TIFR 2014 Problem 14 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 based on Doppler Effect where we find the tone of the whistle and speed of the Train. First, do it yourself and then read the solution. The Problem: Doppler Effect A train passes through a station with constant speed. A stationary observer at the station platform measures the tone of the train […]
TIFR 2014 Problem 13 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 12 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 […]
In this post, let's learn about variation of specific heat by finding out the difference between mean specific heat and specific heat at midpoint. The Problem: The variation of the specific heat of a substance is given by the expression $$ C=A+BT^2$$ where (A) and (B) are constants and (T) is the Celsius temperature. Find […]
TIFR 2014 Problem 11 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 […]
Question: Let (C \subset \mathbb{ZxZ} ) be the set of integer pairs ((a,b)) for which the three complex roots (r_1,r_2,r_3) of the polynomial (p(x)=x^3-2x^2+ax-b) satisfy (r_1^3+r_2^3+r_3^3=0). Then the cardinality of (C) is A. (\infty) B. 0 C. 1 D. (1<|C|<\infty) Discussion: We have (r_1+r_2+r_3=-(-2)=2) (r_1r_2+r_2r_3+r_3r_1=a) and (r_1r_2r_3=-(-b)=b) Also, of the top of our head, we […]
Let's discuss a problem based on light through prisms from Kishore Vaigyanik Protsahan Yojana, KVPY 2010. Try it and then check your solution. The Problem: Light through Prisms White light is split into a spectrum by a prism and it is seen on a screen. If we put another identical inverted prism behind in contact, […]
Let's discuss a problem based on the velocity of efflux at the bottom of a tank. Try the problem yourself and read the solution here. The Problem: A large tank is filled with water. The total pressure at the bottom is (3.0atm). If a small hole is punched at the bottom, what is the velocity […]
TIFR 2014 Problem 9 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 […]