Recently Active Mathematics Questions

If f(x) = f(xy)+f(\frac{x}{y}) \text{for all } x \epsilon \mathbb{R^{+}} and f(1) = 0 , f ' (1) = 0 , then find the f(x). Please Help I just can't make this : f ' (1) = 0 ? ...

If Sn=(1.2)/3! + (2.22)/4! + (3.23)/5! +...............upto n terms. Then find sum of infinite terms. ...

nth term of a series can be written as ar= f(r) - f(r-1), then Sn= \sum_{r=1}^{n}{a_{r}} =f(n) - f(0) and S∞= *Image* Sn , then Value of \sum_{r=1}^{infinity}{(4r-1)5^{r}/(r^{^{2}}+r)} is?? ...

Q) Find the maximum radius of a semi-circle that can be placed inside a square of side 'a' ...

Value of k for which 4x2+4x+1=0 has exactly one point of intersection with k-|x+(1/2)| is equal to: a) 1 b) 2 c) 3/2 d) 3/4? ...

Let P(x) = x^{6}-x^{5}-x^{3}-x^{2}-x Q(x) = x^{4}-x^{3}-x^{2}-1 If a,b,c,d are roots of q(x) then find the value of P(a)+P(b)+P(d) ? ...

\int (x^{3}-3x^{2}+2)^{2012}dx ...

Start with the set S - { 3 , 4 , 12 } . In each step , you may chose two numbers " a " and " b " from S and replace " ( . 6 a - . 8 b) " by " ( . 8 a + . 6 b ) " . Can you form a set P - { 4 , 6 , 12 } by finitely many steps ...

Can anyone explain reciprocal system of vectors? Its the only topic I am not understanding properly! :/ ...

\int_{-10}^{10}{xe^{x[x+\frac{1}{2}]} dx} Where [.] is Floor function. ...

I've got a problem which I am not sure of the method of solving. 3x + 36 x 2 = 37 3x + 729 x 2 = 36 x 3 3x + 1458 = 729 x 3 3x = 2187 - 1458 3x = 729 3x = (3)6 x = 6 But isnt there any other method of solving? Please help ...

\left\{ \left( ^{n}C_{0}+^{n}C_{3}+...\right)-\frac{1}{2}\left(^{n}C_{1}+^{n}C_{2}+^{n}C_{4}+^{n}C_{5}+.... \right)\right\}^{2}+\\\frac{3}{4}\left(^{n}C_{1}-^{n}C_{2}+^{n}C_{4}-^{n}C_{5}+....\right)^{2} = ? ...

If z=log(tan\frac{x}{2}) and \frac{d^2y}{dx^2}+cotx\frac{dy}{dx}+4ycosec^{2}x =0 then show that \frac{d^2y}{dx^2}+4y=0 ...

\hspace{-16}$Prove that\\\\ $\mathbf{\binom{2n+1}{1}.\binom{2n+1}{3}.\binom{2n+1}{5}.......\binom{2n+1}{2n-1}.\binom{2n+1}{2n+1}<\left(\frac{4^n-1}{n}\right)^n} ...

\hspace{-16}\int\frac{1+\sin x}{x\cos x}dx ...

Find " m " such that (x^{2}-5x+4)^{2}+(2m+1)(x^{2}-5x+4)+3=0 has two distinct Real roots. ...

If h(x)= 10/x -2 find directly h-1(2) ...

find the equation to the circle which touches the y-axis at origin and passes through the point (a,b). ...

find the eq. to the circle which touches the x-axis , passes through the pt.(1,1)&whose centre lies in the first quadrant on the line x+y=3 . ...

*Image* ...

In a Triangle ABC, the bisector of angle A meets the opposite side at D. Using vectors Prove that BD : DC = c : b. (AIEEE Question Doubt) ...

Given that the equation x^4+px^3+qx^2+rx+s=0 has four real, positive roots, prove that- (a)pr-16s\geq 0 (a)q^2-36s\geq 0 Is there any proof without using Cauchy-Schwarz? ...

You have bought n chocolates from a shop. Now the shopkeeper offers that if you return the wrappers, then for every 3 wrappers, he will give you 1 more chocolate. And you can continue this exchange offer until you run out of ...

Q1. We have T_{n}=(n^2+1)n! and S_{n}=T_{1}+T_{2}+....+T_{n} , If \frac{T_{n}}{S_{n}} =\frac{a}{b} where gcd(a,b)=1, , then find b-a. Q2. No of ordered pairs (a,b) such that (a+ib)^{2010}=a-ib is Q3. Let A,B,C be three subset ...

Is there any proof to (n!)2≥nn without using induction? ...

\hspace{-16}$Find Max. and Min. value of $\mathbf{f(x,y)=\frac{2x^2+7y^2-12xy}{x^2+y^2}}$\\\\ Where $\mathbf{x,y}$ are Real no. not Simultaneously Zero ...

\hspace{-16}$Find Max. of Constant $k$ such that for any positive real no. \\\\ $a\;b\;,c$ with $abc=1$ satisfy the Inequality\\\\ $a^2+b^2+c^2+3k\geq (k+1)(ab+bc+ca)$ ...

\hspace{-16}$Find all $a > 0,\;$ for which the equation\\\\ $a^{2x}- 4(x+1).a^x + 3x^2 + 10x + 3 = 0$ has $2$ real roots\\\\ in the interval $\left[-1, 2\right]$\\\\ ...

\hspace{-16}$Calculate value of \\\\ $\binom{2010}{1}-\binom{2010}{3}+\binom{2010}{5}+................-\binom{2010}{2007}+\binom{2010}{2009}=$ ...

Call a set of integers "spacy" if it contains no more than one out of any three consecutive integers. How many subsets of {1, 2, 3, ....... 12}, including the empty set, are spacy? ...