Let $${a_1}$$ , $${a_2}$$ , $${a_3}$$ ,....... be a G.P. such that
$${a_1}$$ < 0, $${a_1}$$ + $${a_2}$$ = 4 and $${a_3}$$ + $${a_4}$$ = 16.
If $$\sum\limits_{i = 1}^9 {{a_i}} = 4\lambda $$, then $$\lambda $$ is equal to:

The locus of the mid-points of the perpendiculars drawn from points on the line, x = 2y to the line x = y is :

Let A = [a_ij] and B = [b_ij] be two 3 × 3 real matrices such that b_ij = (3)^(i+j-2)a_ji, where i, j = 1, 2, 3. If the determinant of B is 81, then the determinant of A is:

Let $$\alpha $$ and $$\beta $$ be the roots of the equation x² - x - 1 = 0.
If p_k = $${\left( \alpha \right)^k} + {\left( \beta \right)^k}$$ , k $$ \ge $$ 1, then which one of the following statements is not true?