1
JEE Main 2021 (Online) 20th July Evening Shift
Numerical
+4
-1
If the point on the curve y2 = 6x, nearest to the point $$\left( {3,{3 \over 2}} \right)$$ is ($$\alpha$$, $$\beta$$), then 2($$\alpha$$ + $$\beta$$) is equal to _____________.
2
JEE Main 2021 (Online) 20th July Morning Shift
Numerical
+4
-1
Let y = mx + c, m > 0 be the focal chord of y2 = $$-$$ 64x, which is tangent to (x + 10)2 + y2 = 4. Then, the value of 4$$\sqrt 2$$ (m + c) is equal to _____________.
3
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 __________.
4
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 _________.
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