Recently Active Algebra Questions

1.If A and B are square matrices of the same order and A is non singular then for a positive integer n, (A^-^1 BA)^n is equal to (A) A^-^1 B^nA (B) n(A^-^1 BA) (C) A^-^n B^nA^n (D) None of these 2.Prove that adj(A^-^1)= adj(a ...

plz factorise tis one for me 2m'2 - mm' - m2 okay i know the ans...bt plz do d steps fr me.. thanks in advance!!! [1] ...

Prove that for n ≥ 6, the equation 1/x12 + 1/x22 + 1/x32 + .... + 1/x2n = 1 has integral solutions. ...

why do we say that ax2+bx+c >0 when a>o and D<0 and ax2+bx+c <0 when a<0 and D<0 ...

1.If z is a unimodular complex number, prove that arg(z2 + conjugate of z) = 1/2 arg(z) 2.If \left|z \right| = 1 and z is a non real then prove that z can be expressed in the form of c + \iota /c - \iota where c is real .Also ...

Sum to 'n' terms 1/(1 - x)(1 - x3) + x2/(1 - x3)(1 - x5) + x4/(1 - x5)(1 - x7) + .......... also find Sum if 'n' = ∞ , given that |x|<1 ...

find all positive integer value of n and r that satisfy the equation C(n , r) = 2010.. (hsbhatt sir how can i solve these tupe of question). ...

1)what is the solution of inequality|x+1/x| <4 2)the solution of 2x + 2|x| ≥ 2√2 is: ...

f((x+y)/2)= A.M of f(x) and f(y).. if f'(0) exists and f'(0) = -1 and f(0) = 1 then f(2) =? ...

If a,b ,c,d and p are different real numbers such that :(a2+b2+c2)p2-2(ab+bc+cd)p+(b2+c2+d2)≤0, then show that a,b,c and d are in G.P ...

Let S_{n} = \sum_{1}^{n}{\frac{n}{n^{2}+kn+k^{2}}} and T_{n} = \sum_{1}^{n-1}{\frac{n}{n^{2}+kn+k^{2}}} for n=1,2,3.......then, (A) Sn < Π/3√3 (B) Sn > Π/3√3 (C) Tn < Π/3√3 (D) Tn > Π/3√3 plz somebody ...

If 1/14 + 1/24 + 1/34 +.......∞ is π4/90 , then 1/14 + 1/34 + 1/54 +.......∞= a) π4/96 b) π4/100 c) π4/121 d) π4/108 Plz show the steps also as I dont even know how to start this prob... here,π is pi. ...

If sec(x-y), secx , sec(x+y) are in AP, then (cosx)(sec y/2 )= a)±√3 b)±√5 c)±√7 d)±√2 Plz show the steps for this prob also.. ...

The unit's digit of 1! +2! +3!+.....+97! is a)3 b)4 c)5 d)6 explain yur answer with steps... ...

Prove that 1 + 1/2 + 1/4 + 1/7 + 1/11 + ............................ <= 2*pi T(n) = \frac{2}{2 + n(n-1)} ...

if 4 real nos p, q, r & s are such that, pr=2(q+s) prove, at least one of the 2 foll eqns x2+px+q=0 and x2+rx+s=0 my approach: i found out the discriminant of the 2 which came to be as p2-4q and r2-4s now one must be positive ...

1) A sequence of real number xn is defined as follows... x0 , x1 are arbitary +ve real numbers and xn+2 = 1+xn+1 /xn ,n = 0,1,2,........ Then x2011 is a) 1 b) x0 c) x1 d) x2 2)The eq. log2x 2/x (log2x)2 + (log2x)4 = 1 has a) ...

Locus of z if 3π/4 when !z! ≤ !z-2! arg [z–(1 + i)] = and is ? -π/4 when !z! > !z-2! (A) Straight lines passing through (2, 0) (B) Straight lines passing through (2, 0), (1, 1) (C) A line segment (D) A set of two rays ...

1. Prove that for all real x,y the value of x2+2xy+3y2-6x-2y cannot be less than -11. More I'll Post later. ...

log7 log7{7+[7+(7+.......∞)1/2]1/2}1/2 find its value..... ...

Sum to n terms: 2/3 + 8/9 + 26/27 + 80/81 ... Ans: n - 1/2(1 - 3-n) ...

signum fn is defined as sgn x= |x|/x ={1 if x>0 {0 if x=0 {-1 if x<0 when x=0 sgn x will become 0/0 which is indeterminate. so how is its value 0? ...

1) Why and how any root of an imaginary number is an imaginary number? I would be grateful if someone give me a deep knowledge about it. :) ...

WHAT IS A 9-POINT CENTRE?? ...

Please give solutions for these:- 1) If a2+b2+c2=4, x2+y2+z2=9 then what is the maximum value of ax+by+cz ? 2) Sum of the series upto 11 terms : 1.2.3.4+2.3.4.5+..........+n(n+1)(n+2)(n+3) 3) Prove 1.3.5.7......upto 100 terms ...

If Sn denotes the sum of the products of the first n natural numbers taken two at a time, then find the sum of the infinite series : ∞ Σ Sn/(n+1)! n=1 ...

∞ Σ xn+1 = x2/(1-x) n=1 ...

prove that nth degree polynomial equation has n roots. ...

Column I: A) The no of solutions of the system of equations x+2y = 6 and |x-3| = y is m, then B) If x and y are Integers and (x-8)(x-10) = 2y, the no. of solutions is n, then C) The no. of Integral Solutions for the equation ...

*Image* Help me with this. I don't have the book ...