1
JEE Main 2022 (Online) 30th June Morning Shift
Numerical
+4
-1
Change Language

Let PQ be a focal chord of length 6.25 units of the parabola y2 = 4x. If O is the vertex of the parabola, then 10 times the area (in sq. units) of $$\Delta$$POQ is equal to ___________.

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2
JEE Main 2022 (Online) 30th June Morning Shift
Numerical
+4
-1
Change Language

Consider a triangle ABC whose vertices are A(0, $$\alpha$$, $$\alpha$$), B($$\alpha$$, 0, $$\alpha$$) and C($$\alpha$$, $$\alpha$$, 0), $$\alpha$$ > 0. Let D be a point moving on the line x + z $$-$$ 3 = 0 = y and G be the centroid of $$\Delta$$ABC. If the minimum length of GD is $$\sqrt {{{57} \over 2}} $$, then $$\alpha$$ is equal to ____________.

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3
JEE Main 2022 (Online) 30th June Morning Shift
Numerical
+4
-1
Change Language

The probability distribution of X is :

X 0 1 2 3
P(X) $${{1 - d} \over 4}$$ $${{1 + 2d} \over 4}$$ $${{1 - 4d} \over 4}$$ $${{1 + 3d} \over 4}$$

For the minimum possible value of d, sixty times the mean of X is equal to _______________.

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4
JEE Main 2022 (Online) 30th June Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

Let $${S_1} = \{ x \in [0,12\pi ]:{\sin ^5}x + {\cos ^5}x = 1\} $$

and $${S_2} = \{ x \in [0,8\pi ]:{\sin ^7}x + {\cos ^7}x = 1\} $$

Then $$n({S_1}) - n({S_2})$$ is equal to ______________.

Your input ____
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