The average marks obtained by a class in an examination were calculated as 30.8 . However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 24 instead of 42 . After correcting the marks, the average becomes 31.4. How many students does the class have?

Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. They also decide to work independently. After trying all possible combinations of elements, they conclude that the spell does not work.

How many attempts does each wizard make before coming to this conclusion, independently?

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