If two numbers $p$ and $q$ are chosen randomly from the set $\{1,2,3,4\}$, one by one, with replacement, then the probability of getting $\mathrm{p}^2 \geq 4 \mathrm{q}$ is

The function defined by $\mathrm{f}(x)=\frac{2 x+3}{3 x+4}, x \neq-\frac{4}{3}$ is

The equation $|z+1-i|=|z-1+i|$ represents a (where z is a complex number)

If $\int \frac{2 x+3}{(x-1)\left(x^2+1\right)} d x$

$$ =\log _e\left\{(x-1)^{\frac{5}{2}}\left(x^2+1\right)^2\right\}-\frac{1}{2} \tan ^{-1} x+\mathrm{A} $$

where A is an arbitrary constant, then the value of $a$ is