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

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

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 :

If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then $${{a + b} \over {a - b}}$$ is equal to :