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THIS REMAINS ONE OF MY GREATEST DOUBTS Integrate e x cos a da . ...
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Let y = [ √x ] x x x x x. . . . . . ( infinite times ) Find dy/dx in terms of x , y , log y and log x and no other variable. ...
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If tan x = n tan y , then prove that x = y - m sin 2y + m2/2 sin 4y - m3/3 sin 6y + . . . . . . . . . . . . . where m = 1 - n/1 + n . ...
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A point particle having a mass m is coming from V under the mutual gravitational attraction of the sphere of radius R , in which a negligibly small hole is made so that the particle may enter . Find the time it takes to reach ...
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I guess this is pretty tough for many guys out there -- but yesterday I learned such a great sum that I cannot resist to give it ---------------------- Suppose you don't know any of the equations that are used in S . H . M . ...
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I really want a long discussion on how to draw the following graphs --- 1 > y = [ e[x] ] 2 > y = { e{x} } ...
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Maybe this is pretty easy -- but I liked it a lot -- so here goes -- Find the remainder when 1003 x 1009 x 1017 is divided by 119. ...
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Another one -- down the halogen group , Silver halides form deeper coloured compounds . Why????? ...
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A simple question --why is CO more stable than SiO ?? I initially thought that the size mattered , or simply inert pair effect was there . But that was not the answer at all !!! Try , fellows ...
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Good an' simple --- try this one --- Given four distinct numbers in the interval (0,1) , show that there exists 2 numbers among them x and y , such that ------ 0 < x \sqrt{1 - y^{2}} - y \sqrt{1 - x^{2}} < \frac{1}{2} ...
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Great question --- a must try , In how many parts an integer N >= 5 should be dissected so that the product of the parts is maximized ? Hint …….----- After getting the answer , you will immediately realize why the cond ...
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Great question --- though not difficult --- If the polynomial xn + p1 xn-1 + p2 xn-2 + p3 xn-3 + ...... + pn-1 x + pn = 0 , has n real roots a , b ,c , d ... k , and p1 , p2 , p3 are all real , then find the value of , ( 1 - ...
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Think its a A . Dasgupta question --- anyhow a good one --- there are two methods actually -- lets see Prove that the eqn . a0 x5 + a1 x4 + a2 x3 + a3 x2 + a4 x + a5 = 0 cannot have all real roots if 2 a12 - 5 a2 < 0. ...
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Great question , specially Nishant sir very much liked it , I would ask him not to give the answer , unless and until everyone tries :) Find the total number of integers p , q , r such that the number , 2 p + 3 q + 5 r is a m ...
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3 > How many quadratic eqn. are possible such that it remains unchanged even after its roots are squared ? ( this is one of my favourite questions ever !!!!!!!!!! ) ...
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2 > If a , b are the roots of x2 + px + q = 0 , and they are also the roots of the eqn. x2n + pn xn + qn = 0 , then prove that a / b and b / a are the roots of the eqn. xn + 1 + ( x + 1 )n whenever n is an even integer , a ...
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Some very easy quad sums , hope everyone gives a different process ------------- 1 > If ( x - a ) ( x - b ) = k has the roots c , d ; then roots of the eqn. ( x - c ) ( x - d ) + k = 0 are -- ...
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Maybe these are too tough , maybe very easy , but I would definitely appreciate a good solution of these problems ---- Find 1 > The gravitational field on a point mass due to an infinitely unstreachable thread of density p ...
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Find the greatest common divisor of the following terms . 2mC1 , 2mC3 , 2mC5 ...... 2mC2m - 1 (Hats off to anyone who does this !!!!!! ) ...
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It is not at all hard , ( not only from the view point of sirs ) , so try this ---- 1 > Let a , b , c, d , e …… be the positive divisors of “ n “ except n and 1 . Prove that --------- ( 1 / a ) + ( 1 / b ) + ( 1 / ...
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Few quaries , trying to do them myself ---- would be glad to get help ---- 1 > The cubic equation , x3 + px2 + qx + r = 0 has two roots “ a “ and “ b “ such that ab + 1 = 0 . Prove that r ( r + a+ b + p ) = 0 . ...
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Judging by the popularity of congruences , let's try to do things in a different way , but I don't have a problem in congruences :) especially it would be a treat to watch other solutions too ---- 1 > Find the last 3 digit ...
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Hey guys , this maths musing problem (of MTG December issue ) is really great , please give it a try ---- NOT FOR THE GREAT SIRS Find the last digit of the sum of the roots of the eqn. ( 1/2 x - 1 )2009 = -1 , and also try th ...
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Here is a good enough test for all maths lovers , and I really liked the question patterns , so I am uploading some of them ---- A few are very confusing , so please help in solving those ---- 1 > Find the sum of the follo ...
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Well ,let's make mincemeats of these --- :) 1 > Do try to find the remainder when 21990 is divided by 1990 . I have found a way without using binomial but , still it would good to see the other ways too ---- maybe an easie ...
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Hey guys , hope you are not too bored with maths . I found some good questions which I think don’t require pen and paper , yet are interesting . So please try --- 1 > If xy = 281 . 378 . 534 ( x + y ) , then find the num ...
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Hey guys , hope you are not too bored with maths . I found some good questions which I think don’t require pen and paper , yet are interesting . So please try --- 1 > If xy = 281 . 378 . 534 ( x + y ) , then find the num ...
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Well , how about some good questions to wake you up all night ? I think these are quite intriguing to attempt , so I will definitely post the solutions after a day or two ---- 1> ( a , 1 / a ) , ( b , 1 / b ) , ( c , 1 / c ...
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Well, here are some brainy problems you might want to have a look at only if you are not feeling too sleepy --- :) I am gonna post the solutions after one hour if I can --- 1> If y = x/x2+1 , then find x if d4/dx4 (y) = -3 ...
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I think the following questions require good amount of thinking,but even after such a short stint with targetiit, i realized one thing and that is, no man made problem can escape from the axe of problem solving here :) [I hop ...
