1
JEE Main 2023 (Online) 11th April Evening Shift
+4
-1 Let P be the plane passing through the points $$(5,3,0),(13,3,-2)$$ and $$(1,6,2)$$. For $$\alpha \in \mathbb{N}$$, if the distances of the points $$\mathrm{A}(3,4, \alpha)$$ and $$\mathrm{B}(2, \alpha, a)$$ from the plane P are 2 and 3 respectively, then the positive value of a is :

A
6
B
4
C
5
D
3
2
JEE Main 2023 (Online) 11th April Morning Shift
+4
-1 Let $$(\alpha, \beta, \gamma)$$ be the image of the point $$\mathrm{P}(2,3,5)$$ in the plane $$2 x+y-3 z=6$$. Then $$\alpha+\beta+\gamma$$ is equal to :

A
10
B
9
C
5
D
12
3
JEE Main 2023 (Online) 11th April Morning Shift
+4
-1 If equation of the plane that contains the point $$(-2,3,5)$$ and is perpendicular to each of the planes $$2 x+4 y+5 z=8$$ and $$3 x-2 y+3 z=5$$ is $$\alpha x+\beta y+\gamma z+97=0$$ then $$\alpha+\beta+\gamma=$$

A
15
B
16
C
17
D
18
4
JEE Main 2023 (Online) 10th April Evening Shift
+4
-1 Let the image of the point $$\mathrm{P}(1,2,6)$$ in the plane passing through the points $$\mathrm{A}(1,2,0), \mathrm{B}(1,4,1)$$ and $$\mathrm{C}(0,5,1)$$ be $$\mathrm{Q}(\alpha, \beta, \gamma)$$. Then $$\left(\alpha^{2}+\beta^{2}+\gamma^{2}\right)$$ is equal to :

A
76
B
62
C
70
D
65
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