Recently Active Mathematics Questions

\hspace{-16}\mathbb{I}$f $\bf{a_{0}=0}$ and $\bf{a_{n}=3\left(a_{n-1}+1\right)\forall n>1}$\\\\\\ Then Remainder when $\bf{a_{2010}}$ is Divided by $\bf{11}$ ...

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came across a interesting questin...not hard but... if 60a=3 and 60b=5 find the value of 12x where x= 1-a-b/2(1-b) ? ...

if m,n are integers satisfying 1+cos2x+cos4x+cos6x+cos8x+cos10x= cos mx.sin nx/sinx then (m+n) equals ? A)9 B)10 C)11 D)12 ...

1) tan3x +cos (2.5x) 2) cos(cosx) + cos(sinx) ...

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 ...

2. Triangle ABC is divided into four parts by straight lines from two of its vertices. Area of three triangular parts are 8 , 5 and 10. what is the area of remaining part? *Image* . ...

\hspace{-16}$Is There is any Relation exists b/w the angle $\bf{M\;\;,N}$ and $\bf{P}$ Such \\\\ that $\bf{\cos^2(M)+\cos^2(N)+\cos^2(P)+2.\cos(M).\cos(N).\cos(P)=1}$ ...

\hspace{-16}\bf{\mathbb{F}}$ind a function $\bf{f:\mathbb{R}\rightarrow \mathbb{R}}$ that satisfy\\\\\\ $\bf{2f(x)+f(-x)=\left\{\begin{matrix} \bf{-x^3-3}\;\;\;,\;x\leq 1\\\\ \bf{7-x^3}\;\;\;,\;x> 1 \end{matrix}\right.}$ ...

What will be the graph of (Sinx)/x ? ...

\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 ...

If 0 = 0 Is 00 = 1 and guys I have some doubt about n/0 where n ≠0 Why is it equal to ∞? Please guys, can you explain this to me in a simple way? [7] [7] [7] [7] [7] [7] ...

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 ...

What will be the graph of (Sinx)/x ? ...

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

\hspace{-16}\bf{\mathbb{S}}$olve for $\bf{x}$\\\\ $\bf{(1)\;\; \lfloor 1.5 \rfloor x+\lfloor x \rfloor=5}$\\\\ $\bf{(2)\;\; \lfloor x \rfloor+\lfloor 2x \rfloor \leq \sqrt{3}}$ ...

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 $\bf{8^x+17=y^z}$ ...

∫√x+√x2+2.dx plz help me out to solve dis one ...

\hspace{-16}\bf{\left\lfloor \dfrac{10^{20000}}{3+10^{100}}\right\rfloor=}$\\\\\\ Where $\bf{\lfloor x \rfloor =}$ Floor Function. ...

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{P}}$rove that $\bf{\prod_{k=1}^{n-1}\cos\left(\frac{k\pi}{n}\right)=\frac{\sin \left(\frac{n\pi}{2}\right)}{2^{n-1}}}$ can anyone help me for solving the Given Question. I have Got \hspace{-16}$\displa ...