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Category Archives: IITJEE Foundation Math IITJEE Main and Advanced Math and RMO/INMO of (TIFR and Homibhabha)
Women in Science 2019 UNESCO Awards to Ingrid Daubechies and Claire Voisin
Theory of Equations: III: IITJEE maths: algebra
may overlap a bit with previous lecture(s)…
Applications of Derivatives: IITJEE Maths tutorial problem set: III
Slightly difficult questions, I hope, but will certainly reinforce core concepts:
 Prove that the segment of the tangent to the curve which is contained between the coordinate axes, is bisected at the point of tangency.
 Find all tangents to the curve for that are parallel to the line .
 Prove that the curves , where and , where is a differentiable function, have common tangents at common points.
 Find the condition that the lines may touch the curve .
 If and are lengths of the perpendiculars from origin on the tangent and normal to the curve respectively, prove that .
 Show that the curve , is symmetrical about xaxis and has no real points for . If the tangent at the point t is inclined at an angle to OX, prove that . If the tangent at meets the curve again at Q, prove that the tangents at P and Q are at right angles.
 A tangent at a point other than on the curve meets the curve again at . The tangent at meets the curve at and so on. Show that the abscissae of form a GP. Also, find the ratio of area .
 Show that the square roots of two successive natural numbers greater than differ by less than .
 Show that the derivative of the function , when , and when vanishes on an infinite set of points of the interval .
 Prove that for .
More later, cheers,
Nalin Pithwa.
How to solve equations: Dr. Vicky Neale: useful for PreRMO or even RMO training
Dr. Neale simply beautifully nudges, gently encourages mathematics olympiad students to learn to think further on their own…
Happy Pie with Pi…
Paul Erdos, Mathematics, Russia and USA:
It is true …universally, including India…
Hats off to the “Intellect of the Wise Mathematicians”, late, adorable professor of mathematics, Paul Erdos.
— humble tribute …from Nalin Pithwa.
Birch and Swinnerton Dyer Conjecture from the inimitable Manjul Bhargava
Some light moments with an IITJEE foundation math student
I have a bright kid working towards his IITJEE Foundation math. Some days back I had suggested to him to solve some hard word problems based on simultaneous equations from a very old classic text. He started on his own, almost with some guidance from me. Until he attacked very well — those “age” kind of problems. Father’s age vs. son’s age, etc. But, in this case, he suddenly sprang to his feet: He almost yelled, “Sir! Please check my solution! I am getting the answer as husband’s age is 48 and wife’s age is 23!” Actually, I too was a bit shocked; but, I checked his calculations in detail; they were mathematically correct. It suddenly flashed in my head:
“Do you know Vedant? Mathematics is not human! It has no emotions, no feelings, whatsoever! I told him the following quote of Bertrand Russell: ” Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty, cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.””
And, of course, equations//numbers don’t lie! ðŸ™‚ ðŸ™‚ ðŸ™‚
Nalin Pithwa.