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Src: AOPS *Image* ...
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A very old problem which i saw somewhere and dont think we have discussed it here before... Given the drawing of a parabola, try to find the focus. Nothing is given, no grids nothing. Just the parabola on a blank paper.... ...
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Find all numbers for which the product of all its factors (other than itself) is equal to the number itself. ...
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Prove the expansion of sin(A+B) in as many ways as you can... Simpler proofs fetch higher reward ;) ...
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How do you decide if or not a fraction is terminating? ...
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Simplify \left({\sqrt{75}-\sqrt{12}}\right)^{-2/3} ...
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I am starting this series of question specially for students who are in class XI and have just started preparing... If you are in a higher class (Read XII/ Passout) please hold ur adrenaline rush and give chance to the beginn ...
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n+d(n)+d(d(n))=2000 where d(n) represents the sum of digits on n.... Find n... (Please do not refer to this question as an olympiad based question... it is tricky but the trick required is from class VIII-IX) Ricky killed it ...
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x+y+z=pi (angles of a triangle) show that sin x + sin y + sin z >= 3 3 /2 Solution \frac{\sin x+\sin y+\sin z}{3}\ge(sin x\times\sin y\times\sin z)^{1/3} (AM GM Inequality) Equality holds when all terms are equal.... So si ...
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This is a standard question which appears everywhere.... (almost) sin x = 1 + x + x^2 Find the number of solutions.... PS: Am trying to give sometime here daily just by posting the QOD. A promise that I have often failed to d ...
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A candle should not be blown off because even the gas that we exhale has a lot of oxygen.. But we all know that presence of oxygen should not lead to dying of the flame Explain this very commonly seen phenomenon? ...
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Show that the number 510-310 is divisible by 11 ...
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Simple Graph for XI students first... y=x2-x3 ...
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Suppose you've set up a hot date with a totally happ’nin’ (girl/guy). You decide to meet at Penguin's (thus, you have specified a point in space at which to meet). But your meeting plans are not complete: you might show u ...
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*Image* ...
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Basic Graph (for beginners) Draw the graph of x4, x3, x2 and x on the same sheet of paper. ...
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Draw the graph of Sin x and tan x between -pi/2 to pi/2 on the same sheet. * I am trying to post some very simple graphs for some new users who may not know the basics and I expect them to answer (some of the older/ more adva ...
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Show that the quadratic ax2+bx+c has no rational roots if a, b and c are all odd... ...
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\lim_{x\rightarrow a}\frac{1}{(x-a)}\int_{\sqrt{a}}^{\sqrt{x}}(te^t sin t)dt a>0 ...
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Evaluate: \int \sqrt{x+\sqrt{x^2+a^2}}dx ...
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Roll 3 fair, six-sided dice, and let their sum equal X. Roll 2 fair, six-sided dice, and let their sum equal Y. Find the probability that Y > X. (Src.. Grissom) I dont seem to be able to think of a sleek solution.. (sleek ...
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Solve: x2+ 9x2/(x+3)2 =16 ...
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Which of these is true? Infinity a perfect square? Infinity is a Real Number Infinity is a Even number It is an odd number It is both even and odd It is neither even nor odd It is a Integer It is a rational number It is an ir ...
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\lim_{x\rightarrow \infty}\left(\frac{(1+x)^x}{x^x\times e} \right)^x Source:AOPS ...
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Well I heard a criticism about TiiT today which i kind of agree to... what are your ideas on the same? There is a student of mine who visits tiit and he said that the problem is that everyone asks questions which cannot be so ...
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1002004008016032 has a prime factor p>250000. Find it. Source(David A Santos) Hint: (a^3-b^3)(a^3+b^3) Even though I have put it in the class ix - x level.. it needs a bit of application which is not generally known at ix- ...
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<span class="postbody"><center><embed src="http://www.magicwidgets.com/widgets/mw-cd-countdown/show.swf?clickURL=http://www.magicwidgets.com/&clickLABEL=Flash-Toys&flashLABEL=MagicWidgets&skin=http://www.magicw ...
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Evaluate \lim_{x->0}\left[ \frac{a^x+b^x+c^x}{3}\right]^{1/x} ...
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Why is it that momentum is mv while kinetic energy is 1/2 m v2 and not some other way.. like momentum is 2mv, while KE is mv2 A very very basic and important question which i would like some class IX-X students to answer firs ...
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A solid metallic sphere in a uniform electric field..how to draw..lines of force Now if the solid metallic sphere is to be replaced by a hollow metallic sphere, how will the field lines look like. Again draw the lines of forc ...
