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Column-II
[JEE Advanced-2015]
P
(A) In \( \mathrm{R}^{2} \), if the magnitude of the projection vector of the vector \( \alpha \hat{i}+\beta \hat{j} \) on \( \sqrt{3} \hat{i}+\hat{j} \) (P) \( \quad 1 \)
W is \( \sqrt{3} \) and if \( \alpha=2+\sqrt{3} \beta \), then possible value(s) of \( |\alpha| \) is (are)
(B) Let a and \( b \) be real numbers such that the function \( f(x)=\left\{\begin{array}{cc}-3 a x^{2}-2, & x1 \\ b x+a^{2}, & x \geq 1\end{array} \quad\right. \) (Q) 2 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.
(R) 3
If \( \left(3-3 \omega+2 \omega^{2}\right)^{4+3}+\left(2+3 \omega-3 \omega^{2}\right)^{4+3}+\left(-3+2 \omega+3 \omega^{2}\right)^{4 n+3}=0 \), then possible value(s) of \( \mathrm{n} \) is (are)
(D) Let the harmonic mean of two positive real numbers a and b be 4 .
(S) 4
If \( q \) is a positive real number such that \( a, 5, q, b \) is an arithmetic progression, then the value(s) of \( |q-a| \) is (are)
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