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How to decide if a graph is symmetric abt a line or a point? Example when can we say that a graph is symmetric about the line 2x+y=2? ...

The diagram below shows the section of the pencil... Assume that for the pencil, shape is a regular hexagon, the wooden part is massless compared to the lead inside.. so that there is only mass at the center. The pencil is ro ...

This one is relatively simpler compared to the other question we have solved.. \left[\frac{n}{3}\right]+\left[\frac{n+2}{6}\right]+\left[\frac{n+4}{6}\right]=\left[\frac{n}{2}\right]+\left[\frac{n+3}{6} \right] ...

Prove that for every real number x, [x]+[x+1/n]+[x+2/n]+.........[x+(n-1)/n] = [nx] [x]+[x+\frac{1}{n}]+[x+\frac{2}{n}]+...+[x+\frac{n-1}{n}]=[nx] Where [] denotes greatest integer function Because no one has been able to sol ...

f(1) = 1 f(2n) = f(n) f(2n+1) = f(n)+1 where n is an integer and f is a function defined over integers... Give a simpler explanation for f... ...

We have seen so many polynomial questions.. But I am still giving this one because I cant resist from feeling how many of you have really understood some of what we discussed in thsoe questions.. P(x) is a polynomial of degre ...

If a, b, c are distinct real numbers, then, the number of real roots of \frac{(x-a)(x-b)}{(c-a)(c-b)}+\frac{(x-a)(x-c)}{(b-a)(b-c)}+\frac{(x-b)(x-c)}{(a-b)(a-c)}-1 is? ...

*Image* RR' is a road on which Powerplant P has to be constructed. There are two villages A & B on same side of the road. Find the optimum location of poweplant P such that wiring cost i.e. PA+PB is minimum. Note: You sho ...

1) \int{\frac{{\sin (x+\alpha )}}{{\cos^{3}x}}}\sqrt{\frac{{\cos ecx+\sec x}}{{\cos ecx-\sec x}}}dx 2) \int{\frac{{x^{2}-1}}{{1+x^{2}}}}\frac{{dx}}{{\sqrt{1+x^{2}+x^{4}}}} These questions have been lifted from AOPS .. I found ...

Prove that the function f(x) = ln x is not rational. (Note: ln x means loge x) ...

Find the sum of the infinite series... sin^3x+\frac{sin^33x}{3}+\frac{sin^33^2x}{3^2}+\frac{sin^33^3x}{3^3}+... (Hint recall the questions I have given during the last few days...) ...

A needle has a length of L meters is placed gently on the surface of the water(γ). What is the weight of the heaviest needle that can be floated ? ? (Very easy question. I gave this one so that you study surface tens ...

Find the value of cos (Ï€/5) ...

If sinA+ sin B + sin C = cos A + cos B + cos C = 0 Prove that : 1) sin 3A + sin 3B + sin 3C = 3sin (A+B+C) 2) cos 3A + cos 3B + cos 3C = 3cos (A+B+C) ...

sorry posting almost when day is over :P 1)Calculate the concentrations of the non-ionised acid of the ions in a 0.1 M formic acid at equilibrium. ( Ka =1.7* 10^-4) 2)A certain weak acid has Ka=10^-4 Calculate the equilibrium ...

if 3 continuous and differentiable functions a(x),b(x),c(x) are inserted b/w ex and f(x) , then sequence becomes a GP.If g(x),k(x),l(x) are 3 continuous and differentiable function inserted b/w them ,then sequence is AP.It is ...

Passage *Image* When g(x) and h(x) will be solved by someone..I will post the remaining questions of this passage Sorry Nishant sir ,if u think this question doesnt deserve to be QOD ...

Passage: Curve f(x)=a(x-1)5+b(x-1)4 has 2 identical critical points . b is the constant number satisfying inequality b+1 >b 2 .Also limit lim [ 5ymax-b5 - 25.mod(b) ] b→0 sin5b 25.a2.sinb exists and is equal to L Q1 if u ...

Suppose there was a planet of mass M which was free from any other force from a planet or star... and this planet had a moon of mass m. Now, the rotation is such that the same surface of the moon is visible from the planet... ...

This question has appeared on an online physics site... (given by Rohan to me) Lets have a tall cylindrical vessel filled with water (radius r, height of water h) and spin it around its axis at angular speed ω. At the centre ...

What is the 10000th palindrome? PS: 131, 1441, 1020201 etc are palindromes... which are the same from both sides :) ...

A skier starts from rest at point A and slides down the hill, without turning or braking. The friction coefficient is k. When he stops at point B, his horizontal displacement is s. What is the height difference h between poin ...

*Image* There are two neutral solid spheres of radius r with a seperation d r< < d They are supplied charges constantly such that dq/dx=n for 1st and dq/dt=-n for the 2nd sphere. After what time will the spheres stop pu ...

*Image* Question : What should be the minimum (total) compression in the spring so that the green block leaves contact.... Given: The black wall is rigid Coefficient of friciton between the floor and the masses is μ Spring c ...

*Image* The system above in the diagram iis released. The mass of the black beads is m, while that of blue loop is M What is teh minimum m/M ratio needed for the lower loop to take off from the ground.. (A variation of this q ...

Find the minimum value of a^2+b^2 given that x^4+ax^3+bx^2+ax+1=0 has only real roots... (The question is not very very difficult question.. if you recall the trick often used in solving 4th degree polynomials...) ...

Solve for real values of x \left( \int_{0}^{1}\frac{1}{t^{2}+2t\cos a+1}dt\right)x^2+\left(\int_{-3}^{3}\frac{t^{2}\sin 2t}{t^{2}+1}dt \right)x+2=0 Saw this on another forum... not very tough... only looks dirty... ...

Find the minimum velocity required to send the ball to the top of this infinite structure.... Keep in mind: The successive radius are half of the original ones..... there are infintely many such. The lowest loop has radius R, ...

These days there seem to be a lot of inequalities being discussed here... This one is much simpler... If a, b, c are positive, Prove that : \frac{b^2+c^2}{b+c}+\frac{a^2+c^2}{a+c}+\frac{a^2+b^2}{a+b}\geq a+b+c I hope think on ...

A charged particle of mass m, charge q is in an electric field given by E=E_x\sin(\alpha t)\hat{i}+E_y\sin(\beta t)\hat{j} Find the equation of the position of the charge as a function of time ...