If $X$ is a binomial variate with mean $\frac{16}{5}$ and variance $\frac{48}{25}$, then $P(X \leq 2)=$

$A(a, 0)$ is a fixed point and $\theta$ is a parameter such that $0<\theta<2 \pi$. If $P(a \cos \theta, a \sin \theta)$ is a point on the circle $x^2+y^2=a^2$ and $Q(b \sin \theta,-b \cos \theta)$ is a point on the circle $x^2+y^2=b^2$, then the locus of the centroid of the $\triangle A P Q$ is

The point $P(4,1)$ undergoes the following transformations in succession :

(i) origin is shifted to the point $(1,6)$ by translation of axes.

(ii) translation through a distance of 2 units along the positive direction of $X$-axis.

(iii) rotation of axes through an angle of $90^{\circ}$ in the positive direction.

Then, the coordinates of the point $P$ in its final position are

$L_1 \equiv a x-3 y+5=0$ and $L_2 \equiv 4 x-6 y+8=0$ are two parallel lines. If $p, q$ are the intercepts made by $L_1=0$ and $m, n$ are the intercepts made by $L_2=0$ on the $X$, $Y$-coordinate axes respectively, then the equation of the line passing through the points $(p, q)$ and $(m, n)$ is