Recently Active Mathematics Questions

Sn = x + x2 +x4 + ..... +x2n i remeber man111 posting a question some time ago related to this i think when |x|<1 and n→∞ , this sum should be converging which is why i am interested to find the result. plz try this pr ...

In how many ways can a dice be coloured with 6 different colours? Means all the 6 faces should have 6 different colours. there are no other conditions.. ...

Not my Doubt, Just a share : Normals are drawn from Point P with slopes mi (i=1,2,3) to the parabola y2 = 4x. If the locus of P with m1 . m2 = α is a part of parabola itself, then α C1 + α3 C3 + α5 C 5 + ..... equals? ...

Q: If z3+(3+2i)z+(ai-1) = 0 has a real root, then ' a ' lies in the interval (a ε R) : My Ans: (-1,0) , Given answer (-2,3) ...

\hspace{-16}$Find Minimum value of $\mathbf{xy}\;,$ Given that\\\\ \begin{Bmatrix} \bold{x^2+y^2+z^2=7} \\\\ \bold{xy+yz+zx=4} \end{Bmatrix}\\\\\\ Where $\mathbf{x,y,z\in\mathbb{R}}$ ...

\dpi{120} \hspace{-16}$If $\mathbf{I_{1}=\int_{0}^{\infty}(1+x^2)^{-2012}dx}$ and $\mathbf{I_{2}=\int_{0}^{\infty}(1+x^2)^{-2011}dx}$\\\\\\ Then find value of $\mathbf{\frac{I_{1}}{I_{2}}=}$ Ans=(4021)/(4022) ...

\hspace{-16}\mathbf{\int_{\frac{1}{2}}^{2}\frac{\tan^{-1}(x)}{x^2-x+1}dx} ...

If (z+1)^7+z^7=0 , then find \sum_{k=0}^{k=6} \text{Re}(z_k) , where zk are roots of the the given equation. ...

*Image* *Image* *Image* *Image* *Image* *Image* *Image* please provide solutions. ...

Let P be any point on the parabola *Image* between its vertex and the positive end of the latus rectum. M is the foot of perpendicular from the focus S on the tangent at P. Then find the maximum value of AREA of *Image* ? ...

An elipse of major axis 20√3 and minor axis 20 slides along the co-ordinate axes and always remains confined in the 1st quadrant. The locus of the centre of the ellipse describes the arc of a circle. Find the length of this ...

*Image* Ans : b ...

There r exactly 2 points on the ellipse x2/a2 =+ y2/b2 =1.whose distance from the centre of the ellipse is same and equal to (1/√2 ) x (√(a2+2b2). Find the eccentricity of the elipse. ...

find the remainder when 21990 is divided by 1990? ...

1) Find the sum of [(1/3√4) +(1/3√5) +(1/3√6).............(1/3√1000000)] [.] stans for G.I.F. 3√n denotes the cube root of n. ...

Q) In how many ways can you colour the faces of a cube with six di erent colours, if all the faces are to have a di erent colour ? i am getting 30 . guys, plz try and tell me your answers. ...

the eqn 8x^2 -14xy +3y^2 +10x +10y -25=0 represents adjacent sides of a ||ogram whose diagonals intersect at the points(3,2)...find the eqn of other 2 sides ,.... ...

Show that: cos( π/7 )cos( 2π/7 )cos( 3π/7 )= 1/8 ...

6x + 8y = 48 intersects the coordinate axis at A and B respectively. a line L bisects the area and the perimeter of the triangle AOB. where O is the origin. the number of such lines possible is - (a) 1 (b) 2 (c) 3 (d) more th ...

If a triangle is formed by any 3 tangents of the parabola y2= 4ax, two of whose vertices lie on the parabola x2=4by, then find the locus of the 3rd vertex. ...

For x>0, and A,B,C being the angles of a triangle, Prove that *Image* ...

1) From a point P , Tangents are drawn are drawn to the ellipse x2/a2 + y2/b2 =1. If the chord of contact touches the ellipse x2/c2 + y2/d2 =1 tHEN FIND THE LOCUS OF P. ...

\sum_{0\le i}\sum_{<j\le n} \left(\frac{i}{\binom {n}{i}} + \frac{j}{\binom {n}{j}} \right) = \frac{n^2}{2} \cdot \sum_{r=0}^{n}\frac{1}{\binom{n}{r}} ...

1 + 2w +3w2 +..... nwn-1 find the sum where,w = nth root of unity ...

Wen we r given to find the equation of a circle thru three given points, we go by the family approach..we tend to form the equation of the circle taking the first two points as the end point of the diameter nd den form a stra ...

\hspace{-16}\displaystyle\mathbf{\lim_{n\rightarrow \infty}\frac{1}{\bold{\sqrt[2011]{n^{2011}+1}}}+\frac{1}{\bold{\sqrt[2011]{n^{2011}+2}}}+.......+\frac{1}{\bold{\sqrt[2011]{n^{2011}+n}}}} ...

\hspace{-16}$(1)\;\; Find No. of $\mathbf{\mathbb{R}}$eal Roots of $\mathbf{e^{ax}=bx}$\\\\ Where $\mathbf{a,b>0}$\\\\\\ $(2)\;\; $No. of $\mathbf{\mathbb{R}}$eal Roots of the equation $\mathbf{3^x+4^x+5^x = x^2}$\\\\\\ $( ...

Find the smallest value for the function : f(x) = |x-2| + |x+3| + |x-4| ...

Points whose position vectors are a+b,a-b,a+kb are collinear for: (a) Only one integral value of k (b) All integral values of k (C) None of these ...

\hspace{-16}$If $\mathbf{A=\left\{\frac{2012}{2013}\right\}+\left\{2.\frac{2012}{2013}\right\}+............+\left\{2012.\frac{2012}{2013}\right\}}$\\\\\\\\ and $\mathbf{B=\left\{\frac{2014}{2013}\right\}+\left\{2.\frac{2014}{ ...