$a^2 + b^2 + c^2 = 1 ,$ then $ab + bc + ca$ gives =? In a recent examination this question has been asked, which says:
$a^2+b^2+c^2 = 1$ , then  $ab + bc + ca$ gives = ?
What should be the answer? I have tried the formula for $(a+b+c)^2$, but gets varying answer like $0$ or $0.25$, on assigning different values to variables.
How to approach such question? 

Just knowing that $a^2+b^2+c^2=1$ is not enough to determine the value of $ab+bc+ca$. For example, if $a=b=0$ and $c=1$, then $ab+bc+ca = 0$. On the other hand, if $a=b=c=\frac{1}{\sqrt3}$, then $ab+bc+ca = 1$. In fact, using $$(a+b+c)^2=a^2+b^2+c^2 + 2(ab+bc+ca),$$ you get that $$ab+bc+ca=\frac{(a+b+c)^2 - 1}{2}.$$
