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A particle of mass m and charge q moves at a high speed along the x-axis.It is initially near x = -∞ and it ends up near x = +∞. A second charge Q is fixed at the point x=0,y = -d.As the moving charge passes the stationar ...
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*Image* a)For the first part the expected value would be = E(x)=\frac{1}{2}+2\left(\frac{1}{2}\right)^2+3\left(\frac{1}{2}\right)^3+\cdots=2 b)For the second part the expected value would be = E(x)=\frac{1}{2}+\frac{2}{4}+\fr ...
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Try this problem,it's really interesting. *Image* ...
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\text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n-1}+1)\ \ ...
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If f(x) be a positive function in [a,b] prove that, \left|\left(\int\limits^{b}_{a}f(x)dx\right)\left(\int\limits^{b}_{a}\frac{1}{f(x)}dx\right)\right|\geq (b-a)^{2} ...
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How to find the circumference of an ellipse? ...
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A circle along with one of its diameter AB are given.There lies a point P in the plane.Construct the perpendicular to AB through P using only a ruler.(A ruler can only connect 2 points). ...
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Represent m6+n6 as a sum of 2 squares other than (m3)2+(n3)2. Think its easy....give it a try!:P ...
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\text{Here is an awesome probability question that I solved recently.}\\\text{I know this is quite a popular question so don't just copy-paste it directly from some other site.}\\\text{Try it yourself.It's a really good quest ...
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I know something is wrong in the following proofs.Can't figure out which step is wrong. Proof of -1 =1: *Image* Proof of 1=3: *Image* ...
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1)[easy] Prove that: \dpi{200} asin(x)+bcos(x)\leq \sqrt{a^{2}+b^{2}} 2)[hard] Prove that for any triangle with sides a,b,c and area A. \inline \dpi{200} a^{2}+b^{2}+c^{2}\geq 4\sqrt{3}A 3)[harder] How should n balls be put i ...
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Although some you might have seen this question before give it a try. If p,q are positive integers such that- 1- 1/2 + 1/3 - 1/4 +.........- 1/1318 + - 1/1319 = p/q Show that 1979 divides p. ...
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Can you cut a hale into a cube so that a slightly larger cube can pass through the hole? ...
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Q1:The teacher of a class having a large number of students decides to take a test.After the test ended the teacher took the papers from the students and randomly distributed them among the students to check. Prove that the p ...
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We know that ΣnCr*r2= n*2n-1 + n*(n-1)*2n-2 (see "http://www.targetiit.com/discuss/topic/21790/solve-this-binomial-question/" for the proof) Further we can find ΣnCr*r3 = n*2n-1 + 3*n(n-1)*2n-2 + n(n-1)(n-2)*2n-3 However on ...
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Find the general formula for: 1k+2k+3k+..........+nk ...
