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Trigonometric Functions and Equations question

2022 · Shift 2 · Q27

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JEE Advanced
Mathematics
Trigonometric Functions and Equations
2022 · Shift 2 · Q27

Trigonometric Functions and Equations question

2022 · Shift 2 · Q27

JEE AdvancedMathematicsTrigonometric Functions and EquationsMultiple correct+4 / −2

Let

P Q R S

be a quadrilateral in a plane, where

Q R=1, \angle P Q R=\angle Q R S=70^{\circ}, \angle P Q S=15^{\circ}

and

\angle P R S=40^{\circ}

. If

\angle R P S=\theta^{\circ}, P Q=\alpha

and

P S=\beta

, then the interval(s) that contain(s) the value of

4 \alpha \beta \sin \theta^{\circ}

is/are

A
$(0, \sqrt{2})$
B
$(1,2)$
C
$(\sqrt{2}, 3)$
D
$(2 \sqrt{2}, 3 \sqrt{2})$

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