1
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
Let L be a common tangent line to the curves

4x2 + 9y2 = 36 and (2x)2 + (2y)2 = 31. Then the

square of the slope of the line L is __________.
2
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
A line is a common tangent to the circle (x $$-$$ 3)2 + y2 = 9 and the parabola y2 = 4x. If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then 2(a + c) is equal to _________.
3
JEE Main 2021 (Online) 25th February Morning Shift
Numerical
+4
-1
The locus of the point of intersection of the lines $$\left( {\sqrt 3 } \right)kx + ky - 4\sqrt 3 = 0$$ and $$\sqrt 3 x - y - 4\left( {\sqrt 3 } \right)k = 0$$ is a conic, whose eccentricity is _________.
4
JEE Main 2020 (Online) 3rd September Evening Slot
Numerical
+4
-0
If the tangent to the curve, y = ex at a point (c, ec) and the normal to the parabola, y2 = 4x at the point (1, 2) intersect at the same point on the x-axis, then the value of c is ________ .
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