1
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$y=y(x), x \in(0, \pi / 2)$$ be the solution curve of the differential equation

$$\left(\sin ^{2} 2 x\right) \frac{d y}{d x}+\left(8 \sin ^{2} 2 x+2 \sin 4 x\right) y=2 \mathrm{e}^{-4 x}(2 \sin 2 x+\cos 2 x)$$,

with $$y(\pi / 4)=\mathrm{e}^{-\pi}$$, then $$y(\pi / 6)$$ is equal to :

A
$$\frac{2}{\sqrt{3}} e^{-2 \pi / 3}$$
B
$$\frac{2}{\sqrt{3}} \mathrm{e}^{2 \pi / 3}$$
C
$$\frac{1}{\sqrt{3}} e^{-2 \pi / 3}$$
D
$$\frac{1}{\sqrt{3}} e^{2 \pi / 3}$$
2
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If the tangents drawn at the points $$\mathrm{P}$$ and $$\mathrm{Q}$$ on the parabola $$y^{2}=2 x-3$$ intersect at the point $$R(0,1)$$, then the orthocentre of the triangle $$P Q R$$ is :

A
(0, 1)
B
(2, $$-$$1)
C
(6, 3)
D
(2, 1)
3
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$C$$ be the centre of the circle $$x^{2}+y^{2}-x+2 y=\frac{11}{4}$$ and $$P$$ be a point on the circle. A line passes through the point $$\mathrm{C}$$, makes an angle of $$\frac{\pi}{4}$$ with the line $$\mathrm{CP}$$ and intersects the circle at the points $$Q$$ and $$R$$. Then the area of the triangle $$P Q R$$ (in unit $$^{2}$$ ) is :

A
2
B
2$$\sqrt2$$
C
$$8 \sin \left(\frac{\pi}{8}\right)$$
D
$$8 \cos \left(\frac{\pi}{8}\right)$$
4
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The remainder when $$7^{2022}+3^{2022}$$ is divided by 5 is :

A
0
B
2
C
3
D
4
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