Recently Active Algebra Questions

given that a2 + b2+ c2 = 8 prove that a3 + b3 + c 3 ≥ 16 2/3 . ...

$\textbf{find no. of Integral solution of the equation}\\\\ $\mathbf{x^6 + 3x^4 + 3x^2 + 28 = x^9 - 3x^8 + 3x^7 - x^6}$ ...

f(x)=x2,find {f(1.1)-f(1)}/(1.1-1) ...

i came across a statement in ncert: "Since N is the smallest subset of R which is an inductive set,it follows that any subset of R that is an inductive set must contain N" could somebody plz elaborate what this means? ...

If S=.99999999.......∞ then 10S=9.9999999.....∞ then 9S=9 then S=1 ????? ...

I am starting this series of question specially for students who are in class XI and have just started preparing... If you are in a higher class (Read XII/ Passout) please hold ur adrenaline rush and give chance to the beginn ...

FIND THE SUM upto n terms of the following series:------- 1) 3+7+14+27+52....... 2) (1)+(2+3)+(4+5+6)+...... 3) (33-23)+(53-43)+(73-63)+.......... 4) 1+22-33+4+52-63+7+82-93....... ...

1)For n≥3 determine all real solutions of the system of n equations x1+ x2+...+xn-1 = 1/xn ............ x1+ x2+ ...+xi-1+ xi+1+...xn= 1/xi ....... x2+ ...+ xn-1+ xn = 1/x1 2)Suppose P(x) is a polynomial with real coefficien ...

Find the sum of the series:- 1+ 1/12 + 1/22 + 1+ 1/22 + 1/32 ..... 1+ 1/20072 + 1/20082 a)2008- 1/2008 b)2007- 1/2007 c)2007- 1/2008 d)2008- 1/2007 e)2008- 1/2009 ...

The digit in the unit position of the integer 1!+2!+3!+.....+99! is: a)3 b)0 c)1 d)7 ...

1))fIND THE SUM upto n terms-2 +12+36+80+150+252..... 2))if a,b,c, r in HP then bc,ca,ab r in? ...

An automatic machine makes paper clips from wire coiling. If on an average 1 in 400 paper clips are defective and 100 clips are packed in each box, What are the probabilities that any box of clips will contain : a) No defecti ...

find the least positive value of a+b,where a,b are positive integers and such that 11divides a+13b and 13 divides a+11b ...

1 . Solve - x 3 - 3 x = x + 2 ...

find the number of digits in 5^30. given log 210 = 0.3010 ...

Combinatorics marathon Inspired from artofproblemsolving we are gonna start a combithread maybe some questions will go above iitjee but i would like everyone to participate Rules 1) u need to post solution to the question uns ...

for |x| < 1 1 + 3x + 6x2 + 10x3............. = ? ...

f(x)=x3 +ax2 +bx+c has 3 distinct real roots and (x2 +2x+2)3+ a(x2+2x+2)2 +b(x2+2x+2)+c has no real roots. what are a,b&c?? what is the root of f'(x)??? ...

Prove that if the equation ax2+ bx+ c= 0 has real roots then b2≥4ac Prove this in as many ways you can. nishant sir,i hope u wnt mind me posting qns ;) @ Beginners: If u think this is useless , u will surely miss some thing ...

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ZENO's paradox A man standing in a room can not walk to the wall. In order to do so, he would have to go half the distance, then half the remaining distance, and then again half of what shall remains. This process can always ...

I n how many ways is it possible to arrange 2n persons of different height in two ranks of n persons each so that in each rank they stand according to height and, besides, so that each man in the first rank is taller than the ...

if 1,w w2 are cube roots of unity,then the value of(1+w2-w)(1-w2+w) ...

1. Maximum no. of real solutions for the equation axn+x2+bx+c = 0 , where a,b,c ε R and n is even positive no : a) 2 b) 3 c) 4 d) None 2. The graphs y = 2x3-4x+2 and y = x3+2x-1 intersect exactly at 3 distinct points, then t ...

the problems goes like that.. Teacher: Find number of non-negative integer solutions to the equation x1+ x2 + x3 + ....+ x100 = 10 Student: It's just the co - efficient of x10 in the (1 + x + x3+...)100 = (1-x)-100 Teacher: G ...

A simple combi problem which suppossedly has multiple answers ? Find the number of ways of arranging 5 distingushable balls into 3 distinguishable (differnet) boexes such that each contains at least one ball. My logic (it loo ...

Q. If α,β are the roots of quadratic equationnn ax2+bx+c, then find the equation whose roots are (α2-β2)(α3-β3) and α2β3+α3β2 ? ...

1) Solution of inequality 2|x+1| > x+4 contains which interval? 2) If R is a relation from a finite set A having m elements to a finite set B having n elements, then find the number of relations from A to B.(with proof) Fu ...

\textrm{Let }f:\mathbb{N}\rightarrow \mathbb{N} \textrm{be a function such that }f(n+1)>f(n) ; f(f(n))=3n\textrm{ for all n} \textrm{Evaluate }f(2001) ...

x[y]=y[x] find x and y given that x≠y and x,y > 0 plz solve this mathematically ...