1
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1 A triangle is formed by the tangents at the point (2, 2) on the curves $$y^2=2x$$ and $$x^2+y^2=4x$$, and the line $$x+y+2=0$$. If $$r$$ is the radius of its circumcircle, then $$r^2$$ is equal to ___________.

2
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1 The vertices of a hyperbola H are ($$\pm$$ 6, 0) and its eccentricity is $${{\sqrt 5 } \over 2}$$. Let N be the normal to H at a point in the first quadrant and parallel to the line $$\sqrt 2 x + y = 2\sqrt 2$$. If d is the length of the line segment of N between H and the y-axis then d$$^2$$ is equal to _____________.

3
JEE Main 2023 (Online) 24th January Morning Shift
Numerical
+4
-1 Let C be the largest circle centred at (2, 0) and inscribed in the ellipse $${{{x^2}} \over {36}} + {{{y^2}} \over {16}} = 1$$. If (1, $$\alpha$$) lies on C, then 10 $$\alpha^2$$ is equal to ____________

4
JEE Main 2023 (Online) 24th January Morning Shift
Numerical
+4
-1 Let a tangent to the curve $$9{x^2} + 16{y^2} = 144$$ intersect the coordinate axes at the points A and B. Then, the minimum length of the line segment AB is ________

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