Let `a, b, c, k` be rational numbers such that `k` is not perfect cube if ` a + b k^(1/3) + c k^(2/3) = 0` prove that ` a = b = c =0`

Let a,b,c be distinct complex numbers such that (a)/(1-b)=(b)/(1-c)=(c)/(1-a)=k. Find the value of k.

Let a,b,c be real numbers with sum equals zero,let us denote (a^(k)+b^(k)+c^(k))/(k)=S_(k) then (S_(5)S_(2))/(S_(7)) is equal to :

let a be unit vector, b = 2i + j - k and c = I + 3k. The maximum value of [a b c] is

Let a, b be the roots of the equation x^(2) - 4 x +k_(1) = 0 and c , d the roots of the equation x^(2) - 36 x + k_(2) = 0 If a lt b lt c lt d and a, b,c,d are in G.P. then the product k_(1) k_(2) equals

Let A be a square matrix of order 3xx3 , then |k A| is equal to(A) k|A| (B) k^2|A| (C) k^3|A| (D) 3k |A|

Matrix A=[[1, 0, -k], [2, 1, 3], [k, 0, 1]] is invertible for ..a) k = 1 b) k = − 1 c) k = 0 d) All real k

A+ B = C and tan A = k tan B , then prove that sin (A-B) = (k-1)/(k+1) sin C