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These are some questions . Attempt them and post your solution or part of the solution that you tried to do. I need it by today. PLEASE. Be quick.
1) Show that for any point in time (considering the problems in 3-D), there always exists a pair diametrically opposite points, say P1 and P2 on the surface of a sphere (say earth) such that the temmperature and the atmospheric pressure of both points is the same for any point in time.
2) A PxQxR rectangular solid is made by gluing together 1x1x1 cubes. How many 1x1x1 cubes will an internal diagonal of this solid pass through. Generalize for higher dimensions.
3) How many ways are there to distribute n chocolates among m mathematicians, given that each mathematician gets atleast 10 chocolates.
4) Given n points in the plane. We draw all possible triangles whose vertices are any three of the given points. Atleast how many of them are obtuse-angled triangles. (The highest answer should be considered the best, but not without a proof)
5) In how many ways can a 100 rupees bill be changed into 1,2 and 3 rupees.
6)Count the number of matrices whose entries only consists of 0's and 1's such that determinant is non-zero.
1) Show that for any point in time (considering the problems in 3-D), there always exists a pair diametrically opposite points, say P1 and P2 on the surface of a sphere (say earth) such that the temmperature and the atmospheric pressure of both points is the same for any point in time.
2) A PxQxR rectangular solid is made by gluing together 1x1x1 cubes. How many 1x1x1 cubes will an internal diagonal of this solid pass through. Generalize for higher dimensions.
3) How many ways are there to distribute n chocolates among m mathematicians, given that each mathematician gets atleast 10 chocolates.
4) Given n points in the plane. We draw all possible triangles whose vertices are any three of the given points. Atleast how many of them are obtuse-angled triangles. (The highest answer should be considered the best, but not without a proof)
5) In how many ways can a 100 rupees bill be changed into 1,2 and 3 rupees.
6)Count the number of matrices whose entries only consists of 0's and 1's such that determinant is non-zero.
