Recently Active Algebra Questions

10 women are sitting in a row. All of them get up and reseat themselves in a way such that each woman can sit either in the chair where she was previously sitting or in the chair right next to hers. In how many ways can the w ...

if one of the root of quadratic equation x2+ax+b=0 be the other root of x2+cx+d=0then prove that its other root is of the equation x2+(2a-c)x+(a2-ac+d) ...

if α i a non real root of x7=1 , find the equation whose roots are :α+α6 ; α2+α5 ; α3+α4 . ...

show that 6!5! is a divisor of (6!)! ...

find all linear functions from [-2,4] to [10,15] which are onto??? ...

There are 10 DVD players and 10 DVDs 5 DVD players and 5 DVDs are defective out of 5 correct DVDs 3 are hindi 2 are english DVDs are inserted in players at random find the prob that: i) atleast 1 movie is watched ii) a hindi ...

Given reals numbers a, b, c. Prove that at least one of three euqations x2+(a-b)x+(b-c)=0, x2+(b-c)x+(c-a)=0, x2+(c-a)x+(a-b)=0 has a real root. ...

Find all real numbers a\in(-2,2) satisfying the following condition: The polynomial x^{154}-ax^{77}+1 is a multiple of the polynomial x^{14}-ax^{7}+1 . ...

This functional equation is nice and has a super short and elegant solution: Find all functions f: N --> N such that xf(y) + yf(x) = (x + y)f(x2 + y2) for all x, y and in N, where N = {0, 1, 2, 3, ...}. ...

Let a and b be 2 coprime +ve integers and f(x) =[x] (greatest integer function). show that \sum_{n=1}^{b-1}{f\left( \frac{na}{b}\right)}=\frac{(a-1)(b-1)}{2} ...

A 10 X 10 X 10 cube is formed of small unit cubes. A grasshopper sits at the center O of one the corner cubes. At a given moment it can jump to the center of any of the cubes which has a common face with the cube where it sit ...

Let z_1,z_2,z_3 represent vertices A,B,C of a right angled triangle,right angled at C,if AC = 1 unit and (z_1-z_2)^2 = 2 (z_1-z_3)(z_2-z_3)(-1 + i ) ,find angle A ...

how we will draw d graph of sin x and sin2??? ...

If a,b,c,d are in Gp and ax=by=cz=du,then x,y,z,y are in -- A. AP B. GP C. HP D. none of these ...

Q1. T/F tan\frac{\pi }{9}+tan\frac{5\pi }{18} is the AM of tan\frac{\pi }{9} and tan\frac{7\pi }{18} Q2. If a_{n} = \int_{0}^{\pi }{\frac{sin(2n-1)x}{sinx}}dx then which of the following is true about the progression a1,a2,.. ...

Not for >12th Solve the equation: \frac{x^3}{x^3 + 27+9x(x+3)} = \frac{x-3}{x+6} ...

g(x)=1/2(x^102)-23(x^101)-45/2(x^2)+1035x.....then find g(46) and g(45/2)???????????? ...

Tell me, how to proceed with this one - Solve the inequality : log5(x2-4x+11)2-log11(x2-4x-11)3/ 2-5x-3x2 ≥0 ...

find the coefficient of x50 in the expression (1+x)1000+2x(1+x)999+3x2(1+x)998+...+1000x999(1+x)+1001x1000 may be it is a sum from any common book bu i do not have the solution .i found it in my state book exercise. ...

Please prove the multinomial theorem... i,e (x+y+z)n= Σ n!/p!q!r! xpyqzr . p,q,r are non - negative integer and p+q+r=n ? ...

Does the set {1;2;...;3000} contain a subset A consisting of 2000 numbers such that x belongs to A implies 2x does not belong to A. ...

Arithmetic progressions Consider the following infinite table : 04, 07, 10, 13, 16, 19, ... 07, 12, 17, 22, 27, 32, ... 10, 17, 24, 31, 38, 45, ... 13, 22, 31, 40, 49, 58, ... 16, 27, 38, 49, 60, 71, ... 19, 32, 45, 58, 71, 8 ...

Prove that, the sequence 11,111,1111,11111,...∞ doesn't have any perfect square. ...

Q1.prove thet √2 is irrational. Q2.how we will prove mathematically that 1*0=0 ...

Find all integers a such that x2-x+a divides x13+x+90 ...

Q1)If x,y and z are in AP,prove that 1/√x+√y ,1/√z+√x ,1/√y+√z are in AP Q2)Sum the series to n terms: (1/1+√x) +(1/1-x)+(1/1-√x)+....... Q3)Find the sum of first 19 terms of the AP a1,a2,a3,.........if it is ...

IF S1,S2,S3,......................,Sn ARE THE SUMS OF n TERMS OF n GP's WHOSE FIRST TERM IS 1 IN EACH CASE AND COMMON RATIO ARE 1,2,3,............n RESPECTIVELY,THEN PROVE THat S1+S2+2S3+3S4+...............+(n-1)Sn=1n+2n+3n+. ...

prove 1111111111111111................(91 digits) is not a prime no. ...

IF X=43*46*46*49.............*43X=0.0625-54,THEN VALUE OF X IS_______________________. ...

IF XA=XB/2ZB/2=ZC,THEN PROVE THAT 1/A,1/B,1/C ARE IN A.P. ...