If $$n$$ is a natural number such that
$$n = {p_1}{}^{{\alpha _1}}{p_2}{}^{{\alpha _2}}.{p_3}{}^{{\alpha _3}}........{p_k}{}^{{\alpha _k}}$$ and $${p_1},{p_2},\,\,......,\,{p_k}$$ are distinct primes, then show that $$In$$ $$n \ge k$$ $$in$$ 2

If $$a,\,b$$ and $$c$$ are in A.P., then the straight line $$ax + by + c = 0$$ will always pass through a fixed point whose coordinates are ...............

Two equal sides of an isosceles triangle are given by the equations $$7x - y + 3 = 0$$ and $$x + y - 3 = 0$$ and its thirds side passes through the point $$(1, -10)$$. Determine the equation of the third side.

The lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to the same circle. The radius of this circle is ........................................