Recently Active Algebra Questions

If α and β are roots of z +1/z=2(cosθ +isinθ) ,0<θ<π , show that l α-i l=l β-i l ...

z1,z2,z3,z4 are four complex nos. If z1 + z2 = 0 , and z1z2 + z3z4 = 0 , then prove that these are concyclic. ...

It all started with b555's classic integration siikho thread..and now nishant sir started some more threads on it.... I ma starting one small on inequalities..A lot of inequlaities thread are already there on site..I know tha ...

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Prove that the interval [0,1] can be split into black and white intervals for any quadratic polynomial P(x) , such that the sum of weights of the black intervals is equal to the sum of weights of the white intervals. (Define ...

If a,b ≥ 0 and p,q are rational numbers such that p > 1, and 1/p + 1/q =1, then show that ab ≤ ap/p + bq/q ...

log27 is: a)integer b)rational c)irrational d)complex roots give proof as well ...

21 people take a test with 15 true or false questions. It is known that every 2 people have at least 1 correct answer in common. What is the minimum number of people that could have correctly answered the question which the m ...

16 students took part in a competition. All problems were multiple choice style. Each problem had four choices. It was said that any two students had at most one answer in common, find the maximum number of problems. ...

In a wagon, every m≥3 people have exactly one common friend. (When A is B's friend, B is also A's friend. No one was considered as his own friend.) Find the number of friends of the person who has the most friends. ...

Let f(x) = 4x/4x+2 . What is the value of \sum_{1}^{1000}{f\frac{i}{1000}} Source: Chinese: 1986 ...

if Sn be the sum of n consecutive terms of an A.P.show that (Sn+3)-(3Sn+2)+(3Sn+1)-Sn=0 ...

We say x,y,z can be symmetric in an expression..........pls explain wht do we mean by saying so ? To illustrate my doubt, I'm posting one example : Case I : Let x,y,z be real variables which satisfy xy+yz+zx=7 and x+y+z=6 We ...

how to do summation Tr= 1/ r^r.............. find S∞ ...

Q.If Z1 & Z2 are two complex no such that Z2≠0 and whole mod of Z1-1/Z1+Z2=1.Then prove dat i*Z1/Z2=K,where K is a real no.Find the angle between the lines frm the original to the points Z1+Z2 & Z1-Z2 in terms of K????????? ...

A positive integer n(>1)can be written as a product of power of distinct primes in one and only one way,except the order of factorization. i.e n=p1a1 p2a2......pkak. where 1<p1<p2<.....pk where pi's being prime(i= ...

if the eqn ax^2+2bx-3c=0 has non real roots and 3c/4<(a+b),then c is always -------- ...

if the eqn ax^2+2bx-3c=0 has non real roots and 3c/4<(a+b),then c is always -------- ...

Two players of equal skill, A and B, are playing a set of games; they leave off playing when A wants 3 points and B wants 2. If the stake is Rs. 16, what share ought each to take? ...

PLEASE SIR,CAN YOU FIND A SOLUTION TO THIS? (cos p - 1) x^2 + cos p x + sin p = 0, solve p for x belonging to real numbers? ...

what is remainder when 111111 ......123 times 1 is divided by 271 ...

I learnt this Arihant Differential Calculus book. Please explain how ths has been derived or formulated. 1) If ax2 + bx + c > 0, for all x belonging to R a > 0 and D < 0 2) If ax2 + bx + c > 0, for all x belonging ...

find the possible number of ordered triads (m,n,p) where 1≤m≤100 1≤n≤50 1≤p≤25 and (2^m )+(2^n)+(2^p) is divisible by 3........ ...

PLEASE FIND THE MODULAS AND AMPLITUDE OF ii where i = -1 ...

1.If a^2+b^2=2 and a,b are real.Find the interval of a+b. 2.If a^2+b^2+c^2=1 then find the interval of ab+bc+ca. ...

TRY OUT ....... {\color{red} {\color{red} 1 }} The members of a club took part in a round robin competition in which each player plays every one else once . All the members scored the same no of points exept 4 juniors whose t ...

18b. There are 3 cars of different make available to transport 3 girls and 5 boys on a field trip. Each car can hold upto 3 children, Find b. the numbers of ways in which they can be accomadated if 2 or 3 girls are assigned t ...

sir i have serious problems with fuctions containing fractional part of x .... ex. sin{x} etc...........due to it i am unable to do many definite integrations or graph of the day and many more.........plz plz plz help ...

What is the number of ways can you cover a Nx2 board using 1x2 tiles....?? ...

Find the number of terms in the expansion of (x^2 + 1 + 1/x^2)^n ,n=N ...