1
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 ___________.
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2
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
A function f is defined on [$$-$$3, 3] as

$$f(x) = \left\{ {\matrix{ {\min \{ |x|,2 - {x^2}\} ,} & { - 2 \le x \le 2} \cr {[|x|],} & {2 < |x| \le 3} \cr } } \right.$$ where [x] denotes the greatest integer $$ \le $$ x. The number of points, where f is not differentiable in ($$-$$3, 3) is ___________.
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3
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
Let $$\overrightarrow a = \widehat i + \alpha \widehat j + 3\widehat k$$ and $$\overrightarrow b = 3\widehat i - \alpha \widehat j + \widehat k$$. If the area of the parallelogram whose adjacent sides are represented by the vectors $$\overrightarrow a $$ and $$\overrightarrow b $$ is $$8\sqrt 3 $$ square units, then $$\overrightarrow a $$ . $$\overrightarrow b $$ is equal to __________.
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4
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
Out of Syllabus
If the curves x = y4 and xy = k cut at right angles, then (4k)6 is equal to __________.
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