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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 $\bf{x,y,z\in \mathbb{R^{+}}}$ ...

A man is sitting on a train. A coin drops from his pocket. It falls in front of him. The train is? ...

\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 ...

\hspace{-16}\bf{\mathbb{F}}$ind Real values of $\bf{x}$ that satisfy the equation\\\\ $\bf{4^{x.\sin^{-1}(x)}+4^{x.\cos^{-1}(x)}=2^{\frac{2+\pi.x}{2}}}$ ...

If you have any question to ask, please ask here. ...

The no. of possible triples (a1,a2,a3) such that a1+a2cos2x+a3sin2x=0 for all x is (a)0 (b)1 (c)2 (d)Infinite ...

\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 ...

*Image* ...

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

Two particles A and B start moving simultaneously along the line joining them in the same direction with acceleration of 1 m/s2 and 2 m/s2 and speeds 3 m/s and 1 m/s respectively.Initially A is 10m behind B.What is the minimu ...

If a and b are two vectors then the value of (a+b)x(a-b) is (a)2(bxa) (b)-2(bxa) (c)bxa (d)axb ...

A particle is moving in a circle of radius 4 cm with constant speed of 1m/s.Find average acceleration in a time interval from t=0 to t=T/4.Here,T is the time period if the particle.Give only the magnitude.(T turns out be abou ...

Find the minimum Value of cot1 x cot2 x cot3 x ...... cot44. ...

Explain the Process and what should be the correct answer and why? *Image* ...

\hspace{-16}$If $\bf{x = \prod_{r=0}^{44}\sin \left(\left(2r+1\right)^0)}$\\\\\\ Then $\bf{x}$ is $\bf{\mathbb{R}}$ational or $\bf{\mathbb{I}}$rrational ...

A balloon starts rising from the earth's surface.The ascension rate is constant and equal to vo.Due to the wind,the balloon gathers the horizontal velocity component vx=ky,where k is a constant and y is the height of ascent.F ...

\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 ...