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

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

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

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) 27th July Evening Shift
+4
-1

If the length of the perpendicular drawn from the point $$P(a, 4,2)$$, a $$>0$$ on the line $$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}$$ is $$2 \sqrt{6}$$ units and $$Q\left(\alpha_{1}, \alpha_{2}, \alpha_{3}\right)$$ is the image of the point P in this line, then $$\mathrm{a}+\sum\limits_{i=1}^{3} \alpha_{i}$$ is equal to :

A
7
B
8
C
12
D
14
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