Recently Active Algebra Questions

1) Find 1+2008 1+2009 1+2010 1+2011*2013 2) Find the +ve integers (x,y) which satisfies x2+y2+2xy-2008x-2008y-2009=0 3) an+1 = an + an-1 for n≥2 . a2 = -1 and a10 = 29. Find a1. 4) Find sum of the digits of the number 10002 ...

1) Straight lines are drawn by jining 'm' points on a straght lne to 'n' points on another line. Excluding the given points(m+n), find the number of intersection points if no two drawn are parallel and no three are concurrent ...

1) find all real number a for which the equation x2+(a-2)x+1 = 3|x| has exactly three real solutions in x ( i got a= 1,2,3 is it correct?) 2)if n is an integer greater than 7, prove that (n,7)-[n/7] is divisible by 7 here (n, ...

1) Find the number of positive integers n for which n≤1991 and 6 is a factor of (n2+3n+2) 2)determine all pairs (m,n) of positive integers for which 2m +3n is a perfects square 3)find the remainder when 1992 is divided by 9 ...

1)find the number of quadratic polynomials ax2+bx +x,which satisfy the following conditions: a) a,b,c are distinct b) a,b,c, belongs to {1,2,3,...,1999) c)x+1 divides ax2+bx +x.. 2)let ABCD BE A QUADRILATERAL in which AB is p ...

To write a book 1890 digits were utilised. How many pages does the book have? ...

i am uploading some basic question on NUMBER THEORY.. 1)prove that every cube number,when divided by 7,leaves remainder 0,1 or 6 2)prove that every cube number,when divided by 9,leaves remainder 0,1 or 8 3)if N is any prime g ...

If ax2-bx+c = 0 has two distinct roots lying in the interval (a,b,c) ε N , then 1. log5abc = 1 2. log6abc = 2 3. log5abc = 3 4. log6abc = 4 Find number of ordered triplets (p,q,r) where 1≤p,q,r ≤10 such that 2p+3q+5r is ...

what should be the value of p for the eqn (cos p -1)x2+(cosp)x+sinp=0 to have real roots ans is(-pi , 0) how come? shouldnt it be(0, pi) ...

S1S2S3......S16 are 16 players playing in a tennis tournament no of ways to form teams for doubles is ___ no of teams in which S1 and S2 are is a) same team is _______ b) different team is ______ I expect logical/mathematical ...

Can someone pls explain this .If possible with examples If af(x)>b (1)then if b>0 1)we have f(x)>logab if a>1 2)f(x)<logab if 0<a<1 (2)for a=1 , b<1 ...

1) How many permutations of the letters a, b, c, d, e, f, g have either two or three letters between a and b? ...

1.Find: Π(n3-1)/(n3+1),from n=2 to n=∞. 2 If the equation x4 -4x3+ax2+bx+1=0 has 4 +ve roots then... value of (\a/+\b/)/(a+b)=? \ /=mod.. ...

Show that 101 is prime in easiest possible way......... ...

What's the value of- 1) 1 + 5/8 + 5.8/8.12 + 5.8.11/8.12.16 +..........................∞ 2) 1/2 + 1.3/2.4 ( 1/4 ) + 1.3.5/2.4.6 ( 1/4 )2 + ............∞ post the solution if possible ...

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1.A question paper is split into two groups -A and B.The groups contain 4 questions, each question have an alternative .The group B contain 4 questions.A student has to answer at least one question from each group and he can ...

Show that 2003 cannot be written as the sum of two squares. ...

If a,b,c are odd integers, prove that ax2 + bx + c = 0 does not have a rational number solution. Please show the procedure...... ...

a, b, c and d are four numbers which are in A.P. and relation between a, b and d is a + 3b - d = 6 and between c and d is c - d = -4. Then find the sum till 60 terms of the A.P [Ans. 7200] ...

Today a teacher came in our class. He is a bit sycho... truly he is..... He gave us a linear equation and told to solve it in 10 ways... At first he gave us 2x + 4y = 8 and 4x + 8y = 19. So we said, sir this question will hav ...

1)In how many ways can the letter of the word 'ARRANGE' be arranged so that a)the 2 A's are together but not the 2 R's ? b)neither the two A's nor the two R's are together? 2)How many numbers greater than 10000 can be formed ...

2+3+5+10+20+..................+10240 ...

Show that there are infinitely many prime numbers......... I've some confusion in this proof... We first assume that any number greater than 1 is either a prime or product of primes fine Again we consider a number N = p1.p2.. ...

If a,b,c,d,e,f are in A.P then prove that,.............. (a + 2b + 2c + d + e + f)/(a + 2c + f) = 2 ...

What is meant by permutation of a number?... ...

if, a + b + c = 1 a2 + b2 + c2 = 2 a3 + b3 + c3 = 3 Find, a4 + b4 + c4 and the value of a,b and c ...

In a book, the proof for demorgan's law, (A∩B)* = A*unionB* [*=complement] starts with,saying that for all x belongs to (A∩B)* , x is not a member of AunionB. But how can we say that, for example, if A = {1,2,3} and B = ( ...

Can anyone explain me this step please- coefficient of xn in [C0(1+x)2n - C1(1+x)2n-2 + C2(1+x)2n-4............... ] = coefficient of xn in [-1 + (1+x)2]n Thanks alot ...

Draw the graph of [y] = [sinx] and y =cosx. Hence find the no. of solutions. [.] is GIF. In interval -π to π) Problem: I could draw it approximately but it's getting tougher to find solns. Well, my graph becomes dirty. ...