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Evaluate: \lim_{n\to\infty}\dfrac{1}{n}\sum_{k=1}^n\left(\left[\dfrac{2n}{k}\right]-2\left[\dfrac{n}{k}\right]\right) Here [x] represents the greatest integer less than or equal to . ...
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one for teachers and senior students i was solving a puzzle and i got something like 10∫lnx. ln(1-x) / x.(1-x) dx can it be simplified to give an exact value by an expert with loads of experience ? the ans im expecting shud ...
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2 candidates contested for an election, A & B. A got a votes, while B got b. Given a>b, find probability that A was ahead of B - throughout the competition..... SHOULD IT NOT BE JUST 1/2 ?????????????? ...
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If z = \cos \frac{2 \pi}{n} + i \sin \frac{2 \pi}{n} , n \in \mathBB{N}; n \ge 3 define A = \{1,z,z^2,z^3,...,z^{n-1} \} B = \{ 1, 1+z, 1+z+z^2,...,1+z+z^2+...+z^{n-1} \} Determine A \bigcap{B} ...
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Prove the following (a2<1) a) \int _{0} ^ { \pi } ln(1-2a \cos \theta +a^2) d \theta=\begin{Bmatrix} 0 & a<1\\ 2\pi lna & a>1 \end{Bmatrix} b) \int _{0} ^ { \pi } ln(1-2a \cos \theta +a^2)\cos n \theta d \theta= - \f ...
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find *Image* ...
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There was this one question in ISAT paper-I which had this diagram- *Image* It was asked to describe the bouancy force F on the cylinder as a function of height 'h'. My query- Was 'h' to be taken from top the bottom of the co ...
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Consider a drop of conducting liquid in gravity free space. Its radius is R while the surface tension of the liquid is T. Now the drop is supplied some charge Q. For what values of Q is the drop stable. ...
