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Let's learn to check injectivity with the help a problem from TIFR 2013 problem 36. Try it yourself first, then read the solution here.

Find the flux through a spherical Gaussian surface of radius (a=1m) surrounding a charge of (8.85pC). Solution: The value of (\epsilon_0=8.85*10^{-12}) The flux through the Gaussian surface is the charge (Q) located inside the surface. Therefore, $$ \Phi=\frac{Q}{\epsilon_0}$$ $$=8.8510^{-12}/8.8510^{-12}$$ $$=1Nm^2/C$$

Let's discuss a problem based on Ceva's Theorem from Regional Mathematics Olympiad, RMO, 2002, Problem 1. Watch, learn and enjoy.

Let's discuss a problem where we will find the charge of the sphere with the help of the three charged spheres problem. Try before reading the solution. The Problem: Consider three concentric metallic spheres \(A\), \(B\) and \(C\) of radii of \(a\), \(b\), \(c\) respectively where a<b<c . \(A\) and \(B\) are connected whereas C […]

Let's discuss a problem and find out whether a sequence is bounded or unbounded from TIFR 2013 Problem no. 35. Try before reading the solution.

TIFR 2013 Problem 34 Solution has been written for TIFR entrance preparation series. A problem on countability of sequence from Real analysis.

Two equal masses are connected by a spring satisfying Hooke's law. The spring is elongated a little and allowed to let go.. Let the angular frequency of oscillations be \(\omega\). Now one mass stopped. What is the square of the new frequency? Discussion: $$ \mu=\frac{m}{2}$$ $$ \omega^2=k/\mu=2k/m$$ When one block is stopped $$ \omega_1^2=k/m=\omega^2/2$$ Useful […]

TIFR 2013 Problem 32 Solution has been written for TIFR entrance preparation series. A problem on limit of a sequence from real analysis.

Let's discuss a problem from TIFR 2013 Problem 31 based on inequality. Try this problem yourself, then read the solution.

Let's discuss a problem where we find the stable equilibrium point, useful for Physics Olympiad. Try it yourself before reading the solution.