1
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1

A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x $$-$$ y + 4 = 0, then the area of R is ____________.

2
JEE Main 2022 (Online) 25th June Morning Shift
Numerical
+4
-1

Let the abscissae of the two points P and Q be the roots of $$2{x^2} - rx + p = 0$$ and the ordinates of P and Q be the roots of $${x^2} - sx - q = 0$$. If the equation of the circle described on PQ as diameter is $$2({x^2} + {y^2}) - 11x - 14y - 22 = 0$$, then $$2r + s - 2q + p$$ is equal to __________.

3
JEE Main 2022 (Online) 24th June Evening Shift
Numerical
+4
-1

Let a circle C : (x $$-$$ h)2 + (y $$-$$ k)2 = r2, k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to ___________.

4
JEE Main 2021 (Online) 31st August Evening Shift
Numerical
+4
-1
Out of Syllabus
Let B be the centre of the circle x2 + y2 $$-$$ 2x + 4y + 1 = 0. Let the tangents at two points P and Q on the circle intersect at the point A(3, 1). Then 8.$$\left( {{{area\,\Delta APQ} \over {area\,\Delta BPQ}}} \right)$$ is equal to _____________.