Recently Active Mathematics Questions

∫0∞xeaxdx(limits from 0 to ifinity) ...

Determine all the positive roots of x^{x}=\frac{1}{\sqrt{2}} ...

\int_{0}^{1}\frac{dx}{2+\sqrt{1-x}+\sqrt{1+x}} Solve :) ...

2 candidates contested for an election, A & B. A got a votes, while B got b. Given a>b, find probability that A was ahead of B - throughout the competition..... SHOULD IT NOT BE JUST 1/2 ?????????????? ...

xx =2 . solve ...

if x,y,z are real numbers satisfying the relations \[ x+y+z = 1\quad\textrm{and}\quad\arctan x+\arctan y+\arctan z =\frac{\pi}{4}, \] prove that $ x^{2n+1}+y^{2n+1}+z^{2n+1}= 1 $ holds true for all positive integers n . ...

If f(0)=f(1)= 1/2 ,|f'(1)|<1 and f'(0)=2,then \lim_{x\rightarrow 0} \frac{f(sin x)-f(cos x)}{x} is A. 0 B. 1 C. 2 D. 1/2 ...

consider a town with n people. a person spreads a rumour to a second,who in turn repeats it to a third and so on.suppose that at each stage,the recipient of the rumour is chosen at random from the remaining (n-1) people. what ...

prove that (n!)2 > nn (i know the proof but am looking for a much simpler one) ...

The integer n for which \large \lim_{x\rightarrow 0} \frac{(cos x -1)(cos x - e^{x})}{x^{n}} is a finite non-zero number is A. 1 B. 2 C. 3 D. 4 ...

Let f(x) = ax^2+bx+c be such that |f(x)| \le 1 \ \forall \ x \in \[-1,1] Prove that |2ax+b| \le 4 \ \forall \ x \in [-1,1] This topic is current in mathlinks.ro, and in any case no borrowed solutions please. ...

1) The no. of points at which the function f(x) = max {a-x , a+x, b}, - ∞ < x < ∞ , 0 <a < b cannot be differentiable is: (a)2 (b) 3 (c)1 (d) 0 2) If f(x) = sin (2∩ [ ∩2 - x] )/5 +[x] 2 ; where [.] denotes ...

prove by combinatorial arg.tht 2nCn is div by n+1 ...

Find all real a for which there exist non-negative reals x_i for 1≤i≤5 satisfying the system.... \sum_{i=1}^{5}ix_i=a \sum_{i=1}^{5}i^3x_i=a^2 \sum_{i=1}^{5}i^5x_i=a^3 . ...

STRAIGHT LINES 1 ) Find the area of the triangle formed by the straight lines whose equations are x+2y-5=0; 2x+y-7=0 and x-y+1=0 withought determining the coordinates of the vertices of the triangle. Also compute the tangent ...

Q1 Dividing f(z) by z-i gives remainder i and diviiding by z+i we get remainder 1+i If f(z) is diivded by z2+1,ten remainder is ?? Q2 Represent on argand plane lz+il<lz-xl<lz-il Q3 If lzl≤1 and lωl≤1 then prove lz- ...

let a complex no. s.t. lal<1 and z1,z2,...zn be vertices of polygon such that zk=1+a+a2+..+ak the nvertices of polygon lie within the circle of eqn ?? ...

what does it represent in argand plane arg[ z2-5z+3/3z2-z-2 ]=2Ï€/3 my nas is not matching os seeking help here.. ...

^{5^{3^{5^{7^{9}}}}} find the remainder when divided by 21 (without calculatin) ...

Q. Of the two concentric circles the smaller one has the equation x2+y2=4. If each of the two intercepts on the line x+y=2 made between the two circles is 1, find the equation of the larger circle. just want the answer ...

∫dx/(ax2+bx+c)2=? i heard sumthing called reduction formula.wat is it?do we need to know it? ...

Find all functions from reals to reals satisfying f(x+y) + f(y+z) + f(z+x) ≥ 3f(x+2y+3z) for all x, y, z Belonging to reals. ...

very simple ones bt im stuck.. 1.find minimum value of (a2+3a+1)(b2+3b+1)(c2+3c+1)/abc 2.x,y,z are +ve real no.s satisfy 4xy+6yz+8xz=9 find max value of xyz. ...

ABCD ia a square of side length 6 2 units and EF is parallel to the square and is of length 12 2 units . The faces BCF and ADE are equilateral . The volume(in cubic unit) of the solid ABCDEF is equal to a. 384 b. 576 c.288 d. ...

*Image* dx is { where [.] denotes the greatest integer fnction} : (a) 1000 (b) 0 (c) 1/500 (d)none of these ...

Q1--In a network of railways, a small island has 15 stations.Find the number of different types of tickets to be printed for each class,if every station must have tickets for other station.. Answer--210 Q2--On a railway route ...

7)sin x<1/2 ½=sin 30 =sin(180-30)=sin 150 or, sin30<1/2 and sin 150 >1/2(why? And how?) or, x belongs to (0,30) union (150,360) [given: 0<x<360] I want a complete explanation. 8) Give the general soln of x: lo ...

Let p be a prime number such that p≥11.Let n=p!+1. Find the number of primes in the list n+1,n+2,n+3,....,n+p-1.. ...

In a certain test, ai students gave wrong answers to atleast i questions where i=1,2,3,...k. No student gave more than k wrong answers.Find the total number of wrong answers.. ...

(n!)! is divisible by A--28(2n-1)n-1 B--(3n)! C--(n!)n! D--(n!)(n-1)! ...