Recently Active Mathematics Questions

1) Inside a semi-circle of unit radius, two circle of radii r1 and r2 are drawn, touching the diameter and the semicircle and also touching each other externally. Prove that the maximum value of ( r1+ r2 ) = 2(√2 -1) ...

http://cheentaganitkendra.blogspot.in/2012/02/indian-national-math-olympiad-2012.html ...

let S ≡ f(x,y) , |||x|-2|-1|| + |||y|-2|-1| = 1. If S is made out of a wire then the length of the wire required is? ...

\hspace{-16}\mathbf{(1)::\int\frac{1}{x+\sqrt{x^2+x+1}}dx}\\\\\\ \mathbf{(2)::\int\frac{x^{2001}}{(1+x^2)^{1002}}dx}\\\\\\ \mathbf{(3)::\int\frac{x^3-x}{x^6+4x^4+4x^2+1}dx} ...

Find the points where f(x) is not differentiable. f(x)=|x-1|3 +|x-2|5+|x-3| ...

Prove that the locus of the intersection of AP with the straight line through A' perpendicular to A'P is a straight line which is perpendicular to the major axis of an ellipse. ...

Equation of the common tangent to the parabolas : y^2 = 4ax; x^2 = 4ay ...

Compute: *Image* Where *Image* . ...

\mathbf{\lim_{n\rightarrow \infty}\left(2012.\bold{\sqrt[n]{2010}}-2011\right)^n} ...

\hspace{-16}(1)\;\;\int\frac{25^x}{15^x-9^x}dx\\\\ (2)\;\;\int\frac{1}{1+x^6}dx\\\\ (3)\;\;\int\frac{\sqrt{1-x^2}-x}{x^3-x^2-x+1-\sqrt{1-x^2}+x\sqrt{1-x^2}}dx ...

\hspace{-16}\mathbf{\int\frac{xdx}{\sqrt{1-x^2.(x+\sqrt{1-x^2})^8}}dx}$ ...

\hspace{-16}$Prove that $\mathbf{f(x)=\int_{0}^{\ln (x)}e^t.\sin (\pi.t^2)dt}$. Then prove that \\\\ $\mathbf{\frac{d^2}{dx^2}(f(x))}$ has at least $\mathbf{2}$ positive Real Roots. ...

\hspace{-16}$Find solution of diff. equation $\mathbf{\int_{0}^{\frac{dy}{dx}}\frac{\cos z}{16+9\sin^2 z}dz=\frac{1}{12}\tan^{-1}(x)}$ ans y = x.sin-1(4x/3)-1/4* 9-16x^2 +C ...

Find the limiting value of { (√2 + 1)n} x (-1)[(√2 + 1)n] where n →∞ {} →fractional part [.] →G.I.F. ...

IF a point moves such that twice its distance from axis of x exceeds its distance from axis of y by 2,then its locus is ...

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Points x and y lie on the side QR and RS of a parallelogram PQRS such that QX =2XR and RY=3YS.Thus the value of u such that the diagonal PR meets line XY at Z and PZ=u PR is ?Characters in bold face denote vectors. ...

1) \lim_{x\rightarrow \frac{\pi }{2}} sec^{-1}(sin x) 2) \lim_{x\rightarrow 0}cos\frac{1}{x} 3) \lim_{x\rightarrow 0}(1+sinx)^{1/x^{2}} 4) Let f( x+y/2 ) = f(x)+f(y)/2 for all real x and y.If f'(0) = -1 and f(0) = 1,find f(2) ...

G.C.D of (m,n)=1 1) x ≡3 (mod n) x ≡2 (mod m) Find x. Got it from a frnd. ...

1.pls explain these a)[-2x/pi]+1/2 = -([2x/pi]+1/2) b)-3≤|[x]|≤2 implies -2≤x<3 2. What is the formula to find number surjections from A to B? 3.If f"(x) = -f(x) and g(x) = f'(x) and F(x) = (f(x/2))2+(g(x/2))2 and gi ...

what is the value of sincube.cos+coscube.sin will u please explain me with the help of a solution ...

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1+(2+3)+(3+4+5)+,,,,,,,,,, ...

Who can do this in min 4 different ways \lim_{x\rightarrow 0}\frac{tan^{-1}x-sin^{-1}x}{sin^{3}x} ...

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Find the remainder when 2202 is divided by 101 . ...

*Image* Find the mistake.... ...

1)If x2-y2-84y=2012,x,y belonging to N,find x-3y? 2)Let S={20,21,22,23,.....210).Consider all positive differences of elements of S.If M is the sum of all these differences,find the sum of the digits of M? ...

prove that [√(4n+1)]=[√n+√(n+1)] for n belonging to positive integers. [.]→ G.I.F ...

f(x) is a real valued function satisfying f(x-y)=f(x)f(y)-f(a-x)f(a+x) f(0)=1 then f(2a-x) is a) f(-x) b) f(x) c(-f(x) d f(a) +f(a-x) ...