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Application of Derivatives question

2023 · Shift 1 · Q22

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PYQ Library
JEE Advanced
Mathematics
Application of Derivatives
2023 · Shift 1 · Q22

Application of Derivatives question

2023 · Shift 1 · Q22

JEE AdvancedMathematicsApplication of DerivativesMCQ+3 / −1

Let

Q

be the cube with the set of vertices

\left\{\left(x_1, x_2, x_3\right) \in \mathbb{R}^3: x_1, x_2, x_3 \in\{0,1\}\right\}

. Let

F

be the set of all twelve lines containing the diagonals of the six faces of the cube

Q

. Let

S

be the set of all four lines containing the main diagonals of the cube

Q

; for instance, the line passing through the vertices

(0,0,0)

and

(1,1,1)

is in

S

. For lines

\ell_1

and

\ell_2

, let

d\left(\ell_1, \ell_2\right)

denote the shortest distance between them. Then the maximum value of

d\left(\ell_1, \ell_2\right)

, as

\ell_1

varies over

F

and

\ell_2

varies over

S

, is :

A
$\frac{1}{\sqrt{6}}$
B
$\frac{1}{\sqrt{8}}$
C
$\frac{1}{\sqrt{3}}$
D
$\frac{1}{\sqrt{12}}$

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