1
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1
Out of Syllabus

Let the plane ax + by + cz = d pass through (2, 3, $$-$$5) and is perpendicular to the planes
2x + y $$-$$ 5z = 10 and 3x + 5y $$-$$ 7z = 12. If a, b, c, d are integers d > 0 and gcd (|a|, |b|, |c|, d) = 1, then the value of a + 7b + c + 20d is equal to :

A
18
B
20
C
24
D
22
2
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1
Out of Syllabus

If two distinct point Q, R lie on the line of intersection of the planes $$- x + 2y - z = 0$$ and $$3x - 5y + 2z = 0$$ and $$PQ = PR = \sqrt {18}$$ where the point P is (1, $$-$$2, 3), then the area of the triangle PQR is equal to :

A
$${2 \over 3}\sqrt {38}$$
B
$${4 \over 3}\sqrt {38}$$
C
$${8 \over 3}\sqrt {38}$$
D
$$\sqrt {{{152} \over 3}}$$
3
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1
Out of Syllabus

The acute angle between the planes P1 and P2, when P1 and P2 are the planes passing through the intersection of the planes $$5x + 8y + 13z - 29 = 0$$ and $$8x - 7y + z - 20 = 0$$ and the points (2, 1, 3) and (0, 1, 2), respectively, is :

A
$${\pi \over 3}$$
B
$${\pi \over 4}$$
C
$${\pi \over 6}$$
D
$${\pi \over 12}$$
4
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1
Out of Syllabus

Let the plane $$P:\overrightarrow r \,.\,\overrightarrow a = d$$ contain the line of intersection of two planes $$\overrightarrow r \,.\,\left( {\widehat i + 3\widehat j - \widehat k} \right) = 6$$ and $$\overrightarrow r \,.\,\left( { - 6\widehat i + 5\widehat j - \widehat k} \right) = 7$$. If the plane P passes through the point $$\left( {2,3,{1 \over 2}} \right)$$, then the value of $${{|13\overrightarrow a {|^2}} \over {{d^2}}}$$ is equal to :

A
90
B
93
C
95
D
97
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