Recently Active Algebra Questions

For what values of the parameter a does the function f (x) = x3 + 3(a − 7) x2 + 3(a2 − 9)x −1 have a positive point of maximum? Solution: f '(x) = 3x2 + 6(a − 7) x + 3(a2 − 9) For f (x) to have a maximum at some poi ...

Prove that if z1 and z2 are two complex numbers and c>0 , then |z1+z2|2 ≤ (1+c)|z1|2 + (1+c-1)|z2|2 ...

\frac{9}{1!}+\frac{16}{2!}+\frac{27}{3!}+\frac{42}{4!}+... ...

1. if W is the cube root of unity then (1-W+W2)5 +(1+W-W2) is equal to????? 2.if W is the cube root of unity then (1-W+W2)(1-W2+W6) is eqaul to??? ...

if f(x)= log( 1+x/1-x ) ; g(x) = log( 3x+x3/1+3x2 ) then find f(g(x)) in terms of f(x). 1) -f(x) 2) 3f(x) 3) [f(x)]3 4) -3f(x) ...

find the reflection of the complex no. 2-i in the straight line z = iz ...

http://i41.tinypic.com/kb937n.jpg y do we discard y<y1 in last step?? ...

i have not understood PARTIAL OREDERING,TOTAL ORDERING, and ANTISYMMETRIC RELATIONS. can anyone explain with examples? ...

\texttt{deduce that } \prod_{k=1}^{n-1}{\sin \frac{k\pi}{n}}=\frac{n}{2^{n-1}} ...

1.if a,b,c be the pth, qth and rth terms respectively of an A.P ,prove that a(q-r)+b(r-p)+c(p-q)=0 2.how many terms are identical in the two Arithematic progression 2,4,6,8..... up to 100 terms and 3,6,9 ..... up to 80 terms. ...

*Image* its a doubt ...

find the argument & modules of 3-4i. ...

\sum_{k = 0}^{\infty}\frac{x^{k}}{k+1} ?? ...

1.there are two straight lines. ten points lie on the first line and 8 point lie on the second line. of each points on the other line are joined to each other by line segment , the no. of point of intersction of these lines s ...

*Image* plz tell how we got that second step?? ...

1)Find the number of solutions of the equation *Image* here [.] is greatest integer function 2) evaluate - \int_{0}^{1}{(1+e^{-x^2}})dx 3) \textup{if }I_n=\int_{0}^{1}e^x(x-1)^n \textup{dx} \textup{ and } I_p=24e-65 \\\textup ...

q1) Find the real value of the parameter ' t ' for which there is at least one complex number z = x +iy satisfying the condition | z + 3 | = t2 - 2t + 6 and the inequality |z - 3 3 i| < t2 q2) solve x3 - 3 - { x } = 0 wher ...

*Image* i m getting answer as C///////////plz tell how cum B is right??? ...

Q.1. If p,s>0 and q,r<0 then the roots of the equation (s+q)x^2 + (p+q)x +p-r = 0 are (here p>s , q>r) : (a)Imaginary (b)Real and equal (c)Real and distinct (d) Irrational ...

*Image* ...

Statement 1: The period of *Image* *Image* Statement 2: The period of x - [x] is 1. (a)Statement 1 is false, statement 2 is true (b)Statement 1 is true, statement 2 is true, statement 2 is a correct explanation for statement ...

the fraction exceeding its Pth power by the greatest number possible where P≥2 is...... ans: ( 1/P ) 1/P-1 ...

if 1000!= 2n.I, where I is an odd integer then the value of n??? ...

Mean and variance of a random variable X having binomial distribution are 4 and 2 respectively.Find P(X>6) Edit:Sorry for the mistake,edited it now ...

Statement 1: The period of *Image* *Image* Statement 2: The period of x - [x] is 1. (a)Statement 1 is false, statement 2 is true (b)Statement 1 is true, statement 2 is true, statement 2 is a correct explanation for statement ...

Statement 1: The rank of *Image* is 3. Statement 2: The determinant of the abv matrix is not equal to zero. (A)Statement 1 is false, statement 2 is true (B)Statement 1 is true, statement 2 is true, statement 2 is a correct ex ...

Let A={1, 2, 3, ..., n} Find the number of functions f : A → A having the property that f(f(x)) = f(x). P.S. Edited a bit. ...

BKS FOR GUD AMT OF QUESTION S LIKE OF TOPICS LIKS CALCULUS ...

find the values of k for which l x-1l + l x -2 l + lx + 1 l + l x +2 l = 4k has integral solutions ans in my book is 2 , 3 ,4 ,5 ..............why not one? ( matrix match type) srry i hv edited it now ..........plz proceed no ...

1. If x = 2 + 5i (where i2 = - 1) and 2(1/1!9! + 1/3!7!) + 1/5!5! = 2a/b!, then the value of (x3 - 5x2 + 33x - 19) is equal to (A) a (B) b (C) a - b (D) a + b ...