u/NoOven3448

My unique solution for ISI paper UGB question 1 part 2

Question gave a circle (x-a)^(2)+(y-b)^(2)=r^2, where a,b,r are real numbers and 3 points x1,y1 x2,y2 x3,y3 are all rational values lying on this circle. Now, Lets take r^2 as p+q, where p is rational part and q is irrational part.

Assume a and b are irrational

Then x^(2)+y^(2)-2(ax+by)+a^2+b^2=p+q. Now since x^2 and y^2 is rational for 3 given points we can remove it and only equate irrational lhs to rhs

therefore, -2(ax+by)+a^(2)+b^(2)=q. Note that this is exactly what a line equation looks like. We know 3 solutions of this line but also those same 3 solutions also lie on the given circle. This means that the line and circle have 3 points of intersection, which is impossible. Therefore, our assumption that a and b are irrational was incorrect. Similarly can be proven for a is rational and b is irrational and vice versa.

Thank You

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u/NoOven3448 — 12 days ago

  1. Cloth 1 is a tightly wound fabric while cloth 2 is a soft wool-like fabric which has a tone of air gaps. Now, after sweating a little, the water would be absorbed into the air gaps. and since water is a good conductor of heat, it will not provide much heat retention. therefore, cloth 1 would be better now
  2. At equilibrium, when the velocity of all the gas particles is reversed, absolutely nothing happens. this is because at equilibrium, the distribution of velocities is already uniform in all directions. Reversing it would not change this uniformity.
  3. For fridge, It is due to the excess pressure outside. When we open the door, the hot gases outside come inside the fridge, replacing the cold gases. Now after closing, these same gases will drop in pressure as they cool very quickly. hence, the outside higher pressure puts force against the door

I saw another guys comment on this subreddit that all of these answers are wrong, but I dont agree. If you think there is any problem with the logic please let me know

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u/NoOven3448 — 18 days ago
▲ 19 r/BITSAT

this guy next to me took partial drop at bits goa from one of the top courses. Thats crazy bro IIT paglu ig

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u/NoOven3448 — 20 days ago