JEE Main 2022 (Online) 24th June Evening Shift | Straight Lines and Pair of Straight Lines Question 53 | Mathematics

Let the area of the triangle with vertices A(1, $$\alpha$$), B($$\alpha$$, 0) and C(0, $$\alpha$$) be 4 sq. units. If the points ($$\alpha$$, $$-$$$$\alpha$$), ($$-$$$$\alpha$$, $$\alpha$$) and ($$\alpha$$², $$\beta$$) are collinear, then $$\beta$$ is equal to :

$$-$$8

$$-$$64

512

JEE Main 2021 (Online) 31st August Evening Shift

MCQ (Single Correct Answer)

-1

Let A be the set of all points ($$\alpha$$, $$\beta$$) such that the area of triangle formed by the points (5, 6), (3, 2) and ($$\alpha$$, $$\beta$$) is 12 square units. Then the least possible length of a line segment joining the origin to a point in A, is :

$${4 \over {\sqrt 5 }}$$

$${16 \over {\sqrt 5 }}$$

$${8 \over {\sqrt 5 }}$$

$${12 \over {\sqrt 5 }}$$

JEE Main 2021 (Online) 31st August Morning Shift

MCQ (Single Correct Answer)

-1

If p and q are the lengths of the perpendiculars from the origin on the lines,

x cosec $$\alpha$$ $$-$$ y sec $$\alpha$$ = k cot 2$$\alpha$$ and

x sin$$\alpha$$ + y cos$$\alpha$$ = k sin2$$\alpha$$

respectively, then k² is equal to :

4p² + q²

2p² + q²

p² + 2q²

p² + 4q²

JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)

-1

Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y-axis at C. The locus of the mid-point P of MC is :

3x² $$-$$ 2y $$-$$ 6 = 0

3x² + 2y $$-$$ 6 = 0

2x² + 3y $$-$$ 9 = 0

2x² $$-$$ 3y + 9 = 0

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