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1/2+1/3+1/4.....+1/n is never an integer.. prove Hint: think of the largest prime! ...
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Σk=0 to r rCk×(2n-r)C(n-k) = 2nCn ...
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A uniform rod of length l is pivoted at pt. A.It is struck by horz. force which delivers an impulse J at distance x from pivot.For what value of x , the impulse delivered by pivot is equal to zero?????? ...
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Π/2 statement1) ∫ sin2kxcosxdx=Π/2 ;kε I+ 0 statement2) sin2kx/sinx=2[cosx+cos3x+..........+cos(2k-1)x] are both the statements true if yes then is statement 2 reason of 1 ...
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There is a parabolic shaped bridge across a river of width 100m. The highest point of the bridge is 5m above the level of the banks. A car of mass 1000kg is crossing the bridge at a constant speed of 20m/s. Find the force exe ...
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FIND I I=∫ (x2.tan-1x)/(1+x2)3/2 dx ...
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Two blocks mass m and 2m are kept on smooth horz surface and connected to each other using spring of "k".Initially spring is unstretched.A constant horz. force F applied to heavier block .Suppose at time t , displacem ...
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A particle moves from rest at A on the surface of a smooth circular cylinder of radius R .At B it leaves the cylinder.The equation relating alpha and beta is?? *Image* ...
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Two equal spherical bubbles(radius=a) coalease to form a spherical bubble of radius b.If P is atmospheric pressure,then the surface tension of bubble is???????? ...
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A solid copper (density Ï and specific heat c) of radius r at an initial temperature 200 K is suspended inside a chamber whose walls are at almost 0 K.What is the time required for the temperature of sphere to drop to 100K ...
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*Image* two cylinders having radii R1andR2respectivelyand rotational inertias I1and I2respectiveely are supported by axes perpendicular to the plane.The large cylinder is initilally rotating with angular velocity ω0The small ...
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if f(x) is a continuous function from R->R and attains only irrational values , then 100 summation( f(r) ) = r=1 (a) 200 summation( f(2r+1) ) r=100 (b) 200 summation( f(r) ) r=101 (c) 101 summation( f(r) ) ...
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A small ring of mass `m` is threaded on a horizontal smooth rod which is rotating about its end with constant angular velocity `ω` . The ring is initially located at the axis of rotation.When the distance of the ring from th ...
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Two parallel proton beams are moving in same directions.Will they attract or repel each other ?? ...
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Suppose we take the first n primes, multiply them together, and add one. Does this number have to be prime? Give a proof or a counterexample. be confident in your answer ...
