this massive edifice absorbed large quantities of atmospheric carbon dioxide, altering the earth’s atmosphere and making it better suited for life.

S: Many millennia ago, a breakaway chunk of bedrock from the Antarctic Plate collided with the massive Eurasian Plate.

A person sold two different items at the same price. He made 10% profit in one item, and 10% loss in the other item. In selling these two items, the person made a total of