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It is given that a polynomial with rational coefficients has n real roots. One of them is 1+ 5 Prove that 1- 5 is another root! Please realise that the implication of this are very huge and very very important in guessing sec ...

Now a sitter after the toughie yesterday! 1+ 2 is the root of x3+bx+a find a and b? if both are rationals... ...

This is a very standard question If I can dare to put it that way. Edit: sorry used alcohol instead of aldehyde :(( What do we do if we have to reduce only the ketone group in a compound that contains both ketone and aldehyde ...

*Edited 1 (7-12x+4x2)(1+e3-2x) integrate the above in the limits (0 to 3) ...

Find the probability that the points two randomly chosen numbers in [0,1] are such that the distance between them is less than 1/2 If you remember a similar question of time that two friends meet you can solve it in a flash T ...

Take a (one-dimensional !) rod of length \ell and remove the middle one-third. Then remove the middle one-third of the remaining two pieces, then remove the middle one-third of the remaining four pieces, and so on forever. Le ...

Prove that the circum radius of a triangle is given by R = abc/4Δ where Δ is the area fo the triangle and a,b,c are the sides ...

I think there is a lot of confusion on limits due to a post on forum let us do the following problems... Find the following \\1) \lim_{x\rightarrow 1} (x^{n}) \\ \\2) \lim_{x\rightarrow 1^+} (x^{n}) \\ \\3) \lim_{x\rightarrow ...

Equation of a parabola is x2-y2=100 Find the nearest point on this hyperbola to the line y+3x+1=0 you first solve this .. then i will tell the fallacy! ...

|y|= |sin x| Plot the graph and also find the area in the region (0, 2 π) *Backlog clearing question of the day! ...

I think many of the JEE aspirants fear inequalities a lot so a very simple one. It uses only AM GM inequality That too only once! \frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\geq 3/2 Just give it a try .... Think for just a bit ...

A cube of mass of side a is dipped in water through a spring. At equilibrium , half the cube isimmersed in water The density of the cube is ρ, while that of water is 1 the spring constant is k Is this a SHM. Find the time pe ...

This one is a sitter ;) radius of Earth = 6 378.1 kilometers The Area of India is 3,000,000 Km2 A charge Q=1 Coulomb is uniformly distribute over the earth's volume The Flux Through India is equal to? ...

Prove that among all polygons, of fixed side, a circle has the maximum area! ...

Another Inequality by AM GM alone. \sqrt{\frac{a+b}{c}}+\sqrt{\frac{b+c}{a}}+\sqrt{\frac{c+a}{b}}\geq 3\sqrt{2} Hint: AM GM inequality twice. ...

I saw something like this in Mathematics today sometime.. \sum_{1}^{n}{\frac{k+2}{k!+(k+1)!+(k+2)!}} Find this.... ...

I gave a graph of the day y=\frac{x^{2}+x+1}{x^{2}-x+1} When i was seeing the solution by users, I noticed something very interesting! you have to explain something very interesting that is going on in this graph... the graph ...

This is a very very very very old and well known thing of higher mathematics... Though I am giving you a very simple part or the simple part of that thoery... A line is of length 1. 1/3rd of the segment is removed from the mi ...

Explain how you will fidn the work in expanding a gas from V to 2V If the process is such that first volume is halved at constantpressure, then doubled at constant temperature. Then halved at constant temperature and then inc ...

Two integers are multiplied. What is the probability that their product is a multiple of 8 Then generalize for 2n. ...

This is the biggest question n organic till date in the forum... Enjoy!! [3] *Image* Edit: ( after AgNH3 and H+) after S ... 1 eq of red P HI is added ...

Suppose that there is a bird inside a Large Box. The mass of the bird is m. The mass of the block without the bird is M What is the reading on a spring balance when 1) The bird is on the floor of the block 2) The bird is flyi ...

There is a solid cyllinder of radius R and length L of mass M and a charge Q uniformly distributed on the mass. There is an electric field E along the -ve X axis. gravity acts downwards The cyllinder is kept next to a wall. T ...

To be fair, this question is not relevant to the Syllabus of IIT JEE. It is definitely in the syllabus but it shows how things can go wrong! I will try to show that there are 3 different probabilities attached to finding the ...

*Image* for every 1s revision and time pass[3] 1.the the shape of an ancient clock jug is such that water decends at constant rate at all times ..... if it falls by 4cm per hour ...... determine the shape of the jar(relation ...

what is the probability that the product of two randomly chosen integers is divisible by 12? ...

The coefficient of volumetric expansion of a block of mass is A the desinty of the block at room temperature is D density of a liquid is 2D at room temperature The coefficient of volumetric expansion of the liquid is B Find t ...

Define Heat and Temperature. (Might Seem stupid question for a question of the day..) But this is relevant! ...

A cubical body has a coefficient of expansion a, b, c in the three perpendicular directions. Find the coefficient fo volumetric expansion. Assume whatever you think is not given! ...

*Image* Is the central carbon on this chiral or achiral How many chiral centers are there on the whole structure? ...