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prove with mathematical Rigour that angle of minimum deviation occurs when i1=i2 for a prism of apex angle A ...
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A turntable rotates with constant angular speed \Omega . A ball rolls on it,without slipping .the ball has uniform mass density , so moment of inertia is I=\frac{2}{5}MR^2 show that whatever the (non -slipping )initial condit ...
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\text{Let f(n) be the integer closest to} \ {\sqrt{n}}\\ \text{find the value of }\\ \sum_{i=1}^{2008}{\frac{1}{f(i)}}\\ \text{NOTE: f(6=2),f(7)=3,f(12)=3,f(13)=2 etc.}\\ (A)88\frac{28}{45} \ \ (B)90\frac{3}{5} \ \ (C)87\frac ...
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today is the 122nd birthday anniversary of the man who knew infinity the indian mathematical legend Srinivasa Ramanujan *Image* read more here http://en.wikipedia.org/wiki/Srinivasa_Ramanujan ...
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plz solve this one : [1] *Image* q2 try this one also its not my doubt but wanted to share if log(\frac{1}{1+x+x^2 +x^3 }) is expanded on the ascendind powers of x then prove that coefficient of xn in the expansion is \frac{- ...
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Prophet sir had recently taught a method to deal with recursive functional relations i have doubt regarding that : this thread was solved long back using substitution technique http://targetiit.com/iit-jee-forum/posts/full-th ...
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there is a set A of n elements. now a subset B is formed from A the set A is then reconstructed by replacing elements of B now a subset C is formed from A find the number of ways of selecting B and C so that B and C are non i ...
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rekha married shyam and had 4 sons .Varsha married ajay and had 4 sons.both couples divorced and after that shyam married varsha while ajay married rekha .they too had 3 sons each from their wedlocks .how many selections of 8 ...
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prove that xyz >(y+z-x)(z+x-y)(x+y-z) i have found one solution but i am sure a better is existing in someones brain :) ...
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ram has to attempt 4 papers each paper containing maximum 'n' marks in how many ways he can get a total of 2n marks ..... note: if u want to use multinomial theorem then also provide proof of multinomial thoerem :) ...
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Two squares are chosen at random on a chess board. The probability that they have a side in common is ? ...
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if (1+2x+2x2)n=a0+a1x+a2x2+........a2n2n then prove that : ar=nC0.2nCr + nC1.2n-2Cr-2 +nC2.2n-4Cr-4+..................... ...
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if \alpha _{1},\alpha _{2} are the roots of equation: ax2+bx+c=0 and \beta _{1},\beta _{2} be roots of equation : px2+qx+r=0.if \alpha _{1}y+\alpha_{2}z=0 \beta_{1}y+\beta_{2}z=0 have a non trivial(nonzero solutions) then pro ...
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if x=1 is a real root of ax2+bx+c=0 then show that 4ax2 +3bx +2c =0 has real roots ...
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find t: t=n+1Cn +n+2Cn +..............+2nCn ...
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PROVE : 2<f(n)<3 if n→N n ≥ 2 and f(n)=(1+1/n)n ...
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while solving this sum: find C0+C1/2 +C2 /3 +.............+Cn/n+1 there is an alternate method given in BT that is multiply and divide by( n+1) \frac{1}{n+1}[(n+1)(1+\frac{n}{2} + \frac{n(n-1)}{1.2.3}+...........] then the ex ...
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if a>b>0 n→N prove that an -bn>=n(a-b)(ab)(n-1) /2 ...
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a+b+c=1 then prove (1+1/a)(1+1/b)(1+1/c) >= 64 ...
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if i have to evaluate : S=1.2 +2.3+3.4+..................+(n-1).n +n.1 then i have a ready made formula (with proof also) for evaluating 1.2 +2.3+3.4+..................+(n-1).n as (n+1)! /(r+1)(n-r)! putting r=2 we get (n+1)n ...
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can anyone explain more clearly ,with some diagram if possible ,what metal is saying here..............http://targetiit.com/iit-jee-forum/posts/my-electrostatics-12089.html ...
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prove this inequality *Image* conditions:plz dont use titu lemma,tchebychef and cauchy-schwatz.... only alowwed inequality's are a.m >g.m >h.m and mean power............ i am imposing these conditions because i proved i ...
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ai>0;i=1,2,3,4.........n (n-1)s=a1+a2+a3+a4+..............an prove that a1.a2a3..........an>= (n-1)n(s-a1).(s-a2).(s-a3)(s-a4).........(s-an) ...
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if the sum f an A.P is same for p and q terms, show that the sum of p+q terms is 0........ *Image* S(p+q) >0 from graph ...how can it be 0 ????? and if S(p+q)=0 wat is the other root ...
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where is the flaw......... *Image* ...
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