Claim: If G has no subgroups H /= (e), G, then G must be cyclic of prime order. Proof: One Line Proof: If the order of G is composite, then it has Sylow Subgroups. More than one Line Proof: If the order of G is composite then there exists d that divides |G| and 1 < d < |G|. […]
TIFR 2015 Problem 3 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 […]
TIFR 2015 Problem 2 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 […]
Sine of an angle, half chord and vertical projection Note that half chord corresponding to a half arc is same as the magnitude of vertical projection.
When a gas expands adiabatically, its volume is doubled while its absolute temperature is decreased by a factor (1.32). Compute the number of degrees of freedom for the gas molecules. Solution: The number of degrees can be found from the relation $$ f=\frac{2}{\gamma-1}$$ We can find (\gamma) from the adiabatic relation,$$ T_2V_2^{\gamma-1}= T_1V_1^{\gamma-1} $$ $$( […]
TIFR 2015 Problem 1 Solution has been written for TIFR entrace preparation series. A problem on Linear Algebra using the idea of linear transformation.
Here is a problem where we need to calculate the efficiency of heat engine and work done by it. Let's see how we can solve it.
TIFR 2014 Problem 23 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 […]
TIFR 2014 Problem 30 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 […]