If $x^2+y^2+z^2 \neq 0, \quad x=c y+b z, \quad y=a z+c x$ and $z=b x+a y$,then $a^2+b^2+c^2+2 a b c$ is equal to

$10 \ g$ of a radioactive element is disintegrated to $1 \ g$ in $2.303 \ \text{minutes}$. What is the half-life (in minutes) of that radioactive element?

If two identical bar magnets,each of length $l$,pole strength $m$ and magnetic moment $M$ are placed perpendicular to each other with their unlike poles in contact,the magnetic moment of the combination is

$A$ Wheatstone bridge is balanced. Find the ratio of electric power dissipated in $(P + Q)$ to $(R + S)$.

What are the products formed when ammonia reacts with excess chlorine?