Identify the reagent used in the following reaction.
Benzoic acid $\stackrel{\text{Reagent}}{\Delta}$ Benzoyl chloride + Phosphorous oxychloride + Hydrogen chloride

$A$ vector $\vec{a}$ has components $2p$ and $1$ with respect to a two-dimensional rectangular Cartesian system. This system is rotated through a certain angle $\theta$ about the origin in the counter-clockwise direction. If $\vec{a}$ has components $p+1$ and $1$ with respect to the new system,then:

For a suitably chosen real constant $a$,let a function $f: R - \{-a\} \rightarrow R$ be defined by $f(x) = \frac{a-x}{a+x}$. Further,suppose that for any real number $x \neq -a$ and $f(x) \neq -a$,$(f \circ f)(x) = x$. Then $f\left(\frac{-1}{2}\right)$ is equal to

In an experiment with $15$ observations of $x$,the results $\sum x^2 = 2830$ and $\sum x = 170$ are obtained. If one observation $20$ is found to be incorrect and is replaced by the correct observation $30$,what is the correct variance?

Which of the following is not linear?

If three unit vectors $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ satisfy $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$, then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is