1
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1
Out of Syllabus

If the foot of the perpendicular from the point $$\mathrm{A}(-1,4,3)$$ on the plane $$\mathrm{P}: 2 x+\mathrm{m} y+\mathrm{n} z=4$$, is $$\left(-2, \frac{7}{2}, \frac{3}{2}\right)$$, then the distance of the point A from the plane P, measured parallel to a line with direction ratios $$3,-1,-4$$, is equal to :

A
1
B
$$\sqrt{26}$$
C
2$$\sqrt{2}$$
D
$$\sqrt{14}$$
2
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1
Out of Syllabus

Let the lines

$$\frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}$$ and

$$\frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}$$ be coplanar

and $$\mathrm{P}$$ be the plane containing these two lines.

Then which of the following points does NOT lie on P?

A
$$(0,-2,-2)$$
B
$$(-5,0,-1)$$
C
$$(3,-1,0)$$
D
$$(0,4,5)$$
3
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1
Out of Syllabus

A plane P is parallel to two lines whose direction ratios are $$-2,1,-3$$ and $$-1,2,-2$$ and it contains the point $$(2,2,-2)$$. Let P intersect the co-ordinate axes at the points $$\mathrm{A}, \mathrm{B}, \mathrm{C}$$ making the intercepts $$\alpha, \beta, \gamma$$. If $$\mathrm{V}$$ is the volume of the tetrahedron $$\mathrm{OABC}$$, where $$\mathrm{O}$$ is the origin, and $$\mathrm{p}=\alpha+\beta+\gamma$$, then the ordered pair $$(\mathrm{V}, \mathrm{p})$$ is equal to :

A
$$(48,-13)$$
B
$$(24,-13)$$
C
$$(48,11)$$
D
$$(24,-5)$$
4
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1
Out of Syllabus

The foot of the perpendicular from a point on the circle $$x^{2}+y^{2}=1, z=0$$ to the plane $$2 x+3 y+z=6$$ lies on which one of the following curves?

A
$$(6 x+5 y-12)^{2}+4(3 x+7 y-8)^{2}=1, z=6-2 x-3 y$$
B
$$(5 x+6 y-12)^{2}+4(3 x+5 y-9)^{2}=1, z=6-2 x-3 y$$
C
$$(6 x+5 y-14)^{2}+9(3 x+5 y-7)^{2}=1, z=6-2 x-3 y$$
D
$$(5 x+6 y-14)^{2}+9(3 x+7 y-8)^{2}=1, z=6-2 x-3 y$$
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