1
JEE Main 2022 (Online) 25th July Morning Shift
+4
-1

Let the locus of the centre $$(\alpha, \beta), \beta>0$$, of the circle which touches the circle $$x^{2}+(y-1)^{2}=1$$ externally and also touches the $$x$$-axis be $$\mathrm{L}$$. Then the area bounded by $$\mathrm{L}$$ and the line $$y=4$$ is:

A
$$\frac{32 \sqrt{2}}{3}$$
B
$$\frac{40 \sqrt{2}}{3}$$
C
$$\frac{64}{3}$$
D
$$\frac{32}{3}$$
2
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1

The area enclosed by y2 = 8x and y = $$\sqrt2$$ x that lies outside the triangle formed by y = $$\sqrt2$$ x, x = 1, y = 2$$\sqrt2$$, is equal to:

A
$${{16\sqrt 2 } \over 6}$$
B
$${{11\sqrt 2 } \over 6}$$
C
$${{13\sqrt 2 } \over 6}$$
D
$${{5\sqrt 2 } \over 6}$$
3
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1

The area of the bounded region enclosed by the curve

$$y = 3 - \left| {x - {1 \over 2}} \right| - |x + 1|$$ and the x-axis is :

A
$${9 \over 4}$$
B
$${45 \over 16}$$
C
$${27 \over 8}$$
D
$${63 \over 16}$$
4
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

The area of the region S = {(x, y) : y2 $$\le$$ 8x, y $$\ge$$ $$\sqrt2$$x, x $$\ge$$ 1} is

A
$${{13\sqrt 2 } \over 6}$$
B
$${{11\sqrt 2 } \over 6}$$
C
$${{5\sqrt 2 } \over 6}$$
D
$${{19\sqrt 2 } \over 6}$$
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