A. \( \quad \) Column I \( R^{2} \), if the magnitude of the projection vector of the vector \( \alpha \hat{i}+\beta \hat{j} \) on \( \frac{P .}{\text { Column II }} \) \( \sqrt{3} \hat{i}+\hat{j} \) is \( \sqrt{3} \) and if \( \alpha=2+\sqrt{3} \beta \).
W then possible value(s) of \( |\alpha| \) is/are
is differentiable for all \( x \in R \). Then, possible value(s) of a is/are
C. Let \( \omega(\neq 1) \) be a complex cube root of unity. If \( \left(3-3 \omega+2 \omega^{2}\right)^{4 n+3}+\quad R \), 3 \( \left(2+3 \omega-3 \omega^{2}\right)^{4 n+3} \)
\( +\left(-3+2 \omega+3 \omega^{2}\right)^{4 n+3}=0 \), then the possible value(s) of \( n \) is/are
D. Let the harmonic mean of two positive real numbers \( a \) and \( b \) be 4 . If \( q \) is a \( S \). 4 positive real number such that \( a, 5, q, b \) is in arithmetic progression, then the value(s) of \( |q-2 a| \) is/are
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