JEE Advanced · 2015 · 24 May 2015 · Paper 1 · Chapter_pending

Match the entries in Column I with the entries in Column II.

Column I

(A) In ${\mathbb{R}}^2$, if the magnitude of the projection vector of the vector $\alpha \hat{i}+\beta \hat{j}$ on $\sqrt{3}\hat{i}+\hat{j}$ 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 $f(x)=\{\begin{array}{cc}-3a{x}^2-2,& x<1\\ bx+a^2,& x\ge 1\end{array}$ is differentiable for all $x\in \mathbb{R}$. Then possible value(s) of $a$ is (are)

(C) Let $\omega \ne 1$ be a complex cube root of unity. If ${\left(3-3\omega +2{\omega }^2\right)}^{4n+3}+$ ${\left(2+3\omega -3{\omega }^2\right)}^{4n+3}+{\left(-3+2\omega +3{\omega }^2\right)}^{4n+3}=0$, then 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 positive real number such that $a,5,q,b$ is an arithmetic progression, then the value(s) of $|q-a|$ is (are)

Column II

(P) 1

(Q) 2

(R) 3

(S) 4

(T) 5