Recently Active Algebra Questions

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Solve: xy+x+y=23 xz+z+x=41 yz+y+z=27 ...

Calculate the product for n≥2 *Image* ...

22. There are n triangles of positive area that have one vertex A(0,0) and the other two vertices whose coordinares are drawn independently with replacement from the set {0,1,2,3,4} e.g. (1,2), (0,1), (2,2) etc. Find the valu ...

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Δ= 1+x (1+x)a (1+x)bc 1+x (1+x)b (1+x)ca 1+x (1+x)c (1+x)ab find coeff. of x and x2. ...

EX 2 1 ) Find the no. of ways in which 3 distinct no.s can be selected from the set { 3 , 32,......,3101} so that they form a GP. 2 ) Find the no. of ways in which 12 identical coins can be distributed in 6 diff purses , if n ...

Prove that every circle passing through the points z_{0} and 1/z 0 intersects the circle |z|=1 at right angles ...

Does any body know whats rotation theorem ,locus of a complex nos . if you can explain me in detail its fine or if you have any link or you have any material can you send me at karanmehtaforu@yahoo.com Thanks in advance ...

(x^2+x-2)^3+(2x^2-x-1)^3=27(x^2-1)^3 Source: RMO 2002 ...

Can neone pls explain how n{1+(n-1)+ (n-1)(n-2)/1.2 +...........+1} =n.2n-1 ? AND nx{1+(n-1)x+ (n-1)(n-2)/1.2 x2+........+xn-1} =nx(1+x)n-1 ? Pleaaaaaaaase do explain this... ...

Let x1,x2,x3...xn be roots of equation xn+xn-1+.....+x+1=0 Compute the expression \frac{1}{x_1 -1}+\frac{1}{x_2 -1}+\frac{1}{x_3 -1}...+\frac{1}{x_n -1} Hence prove that \sum_{r=1}^{n}{cot \frac {r\pi}{n+1}} ...

Let P(x) be a polynomial with integral coefficients. Prove that we can never have P(a) = b and P(b) = c and P(c) = a where a,b and c are integers. ( bhatt sir , please stay away) ...

Find the product of these numbers... (1-\frac{1}{2^2})(1-\frac{1}{3^2})(1-\frac{1}{5^2})(1-\frac{1}{7^2})(1-\frac{1}{11^2})... till infinity... Given that \frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+ ...

Given : 2/1!9! + 2/3!7! + 1/5!5! = 2m/n! Find the orthocentre of the Δ with sides x-y+1=0, x+y+3=0 and 2x+5y-2=0 in terms of m and n. Very Good Question....Try it... :-) ...

Let a and b be rel numbers such that sin a+sin b=(√2)/2 and cos a+cos b =(√6)/2 then sin(a+b) will be ???? ...

an unbiased die,with faces numbered 1,2,3,4,5,6 is thrown n times and list of n numbers showing up is noted.what is the probability that among the numbers 1,2,3,4,5,6 only three numbers appear in the list ...

If lzl=1 ,prove that the points represented by \sqrt{\frac{1+z}{1-z}} lie on one or the other of two fixed perpendicular lines ...

(1) Min. value of (x2+y2)+ (x2+(y-1)2) = ...

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Prove that \left|\alpha +\sqrt {\alpha ^2 -\beta ^2} \right|+\left|\alpha -\sqrt {\alpha ^2 -\beta ^2} \right|=\left|\alpha +\beta \right|+\left|\alpha -\beta \right| where α,β are complex numbers ...

If z=i log(2- 3 ),then find cosz . ...

If θ1 ε[0,π/6] ,i=1,2,3,4,5 and sinθ1 z4+sinθ2 z3+sinθ3 z2 +sinθ4 z +sinθ5=2,then prove that lzl<1/2 ...

If p,q,r,s are probablities of raining at 4 diff places at some fixed moment.then find max and min value of 3(p^2+q^2+r^2+s^2)-2(p+q+r+s)+4 ...

if a< b< c< d then(x-a)(x-c)+2(x-b)(x-d)=0then the roots are a)real and imaginary b)real and unequal c)imaginary d)rational The question is a good one for beginners.. so try it :) *Asked by saheli... ...

p(x) is a polynomial with integer coefficients. For some positive integer c, none of p(1), p(2), ... , p(c) are divisible by c. Prove that p(b) is not zero for any integer b. (bhatt sir stay away) ...

Let f(n) be the least number of times you have to hit the key in the calculator to get a number less than 2 starting from n, n being a natural number. e.g. f(2) =1and f(5) =2. For how many natural numbers m such that 1<m&l ...

p(x) is a polynomial with integer coefficients. For some positive integer c, none of p(1), p(2), ... , p(c) are divisible by c. Prove that p(b) is not zero for any integer b. (BHATT SIR STAY AWAY) ...

Find [1+\frac{1}{2}+\frac{1}{3}+....\frac{1}{121}] [] ≡ G.I.F ...

If z=iii.....∞=A+iB then find lzl ...