Try this problem from TIFR 2013 problem 9 based on the existence of an element of order 51. You may use sequential hints if required.
Try this problem from TIFR 2013 problem 9 based on the existence of an element of order 51. You may use sequential hints if required.
TIFR 2013 Problem 10 Solutions is a part of TIFR entrance preparation series. The Tata Institute of Fundamental Research is India's premier institution for advanced research in Mathematics. The Institute runs a graduate programme leading to the award of Ph.D., Integrated M.Sc.-Ph.D. as well as M.Sc. degree in certain subjects. The image is a front […]
Let's discuss a problem, useful for Physics Olympiad based on A Pulley System. Read the problem carefully, find it yourself and then read the solution.
Try this problem from TIFR 2013 problem 7 based on Eigenvectors of Similar Matrices. Question: TIFR 2013 problem 7 True/False? If \(A\) and \(B\) are similar matrices then every eigenvector of \(A\) is an eigenvector of \(B\). Hint: What does similar matrices mean? Discussion: There exists an invertible (change of basis) matrix \(P\) such that […]
Let's discuss a problem useful from Physics Olympiad based on Instantaneous Velocity and Acceleration. The Problem: Let (\vec{v}) and (\vec{a}) be instantaneous velocity and the acceleration respectively of a particle moving in a plane. The rate of change of speed (dv/dt) of the particle is: (a) (|a|) (b) ((v.a)/|v|) (c) the component of (\vec{a}) in the […]
TIFR 2013 Problem 2 Solutions is a part of TIFR entrance preparation series. The Tata Institute of Fundamental Research is India's premier institution for advanced research in Mathematics. The Institute runs a graduate programme leading to the award of Ph.D., Integrated M.Sc.-Ph.D. as well as M.Sc. degree in certain subjects. The image is a front […]
Let's discuss a problem useful for Physics Olympiad based on Dimensional Analysis. The Problem: Dimensional Analysis Consider an expression F=Ax(sin^{-1} (Bt)) where F represents force, x represents distance and t represents time. Dimensionally the quantity AB represents (A) energy (B) surface tension (C) intensity of light (D) pressure Solution: The quantity Ax on RHS must […]
TIFR 2013 Problem 8 Solution is a part of TIFR entrance preparation series. The Tata Institute of Fundamental Research is India's premier institution for advanced research in Mathematics. The Institute runs a graduate programme leading to the award of Ph.D., Integrated M.Sc.-Ph.D. as well as M.Sc. degree in certain subjects. The image is a front […]
Try this problem from TIFR 2013 problem 4 based on Lower bound of roots. Question: TIFR 2013 problem 4 True/False: The equation \(x^3 + 10x^2 − 100x + 1729 = 0\) has at least one complex root α such that |α| > 12. Hint: What happens if \(|\alpha| \le 12\) for all roots \(\alpha?\) Discussion: Let […]
Let's discuss a beautiful Problem, useful for Physics Olympiad based on Force on a Wooden Cube. The Problem: Force on a Wooden Cube A wooden cube is placed on a rough horizontal table. A force is applied to the cube. Gradually the force is increased. Whether the cube slides before toppling or topples before sliding […]