The line $x + y = 4$ divides the line segment joining the points $(-1, 1)$ and $(5, 7)$ in the ratio:

$P$ and $Q$ are points on the line joining $A,(-2, 5)$ and $B,(3, 1)$ such that $AP = PQ = QB$. Then the mid-point of $PQ$ is

Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of set $A$ is $56$ more than the total number of subsets of set $B$. Then the distance of the point $P(m, n)$ from the point $Q(-2, -3)$ is

If the coordinates of two opposite vertices of a square are $(a, b)$ and $(b, a)$,find the area of the square.

The distance of the point $(b \cos \theta, b \sin \theta)$ from the origin is

Let $A = (a_1, a_2)$ and $B = (b_1, b_2)$ be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between $A$ and $B$?