1
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Change Language

A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x $$-$$ y + 4 = 0, then the area of R is ____________.

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2
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

A circle of radius 2 unit passes through the vertex and the focus of the parabola y2 = 2x and touches the parabola $$y = {\left( {x - {1 \over 4}} \right)^2} + \alpha $$, where $$\alpha$$ > 0. Then (4$$\alpha$$ $$-$$ 8)2 is equal to ______________.

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3
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

Let the mirror image of the point (a, b, c) with respect to the plane 3x $$-$$ 4y + 12z + 19 = 0 be (a $$-$$ 6, $$\beta$$, $$\gamma$$). If a + b + c = 5, then 7$$\beta$$ $$-$$ 9$$\gamma$$ is equal to ______________.

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4
JEE Main 2022 (Online) 27th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A projectile is launched at an angle '$$\alpha$$' with the horizontal with a velocity 20 ms$$-$$1. After 10 s, its inclination with horizontal is '$$\beta$$'. The value of tan$$\beta$$ will be : (g = 10 ms$$-$$2).

A
tan$$\alpha$$ + 5sec$$\alpha$$
B
tan$$\alpha$$ $$-$$ 5sec$$\alpha$$
C
2tan$$\alpha$$ $$-$$ 5sec$$\alpha$$
D
2tan$$\alpha$$ $$+$$ 5sec$$\alpha$$
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