Recently Active Mathematics Questions

\hspace{-16}$For $\mathbf{a\;,b>0}$. Evaluate the Integral\\\\ $\mathbf{\int_{0}^{\infty}\frac{e^{ax}-e^{bx}}{x.(e^{ax}+1).(e^{bx}+1)}dx}$ ...

\hspace{-16}$The Solution of the Inequality\\\\ $\mathbf{(\cot ^{-1}x).(\tan^{-1}x)+\left(2-\frac{\pi}{2}\right).\cot^{-1}x-3\tan^{-1}x-3.\left(2-\frac{\pi}{2}\right)>0}$ ...

\hspace{-16}$Calculate all Real $\mathbf{x}$ in $\mathbf{[x]+[\sqrt{x}]=2x-2}$\\\\ Where $\mathbf{[x]=}$ Greatest Integer function. ...

\hspace{-16}$If $\mathbf{\mid z+1-i\mid=\mid \bar{z}+2-3i\mid}.$ Then Find Complex no. $\mathbf{z}$\\\\ with Min. Modulus. and also find Min. Value. ...

\hspace{-16}$In $\mathbf{\left(0,\frac{\pi}{2}\right)},$ one Solution of $\mathbf{\frac{\sqrt{3}-1}{\sin x}+\frac{\sqrt{3}+1}{\cos x}=4\sqrt{2}}$\\\\\\ is $\frac{\pi}{12}$ and other solution is $\mathbf{\frac{\lambda.\pi}{36} ...

\hspace{-16}\mathbf{\sum_{k=0}^{n}\left\{\sum_{r=0}^{k}(-1)^r.\frac{n!.2^{k-r}}{(n-k)!.(k-r)!.r!}\right\}=} ...

\hspace{-16}$Let $\mathbf{P(x)}$ is a Quadratic in $\mathbf{x}$ Satisfying \\\\ $\mathbf{P(0)=\cos^3(40^0)\;, P(1)=\cos (40^0).\sin^2(40^0)\;,P(2)=0}$\\\\ Then $\mathbf{P(3)=}$ ...

\hspace{-16}$Solve for $\mathbf{x}$ in \\\\ $\mathbf{2^x+3^x+4^x+5^x+1=2e^x+3.7^x}$ x=0 ...

\hspace{-16}$Evaluate $\mathbf{\sum_{r=0}^{n-2}2^r.\tan \left(\frac{\pi}{2^{n-r}}\right)}\forall \mathbf{n\in \mathbb{Z}\geq 2}$ ...

\hspace{-16}$Let $\mathbf{a,b,c,d}$ are the Roots of the Quadratic equation \\\\ $\mathbf{x^4+px^2+qx+r=0}$. Then find the equation whose\\\\ Roots are $\mathbf{\frac{ab-cd}{a+b-c-d}\;,\frac{ac-bd}{a+c-b-d}\;,\frac{ad-bc}{a+d ...

\hspace{-16}$Determine The Integer $\mathbf{(x,y)}$ such that \\\\ $\mathbf{\frac{x}{\sqrt{2+\sqrt{3}}}+\frac{y}{\sqrt{4+\sqrt{15}}}=\frac{2}{\sqrt{3+\sqrt{5}}}}$ ...

\hspace{-16}\mathbf{\int\frac{1}{(x^2+a^2).(x^2+b^2).(x^2+c^2)}dx} ...

\hspace{-16}\mathbf{\int_{-\frac{1}{2}}^{\frac{1}{2}}\frac{\sqrt{3-4x-4x^2}}{4x^2+4x+5}dx} ...

Prove that \bf{\sum_{r=1}^{m-1} \frac{2r^2-r(m-2)+1}{(m-r) \binom {m}{r}} = m-\frac 1m } . I'm not able to arrange it in any useful form. Kindly help. ...

What to do and what not to do in the last month before IIT-JEE http://www.youtube.com/watch?v=Z5-AfiJxjOc&context=C4acfebbADvjVQa1PpcFMQX-FKsRHXxJDA7RTt_k4sN1NL6Iapsuo= ...

What is the remainder when 256+3.911+14 is divided by 41? ...

\hspace{-16}$Solve The System of equations\\\\ $\mathbf{x^2+y^2+x+y=18}$\\\\ $\mathbf{\log_{2}x.\log_{3}y=1}$ x=2,y=3 ...

\hspace{-16}\mathbf{\int_{0}^{\pi}\ln(3+\cos x)dx} ...

\hspace{-16}$If $\mathbf{f(0)=1}$ and $\mathbf{f(1)=2}$ and $\mathbf{f(x)=\frac{f(x+1)+f(x+2)}{2}}$\\\\\\ Then $\mathbf{f(2012)=}$ f(x) = 1/3.[4-(-2)x] ...

\hspace{-16}$If $\mathbf{I_{1}=\int_{0}^{1}\frac{\ln(1+x)}{x}dx}$ and $\mathbf{I_{2}=\int_{0}^{1}\frac{\ln(1-x)}{x}dx}$\\\\\\ and $\mathbf{\left(\frac{1}{I_{1}}+\frac{1}{I_{2}}\right).\pi^2=n}$\\\\\\ Then value of $\mathbf{n} ...

Find the no. of real solutions of 2x4+1402-y4 =0 ...

find the smallest number that can be represented by a sum of 9,10 and 11 consecutive integers.....? ...

The circle x^2+(y-4)^2 = 25 intersects x-axis at points A and B . a point p lies on the major segment of the circle . the bisector of the angle APB for any point p can be given by the equation is? answer = y = mx - 1 ...

Q)The no. of rational pts(a pt is rational if both its co-ordinates are rational),on the circumference of a circle having centre (Ï€,e). (a)at most one (b)exactly one (c)exactly two (d)infinite We have to find this for variab ...

given a line with its equation ax + by + c = 0 suppose we rotate the co-ordinate axis with an angle of 78°, what will happen to the eqn. of the line? ...

\hspace{-16}$Determine $\mathbf{\mathbb{R}}$eal value of $\mathbf{x}$ in $\mathbf{1+[x]=[nx]}$\\\\ Where $\mathbf{[x]=}$ Greatest Integer function and $\mathbf{n\in\mathbb{N}}$ ...

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Show that the perpendiculars from the centre upon all chords, which join the ends of perpendicular diameters, are of constant length in an ellipse. ...

Find the coefficient of x^{\frac{n(n+1)}{2}-7} in the expansion of (x-1)(x^2-2)(x^3-3) \; \cdots \;(x^n-n) \quad; n\ge8. Help Please! ...

There is a rectangle with m vertical lines and n horizontal lines (taking the edges too). Find the no.of ways in which a pencil can travel from the North-West to the South-East corner going through the shortest possible dista ...