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JEE Main 2021 (Online) 27th July Evening Shift
Numerical
+4
-1
Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its center at (3, $$-$$4), one focus at (4, $$-$$4) and one vertex at (5, $$-$$4). If mx $$-$$ y = 4, m > 0 is a tangent to the ellipse E, then the value of 5m2 is equal to _____________.
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2
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 _____________.
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3
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 _____________.
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4
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 __________.
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