The equation of the circle which passes through the points $(2, 3)$ and $(4, 5)$ and whose centre lies on a straight line $4x - y - 3 = 0$, is

If $\theta$ is the eccentric angle of a point on the ellipse $\dfrac{x^2}{25} + \dfrac{y^2}{9} = 1$ such that the distance of the point from the center is $5$, then $\theta = $.......

$\lim\limits_{x \to 0}\left[\dfrac{x \cdot \log(1 + 4x)}{\left(e^{4x} - 1\right)^2}\right] = \cdots$

Consider the following statements.
$p$: If $3^4 > 4^3$, then $3^3 > 4^4$
$q$: The roots of the equation $x^2 - 2x + 2 = 0$ are real if and only if Mumbai is in Maharashtra.
$r$: Statement $p$ is true or statement $q$ is false.
Which of the following has truth value T (true)?