Recently Active Mathematics Questions

let a1,a2,a3.......an be n nos such that each a2 is either 1 or -1....If a1a2a3a4 + a2a3a4a5+................ana1a2a3=0.............then prove 4 divides n[1] ...

if α≠1 α5=1 then value of log√3 mod(1+α+α2+α3- 2/α ) i know we hav to use concept of nth root of unity....but not getting ...

Two squares are chosen at random on a chess board. The probability that they have a side in common is ? ...

Q1 Suppose a,b be complex nos. and x3+ax+b has a pair of complex conjugate roots then prove bot ha and b are real Q2 If 0<a< b< c< d,then find location of roots of quad eqn f(x)=ax^2+[1-a(b+c)]x+abc-d=0 on number ...

the value of ∫x2+2 /[(x4+5x2+4)tan-1(x2+2)/x dx ............. ...

rekha married shyam and had 4 sons .Varsha married ajay and had 4 sons.both couples divorced and after that shyam married varsha while ajay married rekha .they too had 3 sons each from their wedlocks .how many selections of 8 ...

\int_{0}^{\propto}\frac{sinx}{x}dx ===??? ...

find all odd prime numbers p which divide 1p-1+2p-1+3p-1+.....................2004p-1 ...

There is a 7 * 11 chessboard placed in front of you. what you have to do is to find the number of rectangles of all shapes and sizes but of odd dimensions(i.e. both the length and breadth have to be odd) !!! ......check out!! ...

1) find the no of right angled triangle with integer sides and inradius 2008 2) evalute this limit \lim_{x\rightarrow \infty }((x-1)(x-2)(x+3)(x+5)(x+10))^{1/5}-x ...

find the sum[1] \frac{3}{1!+2!+3!}+\frac{4}{2!+3!+4!}.................\frac{2008}{2006!+2007!+2008!} certainly not for genius sirs out here[3] ...

2)if a four digit number is chosen at a random.....wht is the probab that it contains not more than 2 different digits....... 3)fnd the area of triangle whose vertices are the incenter ,centroid,and the circumcenter of a tria ...

Judging by the popularity of congruences , let's try to do things in a different way , but I don't have a problem in congruences :) especially it would be a treat to watch other solutions too ---- 1 > Find the last 3 digit ...

Q. If a+ b+ c=0, where a≠b≠c, then a2/2a2+bc + b2/2b2+ac + c2/2c2+ab is equal to (A) 0 , (B) 1, (C) -1 , (D) abc ...

Probability of a bomb hitting a bridge is 1/4. If two direct hits are neede to destroy it, find the least no. of bombs required so tht the probability of the bridge being destroyed is greater than 0.9. Am stuck here - (4/3)n ...

1) 5% of all bulbs made by a manufacturing company are defective. A lot contains 100 bulbs. Find probability tht 6 are defective. Won't the ans be this simply- 100C6(1/20)6(19/20)94 ? Ans given : 100C6(1/20)100 2) 60 dice are ...

*Image* Q.In an equilateral triangle, 3 coins of radii 1 unit each are kept so that they touch each other and also the sides of the triangle. Area of the triangle is???? ...

1) Ina plane there are two families of lines Y = x + r, Y = -x + r , where r belongs to {0,1,2,3,4}. The number of squares of diagonols of length 2 formed by the lines is :- (a) 9 (b) 16 (c) 25 (d) None of these ...

What is the value of \sum_{n=1}^{100}{} K+nCn-1 Where K is a positive integer. ...

Find the focus of the parabola : x2+y2+2xy-6x-2y+3 = 0 Ans : (1,1) ...

\lim_{n\rightarrow \infty }\prod_{r=2}^{r=n}{\frac{r^{3}-1}{r^{3}+1}} ...

Question. Let n b a +ve integer such that sin π/2n +cos π/2n = √n/2 . then (a) 6≤n≤8 (b) 4≤n≤8 (c) 4<n≤8 (d) 4<n<8 Please show ur steps........am doubtful about a step. ...

Find the range of values of λ for which the variable line 3x+4y - λ=0 lies between the circles: x2+y2 - 2x - 2y +1=0 x2+y2 - 18x - 2y +78 = 0 without intercepting a chord on either circle. ...

Prove 2<e<3 ... ...

if I(n)=\int \frac{x^{n}}{(ax^{2}+bx+c)^{1/2}} dx n belongs to N find I(n+1) in terms of I(n) and I(n-1) ...

Prove that 2 is algebraic (For extreme beginners :D) Also prove that 2 + 3 is algebraic ...

let x and y be two numbers chosen at random from set {1,2,3......n}with replacement.let Qn(p) denote probability that (xp-1 -yp-1) is divisible by p then find Qn(p) in terms of p and n and find Q25(3) ...

Q1. [] represents the GINT. Then the value of the infinite series [ 2008/2 ] + [ 2009/4 ] + [ 2011/8 ] + [ 2015/16 ] + [ 2023/32 ] + ...... is? I need a short method for this.. All i could do was calculate tr = [ 2007+2r-1/2r ...

Let f(x) = [3+4Sinx] (where [] denotes greatest integer). Then, find the sum of all the values of "x" in [Ï€ ,2Ï€] where f(x) fails to be differenciable..... Answer : 12Ï€ ...

Ques1) Find the solution of dy/ dx = (x+y) 2 /(x+2) (y-2) Ques2) Find the solution of dy/dx = (x-1) 2 + (y-2) 2 tan -1 ( y-2/x-1 )/(xy - 2x - y+2) tan -1 ( y-2/x-1 ) ...