Recently Active Mathematics Questions

Question of Ramanujan contest... ...

1) Show that [5x]+ [5y] is greater than or equal to [3x+y] + [3y+x] where x,y greater than or equal to 0.. ...

Find range of the following functions 1. y = sin2x+sinx-1/sin2x-sinx+2 2. y = (tan-1x)2 + 2/√(1+x2) ...

Determine the largest number in the infinite sequence 1^1/1 , 2^1/2 , 3^1/3 , 4^1/4 , ............ n^1/n ...

here is a 3 x 3 square.... *Image* how many triangles can be formed with the dots being the three vertices of the triangle?? ...

f(x) is an invertible function and f(x)=xsin x ; g(x)=f -1(x). find the area bounded by y=f(x) and y=g(x). ...

1) [x2+2x] = [x]2+2[x] ....Find the real solution set of x. [.] Stands for G.I.F. (INMO 2009) ...

find the least value of x2cot9+y2cot27+z2cot63+w2cot81 if x+y+z+w=5 ...

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Find the value of \sqrt{7+\sqrt{7-\sqrt{7+\sqrt{7-....\propto }}}} ? my method... let \sqrt{7+\sqrt{7-\sqrt{7+\sqrt{7-....\propto }}}} =x and {\sqrt{7-\sqrt{7+\sqrt{7-....\propto }}}} =y now, x2=7+y and y2=7-x subtracting the ...

1,Prove for positive a,b,c (b≠1) , alogbc = clogba 2,In a small sweet shop people usually buy either one cake or one box of chocolate ,One day the shop sold 57 cakes and 36 boxes of chocolate,How many customers were there t ...

0<x,y<1 , Prove that x^{y}+y^{x} > 1 . ...

\hspace{-16}$Find real values of $\mathbf{x}$ in $\mathbf{x^2-(1+[x]).x+2011=0}$\\\\ Where $\mathbf{[\;.\;]=}$ Greatest Integer function. ...

\hspace{-16}$Find Complex no. $\mathbf{z}$ Which satisfy the equation \\\\ $\mathbf{\left|\frac{z-\bar{z}-i}{z+\bar{z}+2}\right|=\frac{\sqrt{2}}{2}}$ ...

\hspace{-16}$Prove that the equation $\mathbf{2x^{n+2}+1=3x}$ has one real root in $\mathbf{(0,1)}$ ...

\hspace{-16}$If $\mathbf{f(x)=x^{n+8}-10x^{n+6}+2x^{n+4}-10x^{n+2}+x^n+x^3-10x+1}$\\\\ Then Find $\mathbf{f(\sqrt{2}+\sqrt{3})=}\;,$ Where $\mathbf{n\in\mathbb{Z^{+}}}$ ans = 1+ 2 - 3 ...

Note : The question is NOT incorrect A and B are 2 points 30 m apart in a line on the horizontal plane through the foot of a tower lying on opposite sides of the tower,If the distances of the tower from A and B are 20 m and 1 ...

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Roots of the equations x2+px+q=0 & x2+rx+s=0 are respectively (α,β), (γ,δ). Write down the value of {(α-γ)(α-δ)(β-γ)(β-δ)} in terms of p,q,r,s . And find out the condition of having common roots of those equetions ...

can any1 prove the result that number of digits in xy is [ylogx+1]....where [] denotes G.I.F? ...

How do we integrate x2/(a+bx)2.????(indefinite) ...

given for angles A1,A2,A3 ΣcosA = ΣsinA = 0 prove that 1)Σcos2A = Σsin2A = 0 2)Σcos2A = Σsin2A = 3/2 ...

find the first non-zero digit in 80!? ...

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A tank contains 100 Litres of an aqueous solution containing 10 Kg of salt water is entering in the tank at the rate of 3 Litres per minute and the mixture is flowing out at 2 litre per minute, the concentric is maintained un ...

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if 21(x2 + y2 + z2 )=(x + 2y +4z)2 find the relation between x,y,z a)ap b)gp c)hp d)none of them problem form new pattern math-sk goyal ...

1) Find the last digit of ((5!+9)(6!+4))100! How do we do these types of sums? i think we can't do this by taking modulo 10... ...

f(x)= (e[x]+|x| -2)/[x]+|x| Find limit of f(x) when x tends to 0.[x] stands for G.I.F and |x| denotes the modulus sign. ...