Recently Active Mathematics Questions

\hspace{-16}\bold{(Q)::}\; $If $\mathbf{p(z)=|2z-1-i|+|3z-2-2i|+|4z-3-3i|}$\\\\ Then find Min. of $\mathbf{p(z)}$ and also find corrosponding Complex no.$\mathbf{z}$ ...

Prove that the number nm(n-m) is even for any integers n & m ...

1.10.2 F LIM sqrt(2xsquared+3)/4x+2 as x→∞ is given as does not exist!!!! I dont know why. Somebody help me!!! ...

1. Find the largest term of the following sequence: \text{a) } a_{n}=\frac{n^2}{n^3+200} 2. ABC is an isosceles triangle inscribed in a circle of radius r, AB=AC and h is the altitude from A to BC. If the triangle ABC has per ...

what is the remainder of -17/3??:D a very basic and simple one!! ...

Let f be a function from the set of points in the plane to the set of real numbers ,with the property that for any square ABCD, f(A)+f(B)+f(C)+f(D) = 0 Prove that f(P) = 0 , for any point P in the plane. Not a doubt. ...

If O be the circumcentre and O' be te orthocentre of ΔABC then prove that (i) OA + OB + OC = OO' (ii) O'A + O'B + O'C = 2 O'O (iii) OAsin2A + OBsin2B + OCsin2C = 0 bold lines signify vectors and 0 signifies nul vector!! plea ...

got it got it sorry thanks everyone! ...

Givn the integral of sqrt (x^2 - a^2) is it possible to find the integration of sqrt (a^2 - x^2) without using further integration ...

what is the inverse of the matrix 1 3 -2 -3 0 -5 2 5 0 ...

Two of the squares of a 7X7 checkboard are painted yellow. and the rest are painted green..two color schemes are said to be equivalent if one can be obtained from the other by a rotation of the board...how many inequivalent s ...

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The other day i was solving a logical reasoning problem. One of the statement of the problem read as follows: "Consider a two digit INTEEGER x such that the sum of digits is 3" Confusion: We can have x of ±AB form where A an ...

$\textbf{Solve for $\mathbf{x::}$}$\\\\ \mathbf{\sqrt{x+2.\sqrt{x-1}}+\sqrt{x-2.\sqrt{x-1}}=2}$ ...

In a mathematical competition 6 problems were posed to the contestants. Each pair of problems was solved by more than 2 5 of the contestants. Nobody solved all 6 problems. Show that there were at least 2 contestants who each ...

If difference of cubes of two consecutive natural numbers is equal to n2 (n is a positive integer). Prove that 2n-1 is a perfect square. this is not very difficult ...

In how many ways can one go from A to B ,if movement is allowed only the edges, and travelling the shortest distance possible in each case? *Image* ...

Help me frnds. I am struck.the answer requires integral value.but i am gettimg ans in log function. Q. Find (a logbx) if a= 0.2 , b = √5 and x= (1/4 + 1/8 + 1/16+......∞ terms) the options are (A)1 (B)1/2 (C) 2 (D) 4 ...

we know that the centroid of an isocelous triangle is also the centre of the circle circumscribing it. So if it is so then we can't draw two different isocelous triangles inside a circle with different centroids. ...

for 2 circles to intersect in 2 distinct points prove that |r1 - r2| < c1c2 .. ...

find the minimum of (sin2x+3sinxcosx+5cos2x) ...

maths musing is a section in mathematics today(mtg magazine) which has some good iit related mathematics question i have created a pdf of this section and uploaded here ... http://www.scribd.com/doc/56405508/Math-Musing ...

\hspace{-15}$\textbf{Find Integer solution for}\\\\ $\mathbf{x(x+1)(x+2)(x+3)(x+4)(x+5)=y^2-1}$ ...

$If $\mathbf{\color{red}f(x)=\frac{(x-a).(x-b)}{(c-a)(c-b)}+\frac{(x-b).(x-c)}{(a-b)(a-c)}+\frac{(x-c).(x-a)}{(b-c)(b-a)}}$\\\\\\ Then find $\mathbf{\color{green}\frac{d}{dx}\left(f(x)\right)=}$ ...

\hspace{-16}\bold{(Q)::}\; $Find all Complex no. $\mathbf{z_{1}}$ and $\mathbf{z_{2}}$ in \\\\\\ $\mathbf{z^2_{1}-3z_{2}+5=0}$\\\\ $\mathbf{z^2_{2}-3z_{1}+5=0}$ ...

\hspace{-16}\bold{(Q):(1):}\; \mathbf{\lim_{x\rightarrow 0}\left(\frac{b^{x+1}-a^{x+1}}{b-a}\right)^{\frac{1}{x}}=}$\\\\\\ $\bold{(Q):(2):}\;$If $\mathbf{f(x)=}$\begin{cases} \mathbf{\displaystyle \frac{x^2-1}{x^3-1}}\;\;, & ...

\hspace{-16}(1):\; \mathbf{\int x\sqrt{1+\sin x}dx}\\\\\\ (2):\; \mathbf{\int_{0}^{\pi}\frac{2+2(x+1)\sin x-(x^2+1)\cos^2 x}{\sin x-x\cos x+1}dx}\\\\\\ (3):\;\mathbf{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{\cos^2 x}{(e^x+1 ...

x+iy=(1-i*root3)^100.........x=?y=? ...

Try this, it's really appealing.... a,b,c>0 Prove the following inequality: ab(a+b)+bc(b+c)+ca(c+a)\ge \sum_{cyc}ab\sqrt{\frac{a}{b}\left(b+c \right)\left(c+a \right)} ...

\hspace{-15}$(1)\;\;::\;If $\mathbf{f:\mathbb{Z}\rightarrow \mathbb{Z}\;,}$ and $\mathbf{f(x)-f(x-1)=x^3}$ and $\mathbf{f(2)=-1}$\\\\ Then $\mathbf{f(x)=}$\\\\ $\mathbf{Ans:\Leftrightarrow f(x)=\left(\frac{n.(n+1)}{2}\right)^ ...