## OKSBRIDŽO INTERVIU KLAUSIMAI

Šiame puslapyje gali matyti klausimus, surinktus iš Academic Buddy Oksbridžo etapo buvusių moksleivių, dalyvavusių interviu. Daugiau klausimų gali rasti Oksfordo puslapyje, inžinerijos interviu portale, Suomijos fizikos olimpiadinių klausimų portale ir Kembridžo fizikos dėstytojos puslapyje.

**PPE**

- What is forgiveness?
- Define populism. What differences are there between left-wing and right-wing populism?
- Examine the graph (GDP per capita – Measure of democracy). Summarize the graph. What do you think might be the reasons behind these findings?

**PHILOSOPHY**

- Sorites paradox. Say, 1,000,000 grains of sand is a pile. Subtract a grain from any pile, and we still have a pile. However, it follows then that one grain of sand is, too, a pile, if we keep subracting one grain after another until we reach the last one. This is clearly absurd. Where is the problem? How do we avoid absurdities?
- You are offered a million dollars to intend to drink a glass of poison that kills you. You should intend to drink the poison at noon but you would drink it only at midnight. So you get the money if you intend at noon to drink the poison at midnight. Can you collect the money?
- Do you think that other people have minds? How can you prove/give arguments for the idea? How do you know that I have a mind?
- You are offered a million dollars to intend to believe that it is dark in this room now. Can you collect the money?
- Isn’t Philosophy a waste of money because there are no applications?

**ECONOMICS, ECONOMICS & MANAGEMENT**

- You’re a manager of a hospital which is going bankrupt. What will you do?
- There’s a floating sphere in front of you at your eye level. It’s moving in a circle, which is parallel to the ground. Describe how the sphere will appear to you as it moves. How does the speed and the size of the sphere change?
- Draw the function f(x) = x^2 and draw f'(x).
- How much money would I have after three years, if I put 100 pounds into the bank that offers 1,3% yearly cumulative interest rate?
- Draw the demand and supply curves.

**NATURAL SCIENCES**

- Analyze the results of a given electrophoresis.
- DNA sequencing using the bacteria plasmid.
- Decribe the evolutionary processes a whale has undergone.
- How was the backbone formed through evolution?
- Given an atomic model of 4,5-epoxy-pentanethiol you are asked to identify atoms and bonds represented by (standard coloured) balls and sticks. Then, you are asked to draw it on a sheet of paper. If you have drawn it differently, you are explained skeletal representation of molecules and then referring to the atomic model you are encouraged to redraw it in skeletal representation. Then you are asked to draw a reaction product of this molecule in basic aqueous solution. You have to draw an arrow mechanism (if you are not familiar, you are explained the notation representing the movement of electrons, and asked to try). Then you need to identify any alternative reaction products of the reaction.
- In Cambridge, you would very likely need a bicycle as it is the most popular means of transportation. We would like you to estimate what is the required pressure in the bicycle tire?
- A standing wave is set up in a tube full of air sealed at one end. Draw the standing wave. What is the frequency of vibration? How would a change in air pressure affect the frequency? If an entire orchestra were playing and helium were pumped into the room, what would the audience hear?
- A yo-yo and a rock are dropped simultaneously. Which one accelerates faster and why?
- Suppose there is a river flowing through a field of grass. You need to get from the point A to the point B which is on the opposite bank of the river. Suppose that your movement speeds in the field and in water are u and v (with u>v). Sketch how one should move in this setting in order to get from A to B as quickly as possible (you can assume that movement of water does not affect your performance). Note: geometric optics could be handy!

**COMPUTER SCIENCE**

- Prove that, given any sequence of n integers (not necessarily distinct) a
_{1}, a_{2}, . . . , a_{n}, there is some non-empty segment whose elements sum to a multiple of n, i.e. Σ^{p}_{i=q}a_{i}≡ 0 (mod n) for some q and p satisfying 1 ≤ q ≤ p ≤ n. - Alice has four cards. Each card has a letter on one side and a number on the other side. Bob claims that “if a card has a vowel on it, it has an even number on the other side”. Cards are lying on a table, and Alice can see only their sides facing her which reads “E 2 K 7”. Which of the cards must be turned around to verify Bob’s statement?
- You are given the following function

function f(unsigned int n)*{*

if(n == 0) return 1;

return f(n – 1) + 2 * (n + 1) – 1;

}

Can you rewrite it without using recursion? ((n + 1)^2, solve recurrence by guessing and verifying using induction) - Given 25 horses, find the best 3 horses with a minimum number of races. Each race can have only 5 horses. You don’t have a timer. Now the challenge is how we can do it in 7 races.
- You are given 13 balls. All of them have equal weight, except one. The odd ball may be either heavier or lighter. Find out the odd ball in 3 weightings.

**MATHEMATICS**

- Draw the graph for 1/xln(x).
- The sum of the numbers is 100. What is their largest product?
- The perimeter of a cut out of a box is 40. What is its maximum volume?
- What is the largest integral in the interval from 0 to pi/2? ((1) x/sqrt(1+x); (2) sin(x)/sqrt(1+sin(x)); (3) sin(x)/sqrt(1+x)).
- Will the number 2019 be even in the Fibonacci sequence? Prove through induction.
- We have a stick of length 1. We break it at two random points. What is the probability that from the resulting 3 little sticks it will be possible to form a triangle?
- Prove that 4^x – 2^(x+1) + 1 >= 0.
- Solve e^(x^2) = x.
- How many solutions (in positive integers) does the equation x^3 + 6x^2y + 12xy^2 + 8y^3 = 2^(30) have?
- What is the sign of ln(ln(3))?

**MEDICINE**

- What happens during the process of inflammation? What hormone plays a key role in this process? Why does inflammation happen?
- (Requires props) I have this pack of jellybeans. How many packs should I buy in order to acquire a mole of jellybeans? (Follow up upon the realization that that’s too many packs). Ok, I want to have a mole of glucose within these jellybeans – how many packs then?
- Should we legalize euthanasia?
- Organ donation: should it be opt-in or opt-out?
- You see a person lying in the middle of the street, what do you do?
- You see a woman crying at a bus stop, what do you do?
- Walk me through medical training in the UK. What happens after med school?
- Imagine that you’re already a certified doctor and you make a mistake that affects your patient’s health and well-being. What do you do? How do you manage the situation?