If \overrightarrow{{u}}({x})={x} \stackrel{\^}{{i}}+(\sin {x}) \stackrel{\^}{{j}}+(1+\sin {x}) \stackrel{\^}{{k}}, {{v}}({x})=\stackrel{\^}{{i}}+\cos {x}(\stackrel{\^}{{j}}+\stackrel{\^}{{k}}) and {{w}}({x})=\sin {x}(\stackrel{\^}{{j}}+\stackrel{\^}{{k}}), all are linearly dependent vectors for {x}=\\alpha, then (\frac{2 \\alpha}{\\pi})^{2} is divided by 8 leaves remainder ......

JEE Advanced 2021 Full Test 3 Paper 2

SECTION – C (Numerical Answer Type)
This section contains 06 questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to the SECOND DECIMAL PLACE; e.g. XXXXX. XX).

Question : 50 of 54

Marks: +1, -0

→

(x)=x

+(sin‌x)

+(1+sin‌x)

, v(x)=

+cos‌x(

) and w(x)=sin‌x(

), all are linearly dependent vectors for x=α, then (

2α

)2 is divided by 8 leaves remainder ......

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x	sin‌x	1+sin‌x
1	cos‌x	cos‌x
0	sin‌x	sin‌x