We lost a coding contest yet again. Here's the problem:
A is a set containing 'n' elements. '
In how many ways can 3 non-empty subsets of A be chosen, such that their pairwise intersections are empty?
Note: Pairwise intersections of 3 sets P, Q, R
are : P ^ Q, Q ^ R and R ^ P.
Lessons in Capacitance 2:
Consider 2 long and thin conducting wires of radius 'b' separated by distance 'a'. At one end, they are connected to a voltage 'V', and at the other end to an unknown resistance 'R'. Note that two parallel wires form a capacitor.
Neglect all resistance of the wires and the battery. Neglect gravity.
The long wires are at equilibrium. What is 'R'?
Lessons in Capacitance 1:
A semi-circular dielectric plate is partially sandwiched between two semi-circular metallic plates. The plates are stationary, while the dielectric plate is free to rotate.
The thickness of the dielectric plate is .5mm, which is also the separation between the metallic plates.
The metallic plates are connected to a 20V source.
What is the angular acceleration of the dielectric plate?
легкое достижение
If the electric field is xi`+yj`+zk`, then what is the charge contained in the unit sphere centered at origin?
Note: i`, j`, k` are the unit vectors along x, y, and z respectively.
Note: i`, j`, k` are the unit vectors along x, y, and z respectively.
Pauli
Consider a hypothetical model of an atom, where the energy of the orbital is a function of 2 quantum numbers 'n' and 'm'. 'n' and 'm' can take only positive values. The definition of E(n,m) (energy as a function of n and m is given).
What is the possible number of electrons with energy E??
Note:
1) These 'n' and 'm' are not the 'n' and 'm' that you know.
Awesome:
This is easy, yet awesome. There are 8 faces to the arrangement of large-metallic plates. Write the values of the charges on each of the faces, left to right.
The charges should be comma separated.
P.S:
1)Use the judge for checking your answer.
2)What is the of Sin(nx)*Sin(mx) from 0-2pi. The answer is a function of m and n.
Surface Charge:
A metal plate is moved with a fixed velocity 'V' as shown. There is a magnetic field, magnitude=B pointing downwards.
What is the surface charge density 'Sigma' on the plate?
Lessons in number theory:
1) How many ordered pairs (a,b) of natural numbers have 17640 as their LCM?
2) The set of natural numbers {a1,a2,a3,...,an} is called a partition of 'N' if a1+a2+a3+...+an=N.
Consider all the partitions of N=176. There is a partition with the maximum product among all the partitions.
What's this maximum product?
P.S: don't Google these questions.
2) The set of natural numbers {a1,a2,a3,...,an} is called a partition of 'N' if a1+a2+a3+...+an=N.
Consider all the partitions of N=176. There is a partition with the maximum product among all the partitions.
What's this maximum product?
P.S: don't Google these questions.
Microwave oven:
Do you have a microwave at home? Do you know how it works? If you think you do, then you are wrong.
But you can determine the frequency of your household microwave oven easily. . Can you guess it?
There is another way, which requires some chocolate.
Take a big bar of chocolate, and keep it in your oven for 15 seconds. When you take it out, you'll see that there are some regions which are 'badly' molten (yummy!). The distance between consecutive molten regions is 6cm.
So, whats the frequency?
P.S: you need to switch off the rotation for the microwave for this.
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