Recently Active Question Of The Day Questions

Part 1 *Image* here the radius side of the successive square is half of the original one... (The whole thing goes to infinity) Side of the Largest square is 1. Part 2 *Image* Find the CM of this system... Here you successivel ...

Where is the center of gravity of a very long pole of length L placed vertically on the earths' surface.... (If you think that the answer is obvious.. Think again :P) ...

I dont know if this can be solved.. (I havent so far..) but this question just stuck me when i was seeing another one.. On a solid sphere of radius R, or resistivity σ, there are two points a, b on the equatorial line at a d ...

This one is another of those which are very common olympiad type.. but i think are very important for jee aspirants too... if there are 7 distinct real numbers, show that there will be atleast 2 of them say x,y are such that ...

This is a classical question of magnetic flux... *Image* The bluish part is a metalic conductor which is moving with a velocity v There is a magnetic field in the dotted circular region... will there be the current in the loo ...

This is a very old problem... Prove that 4n+n4 is a composite number... ...

\int \frac{x^2}{(x^2-4)\sin x+4x \cos x}dx ...

This one is very old and standard.. but good for those who dont know.... Prove that a function can be written as a sum of an even and odd function. (Also: What is the condition for this to be written as above!) ...

A charge q is placed along the diagonal coloured in red at 1/3rd the distance from the vertex marked (0,0,0) Find the sum of the electric flux through the bottommost and the topmost surfaces *Image* I came up with this questi ...

Based on the question of 29th August, read and try to find a solution to this one... if x1, x2.... xm are distinct numbers, and f(x) is a polynomial of degree m-1 f(x)=f(x_1)\times\frac{(x-x_2)(x-x_3)...(x-x_m)}{(x_1-x_2)(x_1 ...

One integration, that has really taken a lot of my mind space... ∫(tan x)1/6dx ...

f:R→R and g:R→R be two functions such that f(g(x)) is a one one function. then answer the following matrix match type questions: coloumn 1 coloumn 2 A) then f(x) p) must be one-one B) then g(x) q)may not be one -one C) if ...

*Image* A current I flows through a infinitely long metallic conductor of the shape of a half cut hollow cylinder of radius radius r. What is the magnetic field at the center of the "imaginary completed" cylinder? ...

This is a simple standard question... (Which I would rate as a must know for most beginners) A disc of uniform surface charge density σ and radius r is rotated about its center, find the magnetic field induced at the center ...

This is a simple one... if you dont get scared Prove that 1/1 + 1/2 + 1/3+ 1/4..... this sum is not finite.. (as n goes to infinity) ...

If x2+x+a=0 and x2+ax+1 have a common root, find the value of a.... (Give as many proof as possible) ...

Find the number of solutions of x6+x3-2=0 (Got this question today from a student) ...

An ellipsoid is given by x2/a2+y2/b2+z2/c2=1 find the volume of it ...

Solve this integral \int_{0}^{infinity}{\frac{tan^{-1}(\pi x)-tan^{-1}x}{x}}dx ...

1) Prove that there exist arbitrarily long arithmetic progressions with all the terms being powers of integers. ...

the degree of dissociation of HI at a particular temperature is 0.8 . find the volume of 1.5 M sodium thiosulphate required to react completely with iodine present at equilibrium in acidic conditions, when 0.135 mol each of H ...

Decomposition of H2O2 is a second order reaction. A solution of H2O2 labelled as 20 volumes was left open.Due to this, some H2O2 decomposed.To determine the new volume strength after 6 hours,10ml of this solution was diluted ...

The periodic functions f(x): R -> R and g(x): R -> R satisfy the condition: lim (f(x)-g(x))=0 for all x ε R Prove that f(x)=g(x) for every real number x try to prove this. trust me it is really a good one. must try ...

If we take a magnet in the shape of a perfect cube.its one side will act as north pole and teh other side as south pole.Then what will be the polarities of other four sides? How will you decide which 3 adjacent sides of cube ...

Find the least positive value taken by 21x+12y+15z where x,y,z \epsilon Z ...

A straight uniform rigid wire lies on a smooth table; at each end of the wire sits a grasshopper. Show that if the mass M of the wire is not too great compared to the mass m of each of the grasshoppers, they can, by simultane ...

Suppose that f (x) is a polynomial with real coefficients and a is a real number with f (a) ≠0.Show that there exists a polynomial g(x) such that if we define another polynomial p(x) = f (x). g(x), then the following are tr ...

Prove that if m is a natural number m(m+1) can never be a perfect power i.e. not a square or a cube etc. of a natural number. ...

A circle with center O and radius R is drawn on a paper, and A is a given point inside the circle with OA=a. Fold the paper to make a point A' on the circumference coincident with point A, then a crease line is left on the pa ...

starter If two protons are moving at a speed v relative two you through space in the same direction and are separated by a small distance, you will see them exert a magnetic force upon each other, because they are essentially ...