Mathematics Mock Test - 9

Determine the coordinates of the foot of the perpendicular drawn from the origin to the plane $4x-2y+3z-6=0$.

Let $a,b,c$ be distinct non-negative numbers. If the vectors $a\hat{i}+a\hat{j}+c\hat{k}$, $\hat{i}+\hat{k}$ and $c\hat{i}+c\hat{j}+b\hat{k}$ lie in a plane, then $c$ is:

$f(x)=x+\sqrt{x^2}$ is a function from $\mathbb{R}\to \mathbb{R}$. Then $f(x)$ is:

In a job placement event, there are $1000$ aspirants attending a company interview, out of which $430$ are females. It is known that $10\%$ of the females are graduates. Determine the probability that an aspirant selected randomly is a graduate given that the selected aspirant is a female?

The vectors $\vec{a}=x\hat{i}+y\hat{j}+z\hat{k}$ and $\vec{b}=\hat{j}$ are such that $\vec{a},\vec{c},\vec{b}$ form a right-handed system. Then $\vec{c}$ is: