1
JEE Main 2022 (Online) 29th June Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

Let d be the distance between the foot of perpendiculars of the points P(1, 2, $$-$$1) and Q(2, $$-$$1, 3) on the plane $$-$$x + y + z = 1. Then d2 is equal to ___________.

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2
JEE Main 2022 (Online) 29th June Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

The number of elements in the set $$S = \{ \theta \in [ - 4\pi ,4\pi ]:3{\cos ^2}2\theta + 6\cos 2\theta - 10{\cos ^2}\theta + 5 = 0\} $$ is __________.

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3
JEE Main 2022 (Online) 29th June Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

The number of solutions of the equation

$$2\theta - {\cos ^2}\theta + \sqrt 2 = 0$$ in R is equal to ___________.

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4
JEE Main 2022 (Online) 29th June Morning Shift
Numerical
+4
-1
Change Language

$$50\tan \left( {3{{\tan }^{ - 1}}\left( {{1 \over 2}} \right) + 2{{\cos }^{ - 1}}\left( {{1 \over {\sqrt 5 }}} \right)} \right) + 4\sqrt 2 \tan \left( {{1 \over 2}{{\tan }^{ - 1}}(2\sqrt 2 )} \right)$$ is equal to ____________.

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