Recently Active Algebra Questions

$The no. of Real roots of the equation $x^6-x^5+x^4-x^3+x^2-x+\frac{3}{4}=0$ ...

Q1) How many real solutions of the following equation are possible: 6x2+77[x]+147=0 where [x] is GIF. q2) If {x} and [x] are fractional and integral part of a real no. x ,then solve [2x]-[x+1]=2x. ...

A polynomial p(x) when divided by (x-1), leaves the remainder 2, the same polynomial when divided by x-3, leaves the remainder 1. If same polynomial is divided by (x-1)(x-3) what will be remainder? ...

$Determine the minimum value of the expression:\\\\ $A =x^2-10xy+27y^2-8y+8.$\\\\ For what values of $x,y$ take the minimum value of the expression A. ...

Consider these two questions- 1) find the number of non negative integral solutions of x+y+z+w = 20 2) find the number of positive integral solutions of x+y+z+w = 20 answer to 1) is 23C3 and 2) is 19C3 Is there any difference ...

log(1+x)= x - xx/2 + xxx/3 - xxxx/4 ....... x=1, log 2 = 1 - 1/2 + 1/3 -1/4 .... multiply both sides by 2, 2log2 = 2 - 2/2 +2/3 -2/4 +2/5 -2/6... = 2- 1 + 2/3 -1/2 +2/5 -1/3... =1 -1/2 + 1/3 -1/4 .... 2log2 = log 2 2=1 ...

1. If x,y and z are real numbers such that (x - 3)2 + (y - 4)2 + (z - 5)2 = 0. Then, x + y + z = (A) -12 (B) 0 (C) 8 (D) 12 Please do show the steps..! ...

find the solution set for z given that, |z+a| + |z-a| = |a| where a = real number ...

$Find value of $x$ that satisfy the equation $x^{\lfloor \ x\rfloor}=\frac{9}{2}$\\\\ Where $\lfloor x \rfloor $= G.I.F=greatest integer function. ...

Since our exams are approaching fast , I have taken an initiative to post and solve problems that I have found to be quite intriguing . These are all from IIT - JEE syllabus , and I hope to create a field of mutual participat ...

1) If (1-x)n = C0 - C1x + C2x2 -..... + (-1)nCnxn, then the value of C0 - C1 + C2 - .... + C100 is, where n>102 a) 0 b) nC101 c) n-1C101 d) 2nC100 ...

If x,y,z are the roots of 7x3-x-2=0, then the value of Σ(x/y+ y/z) is _____________. (ans= -3) ...

Σ(n=2 to n→∞) ((n^4+3n^2+10n+10))/((2^n)(n^4+4)) ...

1. two integers x and y ar drawn (without replacement) out of set (0,1,2,3,---,10) find the probability that -5<x-y<5? 2. Two natural numbers ( x and y) ar choosen at random. What is the probability that x^2 + y^2 is di ...

Let 0 < a ≤ b. Define a1 = a+b/2 , b1 = a1 b and for each integer k≥1, ak+1 = ak + bk /2 , bk+1 = ak+1 bk . Find the limit of the sequence {bn}. That is find \lim_{n\to\infty} b_n ...

Let S = (z_1,z_2,...,z_{2010}) We construct for each z_i \in S the set S_i = (z_iz_1,z_i,z_2,...,z_iz_{2010}) If it is true that S_i = S for 1 \le i \le 2010 then prove that (1) |z_i| =1 (2) z \in S \Rightarrow \overline{z} \ ...

$Find Max. and Min. value of $\sqrt{x^3-6x^2+21x+18}$\\\\ Where $x,y\in R$ and $-\frac{1}{2}\leq x\leq 1$ ...

1. show that the sum of a nonzero real no and its reciprocal cannot lie in (-2,2). Can we solve this by inequalities? 2.Find m so that 3x^2-2mx-4=0 and x^2-4mx+2=0 may have a common root. Can the eqns have a common non-real r ...

if x , y , z > 0 then the value of x/y + y/z + z/x lies in the interval ...

1. If a,b,c are odd integers , ax^2+bx+c=0 cannot have ratioal roots. Prove it. 2. For what values of a does the eqn (2a+1)x^2-a(x-1)=2 has one root greater than 1 and other less than 1. 3. If a and b are the roots of x^2+px+ ...

find all roots of x4+x3+x2+x+1=0 including complex roots. ...

Ques- Find all complex numbers 'z' which satisfy: 4z^{2} + 8\left|z \right|^{2}=8 Ques- Find all complex numbers 'z' which satisfy z3 = conjugate of 'z' ...

1q) the value of arg(ilog(a-ib/a+ib)) where a,b are real no's is???? 2q)(mod)(Z- Z1+Z2/2)^2 +(MOD)(Z1-Z2/2)^2 =???? 3Q) if mod(Z-2+2i)=1 then least and greatest values of mod (z) are? ...

1. If 2u=5x and the harmonic mean of x is 0.4, What is the harmonic mean of u? 2. Statistics Sum If a variable 'x' takes the values 1,2,3,.....,k with F1,F2,,..... Fk as the corresponding more than type cumulative frequencies ...

1. If sin (log i i) = a+ib. Find a and b. 2. Find the area formed by z , -iz and z+iz. I solved it but I need the Geometrical Interpretation!! ...

1) If a,b,c,d > 1 P.T. 8(abcd+1) > (a+1)(b+1)(c+1)(d+1) 2) If a,b,c ≥ 0 and a+b+c =1 Find the max. value of \sqrt[ 3 ]{a+b} + \sqrt[ 3 ]{b+c} + \sqrt[ 3 ]{a+c} 3) For a,b,c > 0 Prove that x2 + y2/x+y + z2 + y2/z+y ...

1. x+1 - x-1 = 4x-1 has a. no soln b. 1 soln c. 2 soln d.more than 2 soln PLEASE SOLVE THE EQUATION 2. Let a,b,c,p,q be real nos.Suppose m,n are thw roots of the equation x2+2px+q=0 and m,1/n are the roots of ax2+2bx+c=0 wher ...

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1. The real numbers x satisfying √(x + 5)/(1+x) > 1 are precisely those which satisfy? (A) x < 1 (B) 0 < x < 1 (C) -5 < x < 1 (D) -1 < x < 1 2. Let P(X) = 1 + x + x2 + x3 + x4 + x5. What is the remai ...

the funtn f:c-c defined by f(x)= ax+b/cx+d for x belgs c reduces 2 a constant funtion if a) a=c b) b=d c)ad=bc d)ab=cd ...