If the lengths of the tangents drawn from a point $P$ to the three circles $x^2+y^2-4=0$,$x^2+y^2-2x+3y=0$,and $x^2+y^2+7y-18=0$ are equal,then the coordinates of $P$ are

If $\frac{1-x+6x^2}{x-x^3} = \frac{A}{x} + \frac{B}{1-x} + \frac{C}{1+x}$,then $A$ is equal to

Which one of the following is a stimulant?

$A$ number $n$ is chosen at random from $\{1, 2, 3, 4, \ldots, 1000\}$. The probability that $n$ is a number that leaves remainder $1$ when divided by $7$ is:

If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are three non-coplanar vectors,then the vector equation $\overrightarrow{r}=(1-p-q) \overrightarrow{a}+p \overrightarrow{b}+q \overrightarrow{c}$ represents a :

The magnetic induction and the intensity of the magnetic field inside an iron core of an electromagnet are $1 \ Wb \ m^{-2}$ and $150 \ A \ m^{-1}$,respectively. The relative permeability of iron is $\left(\mu_0 = 4 \pi \times 10^{-7} \ H \ m^{-1}\right)$.