Recently Active Algebra Questions

If m and n are any 2 odd positive integers with n<m then largest positive integer which divides all numbers of the form (m2-n2).(my ans is cumin 4 but it is given 8). ...

Find the number of rectangles excluding squares from a rectangle of size 9 X 6.. ...

There are 10 points in a plane of which no three are collinear and 4 points are concyclic.Find the number of different circles that can be drawn through atleast 3 of these points.. Kindly explain also.. ...

There are n concurrent lines and another line parallel to one of them.Find the number of different triangles that will be formed by the (n+1) lines.. ...

There are n people at a party. Prove that there are two of them such that of the remaining n − 2 people, there are at least \left[\frac{n}{2} \right]-1 of them each of whom knows both or else knows neither of the two. [ .] ...

prove 3^{n}>n^{3} for all positive integers `n`. note: open for all ...

Let A=\left( \begin{array}{cc} a & b \\ 0 & a \end{array} \right) , by judging from A^2,\ A^3,\ \cdots to expect An for every positive integer n, then prove that the expectation is true by induction. Src: 1976 Hitotsubashi Un ...

find the number of solutions : x^{2}+4x+1=\sqrt{x+3}-2 ...

There's a square ABCD.....inscribed in a circle, this square is now partitioned into non-overlapping rectangles, and for each rectangle it's circum-circle is drawn. If the sum of areas of all these circles equals the area of ...

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 ...

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) ...

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 . ...

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.. ...

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. ...

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 ...

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)! ...

1) In a batch of 10 articles, 4 articles are defective. 6 articles are taken from the batch for inspection. If more than 2 articles in this batch are defective, the whole batch is rejected. Find the probability that the batch ...

The largest interval in which x12 - x9 + x4 - x + 1 > 0 is: A. [0,∞) B. (-∞,0] C. (-∞,∞) D. none of these ...

There are n straight lines in a plane,no two of which is parallel,and no three pass through the same point.If their points of intersections are joined,find the number of fresh lines thus obtained. ...

Suppose a_1, a_2, a_3,...,a_n are n real numbers It is obvious that if the ai are all positive, then the numbers \sum a_i, \sum_{i<j} a_i a_j \sum_{i<j<k} a_ia_ja_k,..., \prod_{i=1}^n a_i will all be positive Prove t ...

If 1,α1,α2,...,αn-1 are nth roots of unity , then value of (1+α1(1+α2)...(1+αn-1) ...

If the eqn ax2+bx+c=0 (0 < a < b< c) has non real complex roots z1 and z2. Show that |z1| > 1 ; |z2| > 1. ...

A particle is projected at an angle 60degree with speed 17.32 from the point A.At the same time the wedge is made to move with speed 17.32 towards right .Then the time after which the particle will strike the wedge is ------- ...