What is obtained by the decomposition of sodium nitrate at a temperature above $800\,^oC$?

Three non-zero non-collinear vectors $\vec{a}, \vec{b}$ and $\vec{c}$ are such that $\vec{a}+3\vec{b}$ is collinear with $\vec{c}$,and $3\vec{b}+2\vec{c}$ is collinear with $\vec{a}$. Then $\vec{a}+3\vec{b}+2\vec{c}$ equals to

If the sum of two unit vectors is a unit vector,what is the magnitude of their difference?

$(a)$ Show that for every natural number $n$ relatively prime to $10$,there exists a natural number $m$ consisting only of digits $1$ such that $n$ divides $m$.
$(b)$ Hence or otherwise,show that every positive rational number can be expressed in the form $\frac{a}{10^b(10^c-1)}$ for some natural numbers $a, b, c$.

Two positively charged particles $m_{1}$ and $m_{2}$ have been accelerated across the same potential difference of $200 \ keV$ as shown below. Given mass of $m_{1} = 1 \ amu$ and $m_{2} = 4 \ amu$. The de Broglie wavelength of $m_{1}$ will be $x$ times that of $m_{2}$. The value of $x$ is . . . . . . . (nearest integer)

If the sum of two of the roots of $x^3+p x^2-q x+r=0$ is zero,then $p q$ is equal to