1
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
Out of Syllabus
Let S be the set of all real values of $$\lambda$$ such that a plane passing through the points (–$$\lambda$$2, 1, 1), (1, –$$\lambda$$2, 1) and (1, 1, – $$\lambda$$2) also passes through the point (–1, –1, 1). Then S is equal to :
A
{1, $$-$$1}
B
{3, $$-$$ 3}
C
$$\left\{ {\sqrt 3 } \right\}$$
D
$$\left\{ {\sqrt 3 , - \sqrt 3 } \right\}$$
2
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
Out of Syllabus
If an angle between the line, $${{x + 1} \over 2} = {{y - 2} \over 1} = {{z - 3} \over { - 2}}$$ and the plane, $$x - 2y - kz = 3$$ is $${\cos ^{ - 1}}\left( {{{2\sqrt 2 } \over 3}} \right),$$ then a value of k is :
A
$$\sqrt {{3 \over 5}}$$
B
$$- {5 \over 2}$$
C
$$- {3 \over 2}$$
D
$$\sqrt {{5 \over 3}}$$
3
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
Out of Syllabus
The perpendicular distance from the origin to the plane containing the two lines,

$${{x + 2} \over 3} = {{y - 2} \over 5} = {{z + 5} \over 7}$$ and

$${{x - 1} \over 1} = {{y - 4} \over 4} = {{z + 4} \over 7},$$ is :
A
$$6\sqrt {11}$$
B
$${{11} \over {\sqrt 6 }}$$
C
11
D
11$$\sqrt 6$$
4
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
Out of Syllabus
A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(–1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is :
A
cos$$-$$1$$\left( {{{17} \over {31}}} \right)$$
B
cos$$-$$1$$\left( {{{9} \over {35}}} \right)$$
C
cos$$-$$1$$\left( {{{19} \over {35}}} \right)$$
D
cos$$-$$1$$\left( {{7 \over {31}}} \right)$$
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