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

The area enclosed by the curves $$y=\log _{e}\left(x+\mathrm{e}^{2}\right), x=\log _{e}\left(\frac{2}{y}\right)$$ and $$x=\log _{\mathrm{e}} 2$$, above the line $$y=1$$ is:

A
$$2+\mathrm{e}-\log _{\mathrm{e}} 2$$
B
$$1+e-\log _{e} 2$$
C
$$e-\log _{e} 2$$
D
$$1+\log _{e} 2$$
2
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$y=y(x)$$ be the solution curve of the differential equation $$ \frac{d y}{d x}+\frac{1}{x^{2}-1} y=\left(\frac{x-1}{x+1}\right)^{1 / 2}$$, $$x >1$$ passing through the point $$\left(2, \sqrt{\frac{1}{3}}\right)$$. Then $$\sqrt{7}\, y(8)$$ is equal to :

A
$$11+6 \log _{e} 3$$
B
19
C
$$12-2 \log _{\mathrm{e}} 3$$
D
$$19-6 \log _{\mathrm{e}} 3$$
3
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The differential equation of the family of circles passing through the points $$(0,2)$$ and $$(0,-2)$$ is :

A
$$2 x y \frac{d y}{d x}+\left(x^{2}-y^{2}+4\right)=0$$
B
$$2 x y \frac{d y}{d x}+\left(x^{2}+y^{2}-4\right)=0$$
C
$$2 x y \frac{d y}{d x}+\left(y^{2}-x^{2}+4\right)=0$$
D
$$2 x y \frac{d y}{d x}-\left(x^{2}-y^{2}+4\right)=0$$
4
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the tangents at two points $$\mathrm{A}$$ and $$\mathrm{B}$$ on the circle $$x^{2}+\mathrm{y}^{2}-4 x+3=0$$ meet at origin $$\mathrm{O}(0,0)$$. Then the area of the triangle $$\mathrm{OAB}$$ is :

A
$$\frac{3 \sqrt{3}}{2}$$
B
$$\frac{3 \sqrt{3}}{4}$$
C
$$\frac{3}{2 \sqrt{3}}$$
D
$$\frac{3}{4 \sqrt{3}}$$
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