The equation of the parabola with the focus $(3,0)$ and the directrix $x+3=0$ is:

The angle between the straight lines represented by $(x^2+y^2) \sin^2 \alpha = (x \cos \alpha - y \sin \alpha)^2$ is

$A$ machine gun fires a bullet of mass $40\, g$ with a velocity $1200\, m/s$. The man holding it can exert a maximum force of $144\, N$ on the gun. How many bullets can he fire per second at the most?

$x A_{(s)} \rightleftharpoons y B_{(g)} + z C_{(g)}$. If $\frac{K_c}{K_p} = (RT)^{-2}$,then which is correct?

$A$ circle $C_1$ of radius $2$ touches both $x$-axis and $y$-axis. Another circle $C_2$ whose radius is greater than $2$ touches circle $C_1$ and both the axes. Then the radius of circle $C_2$ is-

The coefficient of $x^{24}$ in the expansion of $(1+x^2)^{12}(1+x^{12})(1+x^{24})$ is