In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is 1/4^th of the number of students who like other branches. The number of students who like both their core and other branches is 500.

The number of students who like their core branches is

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

Consider the following sample of numbers:

9, 18, 11, 14, 15, 17, 10, 69, 11, 13

The median of the sample is