The value of \( -{ }^{15} \mathrm{C}_{1}+2 \cdot{ }^{15} \mathrm{C}...

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The value of \( -{ }^{15} \mathrm{C}_{1}+2 \cdot{ }^{15} \mathrm{C}_{2}-3 \cdot{ }^{15} \mathrm{C}_{3}+\ldots-15 \cdot{ }^{15} \mathrm{C}_{15}+{ }^{14} \mathrm{C}_{1} \) \( +{ }^{14} \mathrm{C}_{3}+{ }^{14} \mathrm{C}_{5}+\ldots+{ }^{14} \mathrm{C}_{11} \) is
P
IV
(a) \( 2^{14} \)
[JEE Main-2021 (February)]
(b) \( 2^{13}-13 \)
(c) \( 2^{16}-1 \)
(d) \( 2^{13}-14 \)
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