Two unit negative charges are placed on a straight line. $A$ positive charge $q$ is placed exactly at the midpoint between these unit charges. If the system of these three charges is in equilibrium,the value of $q$ (in $C$) is

Cyclic hydrocarbon molecule $A$ has all the carbon and hydrogen atoms in a single plane. All the carbon-carbon bonds are of the same length,which is less than $1.54 \ \mathring{A}$ but more than $1.34 \ \mathring{A}$. The $C-C$ bond angle will be

$\sim (p \vee q) \vee (\sim p \wedge q)$ is logically equivalent to

If $A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix}$ and $hA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}$,then the values of $h, a, b$ are respectively

$\int \frac{1+\cos 4 x}{\cot x-\tan x} d x$ is equal to

$ABC$ is a triangular plate of uniform thickness. Its sides are in the ratio as shown in the figure. Let $I_{AB}$,$I_{BC}$,and $I_{CA}$ be the moments of inertia of the plate about the sides $AB$,$BC$,and $CA$ respectively. Which of the following relations is true for this arrangement?