Recently Active Algebra Questions

if f'(x/y).f(y/x) = \frac{x^{2}+y^{2}}{xy} for all x,y belongs to positive R and f(1)= 1 then f2(x) is????????? ...

the number of ordered pair (a,b) such that (a + ib)^2010 = a - ib is??? ...

Let A= \begin{bmatrix} 3 & -4\\ 1 & -1 \end{bmatrix} if det. (A+A^2+A^3......A^n)=64, then what is the value of n??? ...

a bag contains 10 white and 10 black balls. a person draws 2 balls at a time without replacement and repeats the process till bag is empty. what is the probability that he draws the balls of same colour each time? ...

Good an' simple --- try this one --- Given four distinct numbers in the interval (0,1) , show that there exists 2 numbers among them x and y , such that ------ 0 < x \sqrt{1 - y^{2}} - y \sqrt{1 - x^{2}} < \frac{1}{2} ...

i feel that the question has some printing errors i am typing the question as given in the book consider \ the \ sequence \ x_n \ defined \ by \ \\ x_1 = \frac{1}{2} ,x_{n+1}=x_n^2 + x_n \\ define \ S = \frac{1}{x_1 +1}+\frac ...

let Zr,r=1,2,3.....n are n distinct roots of eq ^{n}C_{1}x+^{n}C_{2}x^{2}+^{n}C_{3}x^{3}+.......^{n}C_{n}x^{n}=0 in argand plane.If der exist exactly one Zr, rε{1,2....n} such that arg\left(\frac{Z_{r}-(-1+\sqrt{2}i}{(-1)-(- ...

If a1, a2, a3, a4,..........., a100 are the 100 roots of unity then find the value of \sum_{1\leq i \leq j \leq 100}^{}{} (aiaj)5 . ...

*Image* please explain the consequtive steps.... ...

find the product \frac{(1^4 +\frac{1}{4})(3^4 +\frac{1}{4})(5^4 +\frac{1}{4}).......(49^4 +\frac{1}{4})}{(2^4 +\frac{1}{4})(4^4 +\frac{1}{4})(6^4 +\frac{1}{4}).......(50^4 +\frac{1}{4})} ...

i was trying to practise maths but got 1 thing either the buks were 2 easy or it were 2 hard taking the case of trignometry and algebra i used sl loni and hall and knight but found there level easy when i saw arihant ofund it ...

n to the power p -n;divisible by p. p is a prime number. prove it ...

Let P(x)=x^5+ax^4+bx^3+cx^2+dx+e . If the graph of y = P(x) cuts the x-axis at five distinct points and P(0)=0, then which of the coefficients cannot be zero? ...

A sequence is obtained by deleting all the perfect squares from set of natural numbers . Find the remainder when 2003rd term of new sequence is divided by 2048 ?? ...

Q1 A point chosen from 1st quadrant x,y ε[0,4] ,the probablity that it satisfies [x]+[y]=3 is ?? I am getting 1/16 Q2 3 points P,Q,R are selected at random from circumference of circle.Find probablity that they lie on semici ...

if p and q are the roots of the equation x^2 + px + q =0 then a)--- p=1 b)--- p = 1 or 0 c)--- p = -2 d)--- p = -2 or 0 ...

let S={1,2,3,.......,100} the number of unordered pairs (A,B)of subsets of S such that A and B have no ekements in common , where A or B both may be φ(null set) is ? answer : \frac{3^{100} + 1}{2} the no.of order pair is 310 ...

if \ a+b+c =1 ,; a,b, c \rightarrow R^+ \\ prove \ that \ \\ \\ \sum_{cyclic}{} {\frac{a}{1+bc}}\geq \frac{9}{10} ...

If the number of 5 digit numbers in which each of the digits 2 and 5 occur only once is 64k . Then find the value of k . options --- 150 , 148 , 248 , 128 . ...

If x can be any real number, then find the value of \frac{(x-a)(x-b)(x-c)}{(d-a)(d-b)(d-c)}+\frac{(x-b)(x-c)(x-d)}{(a-b)(a-c)(a-d)}+\frac{(x-c)(x-d)(x-a)}{(b-c)(b-d)(b-a)}+\frac{(x-d)(x-a)(x-b)}{(c-d)(c-a)(c-b)} - 1 ...

show that following hold for x include in R *Image* ...

1.An unlimited number of red, white, blue and green balls are given. The number of ways of selecting 10 balls is ? 2.The greatest possible number of points of intersection of 8 straight lines and 4 circles is? ...

\left ( l-m \right )^2 + \left ( p-q \right )^2 = 9 ...

f(x)=\frac{1}{1+x} a)find a no c such that f(cx)=f(x) b)for wat values of c f(cx)=f(x) for 2 values of no x.... ...

A dice is thrown 2n+1 times, n ε N. The probability that faces with even numbers show up odd number of times is = ? ...

for a≤0 the roots of the equation x^2 - 2a|x-a| - 3a^2 = 0 is............ ...

find the sum of the series 1-\frac{1.3}{2.4}+\frac{1.3.5.7}{2.4.6.8}-\frac{1.3.5.7.9.11}{2.4.6.8.10.12}.......\infty forgive teh joker if it has been asked befor btw its not a doubt[6] ...

The set of integers is divided into n infinite APs. If the common differences of the APs are denoted by di, find \sum_{i=1}^n \frac{1}{d_i} ...

for x>1 evaluate \frac{x}{x+1}+\frac{x^{2}}{(x+1)(x^{2}+1)}+\frac{x^{4}}{(x+1)(x^{2}+1)(x^{4}+1)}...........\infty ...

Good prob flicked from another forum: Given complex numbers a,b,c,d such that \frac{a-d}{b-c} and \frac{b-d}{c-a} are purely imaginary, prove that \frac{c-d}{a-b} is also purely imaginary ...