For the following questions, choose the correct answers from the codes (a), (b), (c) and (d) def...

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For the following questions, choose the correct answers from the codes (a), (b), (c) and (d) defined as follows.
(a) Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I
(b) Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I
(c) Statement I is true, Statement II is false
(d) Statement \( I \) is false, Statement II is true
\( f(x) \) is a polynomial of degree 3 passing through origin having local extrema at \( x=\pm a \).
Statement I Ratio of areas in which \( f(x) \) cuts the circle \( x^{2}+y^{2}=36 \) is \( 1: 1 \).
Statement II Both \( y=f(x) \) and the circle are symmetric about origin.
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