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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.... ...

Vm = man's velocity (w.r.t. stationary frame of reference viz. ground) Vw = river's velocity (w.r.t. stationary frame of reference viz. ground) Vmw = man's velocity w.r.t. the river. Given, |Vmw| = |Vw| = v width of the river ...

Classify the 10 compounds given below into three groups: a) Aromatic. b) Anti-Aromatic. c) Non-Aromatic. Mention reason for every grouping! [1] *Image* *Image* *Image* *Image* *Image* *Image* *Image* *Image* *Image* *Image* ...

*Image* m1=m m2=m M =4m *Edit: system was initially released from rest. All surfaces frictionless! Find the acceleration of all the three blocks and the direction of acceleration.. More interested to see the relations between ...

An ionic compound AB2 has cubic closed pack structures, A occupying lattice positions and B occupies only one kind of void throughout (either tetrahedral or octahedral). a) what kind of void is occupied by B? b) what percenta ...

Prove the expansion of sin(A+B) in as many ways as you can... Simpler proofs fetch higher reward ;) ...

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 ...

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 ...

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 ...

The chicken wants to cross the road on which cars circulate (all cars run at the same constant speed - 30km/h and occupy the entire width of the road). The chicken follows the trajectory that leaves him the best chance of sur ...

what are d necessary n sufficient conditions for a no. to be divisible by 7,8,9,10,11...30 individually...??? "Asked by MAK" 7 is the only non - trivial one :) ...

Given x0>0 and a>0, show that there exists one and only one sequence {x0, x1, x2,...) such that x_n = \sum_{j=n+1}^{\infty} x_j^a ...

Find out integers such that (a+b+c+d)2=a3+b3+c3+d3 Let me make it simpler .. find integers so that (a1+a2+a3...an)2=a13+a23+a33...an3 ...

what is the oxidation number of C and N HCN and HNC? ...

\lim_{x\rightarrow a}\frac{1}{(x-a)}\int_{\sqrt{a}}^{\sqrt{x}}(te^t sin t)dt a>0 ...

Now that we have solved the probability of product of 2 integers being a multiple of 2n can we generalize this to probability that the product of n integers is divisible by 2m? ...

Find the square root of... \sqrt{a-b}+\sqrt{b-c}+\sqrt{c-a} ...

What is the number of pairs of 2 consecutve 4 digit integers which can be added without any carry? ...

What is 00 Warning: Either dont get confused after seeing the solution or dont see the solution at all....... This might be really dangerous for your limits concept! ...

What is the energy needed to accumulate a sphere of a mass M and radius R (better language?) * A very standard question... ...

A projectile is fired from the ground and it bursts at the highest point and explodes into two halves.We apply law of conservation of momentum in horizontal direction.Gravity is purely vertical , so we have no problem conserv ...

Product of any 4 consecutive integers is always 1 less than a perfect square. ...

Under what condition on n, will n consecutive integers exist whose sum is nk Hint: Consecutive integers are in AP [6] ...

x+x+x..x times = x^2 differentiate both sides w.r.t x 1+1+1..x times = 2x x =2x what is happenning ? ...

Show that the quadratic ax2+bx+c has no rational roots if a, b and c are all odd... ...

Evaluate: \int \sqrt{x+\sqrt{x^2+a^2}}dx ...

Solve: x2+ 9x2/(x+3)2 =16 ...

Evaluate \lim_{x->0}\left[ \frac{a^x+b^x+c^x}{3}\right]^{1/x} ...

\lim_{x\rightarrow \infty}\left(\frac{(1+x)^x}{x^x\times e} \right)^x Source:AOPS ...

*Image* And finally, a bonus question -: Q6. I have with me Br-(CH2)4-OH. I have to transform it into HO-(CH2)4-COOH. I can do this by the Grignard method(CO2) and by the Cyanide method(substitution and then hydrolysis). Whic ...