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

The value of $a$ for which the system of equations $a^3x + (a + 1)^3y + (a + 2)^3z = 0$,$ax + (a + 1)y + (a + 2)z = 0$,$x + y + z = 0$ has a non-zero solution is

In which of the following reactions is the product an ether?

$X$-rays are used in:

$A$ police party is moving in a jeep at a constant speed $v$. They see a thief at a distance $x$ on a motorcycle which is at rest. The moment the police see the thief,the thief starts moving with a constant acceleration $a$. Which of the following relations is true if the police are able to catch the thief?

Which one of the following elements on doping with germanium,makes it a $p$-type semiconductor?