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October 27, 2017
TIFR 2014 Problem 13 Solution - Supremum of Function

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 […]

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October 26, 2017
TIFR 2014 Problem 12 Solution - Mapping Properties

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 […]

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October 25, 2017
Variation of Specific Heat

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 […]

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October 25, 2017
TIFR 2014 Problem 11 Solution - Nilpotent Matrix Eigenvalues

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 […]

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October 24, 2017
Theory of Equation (TIFR 2014 problem 10)

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 […]

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October 23, 2017
Light through Prisms (KVPY '10)

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, […]

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October 23, 2017
Velocity of Efflux at The Bottom of A Tank

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 […]

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October 23, 2017
TIFR 2014 Problem 9 Solution - Eigenvalues of Rotation

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 […]

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October 23, 2017
TIFR 2014 Problem 8 Solution -Checking one-one/onto-ness

TIFR 2014 Problem 8 Solution has been written for TIFR entrance preparation series. A problem on function from real analysis.

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October 22, 2017
Power Consumption of Electric Heater (KVPY '10)

Let's discuss a problem and know how to find the power consumption of electric heater. Try the problem and read the solution here. The Problem: An electric heater coonsists of a nichrome coil and under (220V) consuming (1KW) power. Part of its coil burned out and it was reconnected after cutting off the burnt portion. […]

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