Recently Active Algebra Questions

find the no. of real solutions of e|x|-|x|=0 please solve graphically.. ...

Please visit this link:: http://www.artofproblemsolving.com/Forum/search.php ...

\hspace{-16}$Prove that for all Natural no. $\bf{k}$\\\\ $\bf{(k^3)!}$ is Divisible by $\bf{(k!)^{1+k+k^2}}$ any method other then Induction ...

A and B alternately throw a die....The numbers they get on their throws are individually added......the first person to get a overall sum of 10 wins....what is the probability that A wins the game given that it is the first t ...

if the range of tan-1 (3x2 + bx + c) is [0,pi/2) then relate b and c. ...

Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can formed such that Ysubset X, Z subset X and Y∩Z is empty, is? ...

\hspace{-16}$If $\bf{xyz=10^{81}}$ and $\bf{\ln(x).\ln(yz)+\ln(y).\ln(z)=468}$\\\\\\ Then $\bf{\sqrt{(\ln(x))^2+(\ln(y))^2+\ln(z)^2}=}$\\\\\\ Where $\bf{x,y,z\in \mathbb{R^{+}}}$ ...

\hspace{-16}$Is There is any Positive Integer Triplet $\bf{(x,y,z)}$ for which $\bf{8^x+17=y^z}$ ...

A family has two children. Assume that birth month is independent of gender, with boys and girls equally likely and all months equally likely, and assume that the elder child’s characteristics are independent of the younger ...

\hspace{-16}$Find all Positive Integer Triplet $\bf{(x,y,z)}$ that satisfy\\\\ $\bf{x!+y!=15\times 2^{z!}}$ ...

\hspace{-16}\bf{(1)}$\;\; Find value of $\bf{x}$ in $\bf{\lfloor 19x+97 \rfloor = 19+97x}$\\\\ $\bf{(2)}$\; \; Calculate Sum of $\bf{\sum_{k=1}^{2012}\lfloor \sqrt{k} \rfloor =}$\\\\ Where $\bf{\lfloor x \rfloor =}$ Floor Fun ...

\hspace{-16}$If The Polynomial can be express in the form of Diff. of $\bf{2}$ cubes like\\\\ $\bf{9x^2-63x+c=(x+a)^3-(x-b)^3}$. Then $\bf{\mid a-\mid b \mid +c\mid=}$ ...

\hspace{-16}$If $\bf{f(x)=x^m(b^n-c^n)+(c^n-x^n)+c^m(x^n-b^n)}$. Then Prove that\\\\ $\bf{f(x)}$ is Divisible by $\bf{x^2-(b+c).x+bc}$\\\\ Where $\bf{m,n,p\in\mathbb{Z^{+}}}$ http://www.goiit.com/posts/list/algebra-challenge- ...

\hspace{-16}$If $\bf{xy=1}$ and $\bf{x,y\in\mathbb{R}}$ and satisfy the Relation $\bf{\left\{(x+y)^2+4\right\}.\left\{(x+y)^2-2\right\}\geq \mathbb{A}.(x-y)^2}$\\\\ Then $\bf{\mathbb{A}}$ is ...

\hspace{-16}$If two equations $\bf{ax^4+bx^3+c=0}$ and $\bf{cx^4+bx^3+a=0}$ have one root\\\\ in common.\; Then find all the possible values of $\bf{b}$ ,if $\bf{a+c=100}$ \\\\ and also the common root. ...

\hspace{-16}\bf{\mathbb{F}}$ind all Matrix $\bf{\mathbb{X}}$ that satisfy the Matrix Equation\\\\ $\bf{\begin{pmatrix} \bf{1} & \bf{2}\\ \bf{3} & \bf{5} \end{pmatrix}\mathbb{X}=\begin{pmatrix} \bf{1} & \bf{2}\\ \bf{3} & \bf{5 ...

\hspace{-16}$Find total no. of matrices for which Inverse of a matrix is exists\\\\ If its element are taken from the set $\bf{\left\{0,1\right\}}$ ...

\hspace{-16}$Find all Real values of $\bf{x}$ that satisfy the equation\\\\ $\bf{x^2=4+[x]}$\\\\ Ans = - 2 and x = 6 I have solved it using very Lengthy Method can anyone have a analytical Method without Using Graph ...

Let S={1,2,3,..........n}.If x denotes the set of all subsets of S containing exactly two elements having 1 as least element,then what is the cardinality of X? ...

\hspace{-16}\bf{\mathbb{I}}$f $\bf{a\in \mathbb{Z}}$. Then Find all Integer Roots of the equation \\\\ $\bf{x^3+ax-13x+42=0}$ ...

\hspace{-16}$Find Real values of $\bf{x}$ in \\\\$\bf{2012^{\log_{2010}(x-1)}-2010^{\log_{2012}(x+1)}=2} ...

\hspace{-16}$The no. of solution of the equation\\\\ $\bf{e^{-\sqrt{\mid \ln\{x\}}\mid}-\{x\}^{\frac{1}{\sqrt{\mid \ln\{x\}}\mid}}=\left[sgn(x)\right]}$\\\\ Where $\bf{\{x\}=}$Fractional part and $\bf{\left[x\right]=}$Integer ...

1) Let f : R -> (0,pi/2] then find the set of val. of a for which f(x) = cot-1 (x2 - 2ax + a + 1) is surjective ..... !! sorry for the irrelevant title....!! ...

x^2 - a*x + b = 0 x^2 - b*x + a = 0 Both these equations have positive,integral and distinct roots. Find a and b. ...

\hspace{-16}\bf{\sum_{n=1}^{\infty}\;\sum_{m=1}^{\infty}\frac{m.n}{(m+n)!}}= ...

every now n then in calculus we encounter this function........moreover surprisingly while solving problems we come across a few properties which r usually not given under standard list given in books.........so i request all ...

\hspace{-16}\bf{\mathbb{C}}$alculate Integer value of $\bf{n}$ in \\\\\\ $\bf{\frac{1}{i}+\frac{2}{i^2}+\frac{3}{i^3}+.........+\frac{n}{i^n}=405}$ ...

\hspace{-16}$Find Sum of $\bf{4}$ digit no. that can be formed with the digit $\bf{1,2,3,4,5....,9}$\\\\ Repetition not allowed ...

\hspace{-16}\bf{\mathbb{S}}$olve the inequality\\\\ $\bf{\mid x-1 \mid+3\mid x-3 \mid+5\mid x-5 \mid+.......+2009\mid x-2009\mid}$\\\\\\ $\bf{\geq 2 \mid x-2 \mid+4\mid x-4 \mid+6\mid x-6 \mid+.......+2008\mid x-2008\mid}$ ...

\hspace{-16}$find the last six digit of the product $\bf{(2010)\times (5)^{2014}}$ ...