**Biochemistry**

Given that the selectivity filter is lined with carbonyl oxygens, how might K^{+} channel allow K^{+} through but not Na^{+} when Na^{+} is smaller?

**Chemistry**

List the following in increasing order of basicity: ammonia, water, ethylamine

**Computer Sciences**

You are in a room where everyone including you has a white hat and black hat put on their heads. can you guess the color of your hat with more than 50% probability?

**Classics**

To what extent can you justify heroism in the Iliad?

**Engineering**

How long would it take to pump water out of a cellar 2m and floor space 25m^{2}?

**Economics**

There are 8 coins to be divided between A and B. A first makes an offer of how to divide the
8 coins between them. If B refuses A’s offer, then now it is B’s turn to make the offer, but
this time 4 coins are taken away so that only 4 coins can be divided between them. Again, if
A refuses B’s offer then now A can make an offer again, but again the stake is halved to two
coins. Once a single coin remains, whoever makes the offer takes the coin. What offer should
A make at the beginning? (assuming B is rational, and A knows that B is rational)

**Geography**

Does ivy growth protect or destroy walls?

**Law**

If the punishment for parking on double yellow lines were death, and therefore nobody
did it, would that be a just and effective law?

**Maths**

(i) State the triangle inequality in a triangle with lengths of sides a, b, c.

(ii) Derive relations between the lengths of its 4 sides and 2 diagonals using the triangle
inequality.

**Materials Sciences**

Find the area of a solar panel, that can allow a person to take shower for 24-hours (never stop).

**Natural Sciences (biological)**

There are two lab mice where one is brown and the other is yellow. Given that both of them are pure breed mice, how can you know the allele for brown color mice is recessive or dominant?

**Medicine**

How would pregnancy affect the speed of metabolism of the drugs? Where are drugs metabolised? Where are they excreted? How might you compensate for the change in metabolism of drugs in pregnant women?

**Philosophy**

If the probability of winning a lottery is low but someone still wins and the probability of sun not rising tomorrow is also low, can we assume that the sun will not rise tomorrow?

**Physics**

A ball bearing is flying through space (vacuum and no overall gravitational field).
It heads towards a doughnut, through its centre and out the other side. Draw graphs of
1) speed vs time and 2) acceleration vs time