I have pdf solutions for three good maths problems. I'll post the problems now, and the pdfs some days later. The source of these problems might be brilliant, but I'm not sure of this. They are a bit beyond JEE, but they're doable with a day of effort :).
I'll post more hints as time goes by.
I'll post more hints as time goes by.
- If F is a degree 8 function such that F(i) = 2^i for i in {0,1,2,...,8}, then find F(9).
- Given n+1 points, there is a unique function of degree n that passes through them.
- Can you construct F? Try to think of F as a sum of 9 degree 8 functions.
- How can a circle cut the graph of ln(x) at 4 points? You don't need to find a circle which does the job, just say something interesting.
- Show that if F is a bijective function from natural numbers to natural numbers, then there exist a and d such that F(a) < F(a+d) < F(a+2d).
- Can you prove that there exist a and d such that F(a) < F(a+d)?
- Can you construct a bijection, F, where F(a) < F(a+d) < F(a+2d) < F(a+3d) is impossible for all pairs of a and d?
1) 511.
ReplyDelete2) Consider a circle with huge radius touching y = ln(x) at two points internally once in first quad. and again in 4th quad. , now stretch this circle to see a circle intersecting y = ln(x) at 4 points.
1) 511.
ReplyDelete2) Consider a circle with huge radius touching y = ln(x) at two points internally once in first quad. and again in 4th quad. , now stretch this circle to see a circle intersecting y = ln(x) at 4 points.
Your answer for (1) is correct. For (2), there is an interesting point on the x-axis that you should think about.
ReplyDeleteOk. i couldn't find such a point , please tell about it. , But qualitatively, i could draw such a circle
ReplyDeletebhaiya please post some new physics problems
ReplyDeletewaiting for them for a long time