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A stone of weight W is thrown straight up from the ground with an intial speed u. If a drag force of constant magnitude f acts - on the same through out its flight , the speed of stone just before reaching the ground is (1) usqrt((W-f)/W) (2) usqrt((W+f)/f) (3) u sqrt((W+f)/(W-f)) (4) u sqrt((W-f)/(W+f))

A continuous,even periodic function f with period 8 is such that f(0)quad =0.f(1)=2.f(2)=1f(3)=2.f(4)=3 then the value of cos^(-1)(cos(f(9)+2f(20))) is equal to

Find the zeros of the polynomial f(u)=4u^(2)+8u, and verify the relationship between the zeros and its coefficients.

A short linear object of length b lies on the axis of a concave mirror of focal length F at a distance u from the pole. The length of the image will be

Let f(x) =cos^(-1) 2x. Then dom (f )=?

If for all real values of u and v,2f(u)cos v=(u+v)+f(u-v) prove that for all real values of x,f(x)+f(-x)=2a cos xf(pi-x)+f(-x)=0f(pi-x)+f(x)=2b sin x. Deduce that f(x)=a cos x+b sin x, where a,b are arbitrary constants.

An apple falls from a tree because of gravitational between the earth and apple. If F_(1) is the magnitude of force exerted by the earth on the apple and F_(2) is the magnitude of force exerted by apple on earth, then