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*Image* RR' is a road on which Powerplant P has to be constructed. There are two villages A & B on same side of the road. Find the optimum location of poweplant P such that wiring cost i.e. PA+PB is minimum. Note: You sho ...
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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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Take a (one-dimensional !) rod of length \ell and remove the middle one-third. Then remove the middle one-third of the remaining two pieces, then remove the middle one-third of the remaining four pieces, and so on forever. Le ...
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Take a square of side \ell , and remove the "middle'' square (1/9 of the area). Then remove the "middle'' square from each of the remaining eight squares, and so on, forever. Let the final object have mass m . Find the moment ...
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*Image* Q. A thin spherical shell having uniform density is cut in two parts by a plane and kept separated as shown in fig. The point A is the centre of the plane section of the first part and B is the centre of the plane sec ...
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A heavy, flexible, inelastic chain of length L is placed almost symmetrically onto a light pulley which can rotate about a fixed axle, as shown in the figure. *Image* What will the speed of the chain be when it leaves the pul ...
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A tree trunk in form of a cylinder of radius R lies on a horizontal field. A lazy grasshopper wants to jump over it. What minimum launching speed will suffice for it? Assume that the air resistance is negligible and that the ...
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*Image* A fountain consists of a small hemispherical rose (sprayer) which lies on the surface of the water in a basin, as illustrated in the figure. The rose has evenly distributed small holes in it, through which water spurt ...
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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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*Image* The setup shown consists of two identical rods (mass m) hinged together at the ends. This setup is held in the position shown. Now we start applying a constant force F to the free end as shown Find the initial angular ...
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I C or Instantaneous Centre of Rotation It is a simple theory to make problems of specific type easier......... if wisely used..... It states When a body is moving on horizontal floor with pure rolling, then it is as good as ...
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Evaluate: \int_{0}^{a}{\frac{ln(1+ax)}{1+x^2}}dx ...
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The cube shown below has 5 faces grounded. The sixth side, insulated from the others, is held at a potential V0. What is the potential at the center of the cube and why? *Image* ...
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Find the following limit for \alpha >1 : \lim_{n\to \infty} n\left(\dfrac{1^\alpha + 2^\alpha + \ldots + n^\alpha}{n^{\alpha+1}}-\dfrac{1}{\alpha +1}\right) Here n is a natural number. ...
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if we keep a fish in btw the plates of a capacitor can we detect the freshness of fish ?????if yes then how??? try it .................................think!/..if u r able 2 answer it this really mean the surety of ur basics ...
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This is a question that came in our 2007 midsem which i have no clue how to do. Question : A particle follows a trajectory given as R = Aθ, where θ is the polar angle.in a horizontal plane. The trajectory is such that the w ...
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What is \huge \lim_{n \rightarrow \propto }\frac{x^{n}}{n!} ????? ans : 0 (Right now I am studying in a state engg colg. in 1st yr. I came across this qsn once in success magnet of Aakash Inst. and another time while the teac ...
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Suppose you drill a narrow tube (with cross sectional area A) from the surface of the earth down to the center. Then line the cylindrical wall of the tube with a frictionless coating. Then fill the tube back up with the dirt ...
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*Image* *Image* A cylindrical vessel of area of cross section A and filled with liquid to a height of h1 has a capillary tube of length l and radius r protruding horizontally at its bottom.If the viscosity of liquid is \eta a ...
