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f is a real-valued differentiable function defined on [0,1]. If f(0)=0 and f(1)=1, then prove that there exist distinct points x1,x2 in [0,1] satisfying 1/f'(x1) + 1/f'(x2) = 2 ...
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1)The metre is defined as the distance by travelled light in 1/299,792,458 second. Why didn't people choose some easier number such as 1/300,000,000 second? Why not 1 second? 2)Suppose you are told that the linear size of eve ...
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A comet is moving in a parabolic path around the Sun in the same plane as the orbit of Earth (without any collision with the Earth, obviously!). Determine the maximum time that this comet can spend within the Earth's orbit, w ...
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the uniform bar of mass M and length l has a small roller of mass m with negligible bearing friction at each end.............determine the time period of the system for small oscillation on the curved track.... *Image* ...
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Suppose a_1, a_2, a_3,...,a_n are n real numbers It is obvious that if the ai are all positive, then the numbers \sum a_i, \sum_{i<j} a_i a_j \sum_{i<j<k} a_ia_ja_k,..., \prod_{i=1}^n a_i will all be positive Prove t ...
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First look this might seem an olympiad problem that may scare some of you... but try this problem to get an insight on how to solve such problems... x+y+z = w 1/x + 1/y + 1/z = 1/w Solve for x, y and z... (Not that you have t ...
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First look this might seem an olympiad problem that may scare some of you... but try this problem to get an insight on how to solve such problems... x+y+z = w 1/x + 1/y + 1/z = 1/w Solve for x, y and z... (Not that you have t ...
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First look when i saw this question, I got bowled.. Then the feeling of solving this one was good.. [1] .. I thought THis is a nice question that you guys should try F(x) is a polynomial of degree n such that f(k)=1/k for k=1 ...
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I look at askiitians.com only when I am VERY VERY BORED. But one post took me quite by surprise, when the student asked, if f:N→N is a strictly increasing function satisfying f(f(n)) = 3n for all n, find f(11). ...
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I look at askiitians.com only when I am VERY VERY BORED. But one post took me quite by surprise, when the student asked, if f:N→N is a strictly increasing function satisfying f(f(n)) = 3n for all n, find f(11). ...
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Prove that for any n, \frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...... + \frac{1}{n^2}<1 Note:This is not a very strict inequality since the exact value of this limit as n goes to infinity is 0.645 ...
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"A particle is placed on a rough plane inclined at an angle theta, where tan θ = μ = coefficient of friction(both static an dynamic). A string attached to the particle passes through a small hole in the plane. The string is ...
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Nr= 2x^1/2 +3 x^1/3 + 5 x^1/5 Dr=(5x-2)^1/2 +(3x-2)^1/3 lt---->∞ Nr/Dr plz do without l'hospitol rule........ and plz tell me the logic behind l' hopitol ...
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If f:R→R is a monotonic,differentiable real valued function a,b are two real numbers and ∫f(x)+f(a))(f(x)-f(a))dx=I1 upper limit→ b and lower limit→a ∫x(b-f-1(x))dx=I2 upper limit→f(b) lower limit→f(a) I2/I1=___ ...
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I want to toast Nishant Sir for opening a section for 9th-10th students. It is a superb move and should prove pretty useful I had proposed some such thing in goiit.com and it was totally ignored. The Olympiad section is anywa ...
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A positive integer n is a good number if it can be written as the sum of two positive integers a and b, i.e. n=a+b, such that n|ab. It is a very good number if a,b are distinct. Find all numbers n such that n is good but it's ...
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A positive integer n is a good number if it can be written as the sum of two positive integers a and b, i.e. n=a+b, such that n|ab. It is a very good number if a,b are distinct. Find all numbers n such that n is good but it's ...
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All tiitians post ur full name , college , branch so that we can know someone better whos joining the same college ...
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A point-like electric dipole (dipole moment = p) is kept at the origin, pointing along the +z direction. A point charge q having mass m is released at rest from a point on the xy plane at a distance R from the origin. Assumin ...
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I think everyone has come across this familiar problem: Three snails A, B, C are initially located at the vertices of an equilateral triangle. Starting at t=0, they all move with the same constant speed such that A always poi ...
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Consider two sets of distinct real numbers A and B such that A={A1,A2,...A100) B={B1,B2,....B50) Consider all kinds of onto mappings from set A to set B such that f(A1)≤f(A2)≤....f(A100) Find the number of such mappings. ...
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Consider two sets of distinct real numbers A and B such that A={A1,A2,...A100) B={B1,B2,....B50) Consider all kinds of onto mappings from set A to set B such that f(A1)≤f(A2)≤....f(A100) Find the number of such mappings. ...
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Consider two sets of distinct real numbers A and B such that A={A1,A2,...A100) B={B1,B2,....B50) Consider all kinds of onto mappings from set A to set B such that f(A1)≤f(A2)≤....f(A100) Find the number of such mappings. ...
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Point A moves uniformly with velocity 'v' so that the vector 'v' is continually "aimed" at point B which in its turn moves rectilinearly and uniformly with velocity u<v. At the initial moment of time v perpendicular to u a ...
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Help fellow targetiitians , it seems that a great fellow like me cannot even solve this very naive question: A ball dropped from certain height makes an elastic collission with an inclined plane with angle of inclination = 45 ...
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Let x,y>0 be real numbers and let s be the smallest of the numbers x,y+(1/x),1/y Find the greatest possible value of s . For which x,y is this value assumed? Again for beginners .. but experienced ones can answer if they w ...
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Let x,y>0 be real numbers and let s be the smallest of the numbers x,y+(1/x),1/y Find the greatest possible value of s . For which x,y is this value assumed? Again for beginners .. but experienced ones can answer if they w ...
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im stuck at this one [41] Find f(x) if f(x + y) = x. f(y) + y. f(x) and f '(0) = 1 ...
