1
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
Let ($$\lambda$$, 2, 1) be a point on the plane which passes through the point (4, $$-$$2, 2). If the plane is perpendicular to the line joining the points ($$-$$2, $$-$$21, 29) and ($$-$$1, $$-$$16, 23), then $${\left( {{\lambda \over {11}}} \right)^2} - {{4\lambda } \over {11}} - 4$$ is equal to __________.
2
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
A line 'l' passing through origin is perpendicular to the lines

$${l_1}:\overrightarrow r = (3 + t)\widehat i + ( - 1 + 2t)\widehat j + (4 + 2t)\widehat k$$

$${l_2}:\overrightarrow r = (3 + 2s)\widehat i + (3 + 2s)\widehat j + (2 + s)\widehat k$$

If the co-ordinates of the point in the first octant on 'l2‘ at a distance of $$\sqrt {17}$$ from the point of intersection of 'l' and 'l1' are (a, b, c) then 18(a + b + c) is equal to ___________.
3
JEE Main 2021 (Online) 24th February Evening Slot
Numerical
+4
-1
Let $$\lambda$$ be an integer. If the shortest distance between the lines

x $$-$$ $$\lambda$$ = 2y $$-$$ 1 = $$-$$2z and x = y + 2$$\lambda$$ = z $$-$$ $$\lambda$$ is $${{\sqrt 7 } \over {2\sqrt 2 }}$$, then the value of | $$\lambda$$ | is _________.
4
JEE Main 2020 (Online) 4th September Morning Slot
Numerical
+4
-0
If the equation of a plane P, passing through the intersection of the planes,
x + 4y - z + 7 = 0 and 3x + y + 5z = 8 is ax + by + 6z = 15 for some a, b $$\in$$ R, then the distance of the point (3, 2, -1) from the plane P is...........
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