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If the complex sequence of numbers z0, z1, z2........satisfy z_0=i+\frac{1}{137} and for n≥1 z_{n+1}=\frac{z_n+i}{z_n-i} then find the value of z2007 ...
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find the value of summation \sum_{r=0}^{2008}\left [ \frac{2^r}{3} \right ] \\ \\\textup{where [.] is GIF} ...
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solve for x 16x+30\sqrt{1-x^2}=17\sqrt{1+x}+17\sqrt{1-x} where 0<x<1 ...
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....................................................................................................................... *Image* ...
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evaluate 1) \sum_{n=1}^{\infty }\frac{1}{n^3(n+1)^3} 2) \sum_{n=1}^{\infty }\frac{1}{n^2(n+1)^2} ...
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evaluate- \sqrt{2011+2007\sqrt{2012+2008\sqrt{2013+2009\sqrt{2014+.........\infty}}}} ...
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\boxed{1} Find the value of a for which \int_{0}^{\pi}\{ax(\pi^{2}-x^{2})-\sin x\}^{2}dx is minimized. (easy one) for prac. \boxed{2} Let f(x) be a continuous function satisfying *Image* Find the value of k for which *Image* ...
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*Image* how u solve it ? ...
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\texttt{The number of natural numbers between 1 to 2000 such that sum of digits of their sqaures is eqaul to 21} ...
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\\\texttt{ Given the three digit number } N= a_1a_2a_3.. m_1,m_2,m_3 \\\texttt{ are the smallest possible natural number such that N is divisible by 7 whenever } \\ m_1a_1+m_2a_2+m_3a_3 \texttt{ is divisible by 7 then} \\ \te ...
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\texttt{the number of ordered triplet(x,y,z) such that LCM(x,y)=3375,LCM(y,z)=1125,LCM(z,x)=3375 is} ...
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find the point inside the traingle such that sum of squares of the distances of that point from vertices of triangle is minimum i hav read somewer its centriod is it correct? if correct how u prove it? ...
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Let n is a positive integer greater than 7 and let f(x) is a biquadratic polynomial with *Image* and *Image* .Let *Image* and remainder when g(x) is divided by f(x) is *Image* then find the value of a b and c in terms of n ...
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In a triangle ABC ,AD is the perpendicular to BC .the inradii of ADC,ADB and ABC are x,y,z .find the relation between x ,y and z? note::the relationship shud have only x y and z.....no oder variable. ...
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k= \lim_{n\to\infty}\frac{(2n+1)\int_{0}^{1}x^{n-1}\sin\left(\frac{\pi}{2}x\right)dx}{(n+1)^{2}\int_{0}^{1}x^{n-1}\cos\left(\frac{\pi}{2}x\right)dx}\ \ (n=1,\ 2,\ \cdots). find k ...
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EVALUATE *Image* ...
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\\\texttt{Given\; that\;} \\H_k=\frac{k(k-1)}{2}cos\left ( \frac{k(k-1)\pi}{2} \right )\\\texttt{Find \;teh\; value}\; of\\\;H_{19}+H_{20}+H_{21}......H_{98} try it..for practice ...
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find the angles and the side lengths of the pedal triangle of triangle ABC ....a ,b ,c as usual side lengths of triangle ABC with angle A B and C **EDITED** LEAVE IT I GOT IT ...
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Find teh sum of all four digit palindromes............. u must be knowing wat a palindrome is if not *Image* it is a word or number that reads the same backwards as forwards i want a soln :) ...
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Find f(x) which is a continuos fuction such that f(x)=\frac{e^{2x}}{2(e-1)}\int_{0}^{1}e^{-y}f(y)dy+\int_{0}^{\frac{1}{2}}f(y)dy+\int_{0}^{\frac{1}{2}}\sin^{2}(\pi y)dy for practice. ...
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1)find the nth term of the sequence *Image* such that *Image* 2)Find the nth term of the sequence *Image* such that *Image* 3)Find the nth term of the sequence *Image* such that *Image* then Calculate *Image* 4)Find the n th ...
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Prove that for any triangle inscribed in a rectangular hyperbola its orthocenter also lies on that same rect hyperbola ...
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*Image* ...
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\\\texttt{If} \: f_{n}=\sum_{k=0}^{n}\binom{n-k}{k} \\\texttt{evaluate}\\ \\ \begin{vmatrix} f_{n}& f_{n+1}&f_{n+2} \\ f_{n+1}& f_{n+2}&f_{n+3}\\ f_{n+2}&f_{n+3}& f_{n+4} \end{vmatrix} ...
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1) let polynomials A(x),B(x),C(x),if dey exist satisfy for all x *Image* find polynomials A(x),B(x),C(x) 2) Find all (x,y) such that *Image* . ...
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find teh greatest value of the expression (a-x)(b-y)(c-z)(ax+by+cz) where a,b,c are known +ve quatities and a-x,b-y,c-z are also +ve. ...
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\\1)\: solve\: \frac{x-a}{b}+\frac{x-b}{a}=\frac{b}{x-a}+\frac{a}{x-b}\\ \:\:2)\: if\:f(n)=\sum_{r=1}^{n}\frac{1}{r}...then \:show \:that\:\frac{n}{2}<f(2^n-1)<n\\ 3)\:if\:(1+x)^n=\sum_{r=0}^{n}^{n}C_{r}x^r\:find \:teh\ ...
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with appropriate working f(x)= \left(1+\frac{1}{x} \right)^{x} ...
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*Image* ...
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*Image* ...
