Let p(x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x$$-$$ 1 and it leaves remainder 6 when divided by x + 1; then :

Let A be any 3 $$ \times $$ 3 invertible matrix. Then which one of the following is not always true ?

If (27)⁹⁹⁹ is divided by 7, then the remainder is :

The number of real values of $$\lambda $$ for which the system of linear equations

2x + 4y $$-$$ $$\lambda $$z = 0

4x + $$\lambda $$y + 2z = 0

$$\lambda $$x + 2y + 2z = 0

has infinitely many solutions, is :