JEE Advanced · 2015 · 24 May 2015 · Paper 1 · Properties of Triangle

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

Column I

(A) In a triangle $△XYZ$, let $a,b$ and $c$ be the lengths of the sides opposite to the angles $X,Y$ and $Z$, respectively. If $2\left(a^2-b^2\right)=c^2$ and $\lambda =\frac{\sin (X-Y)}{\sin Z}$, then possible values of $n$ for which $\cos (n\pi \lambda )=0$ is (are)

(B) In a triangle $△XYZ$, let $a,b$ and $c$ be the lengths of the sides opposite to the angles $X,Y$ and $Z$, respectively. If $1+\cos 2X-2\cos 2Y=2\sin X\sin Y$, then possible value(s) of $\frac{a}{b}$ is (are)

(C) In ${\mathbb{R}}^2$, let $\sqrt{3}\hat{i}+\hat{j},\hat{i}+\sqrt{3}\hat{j}$ and $\beta \hat{i}+(1-\beta )\hat{j}$ be the position vectors of $X,Y$ and $Z$ with respect to the origin $O$, respectively. If the distance of $Z$ from the bisector of the acute angle of $\overrightarrow{OX}$ with $\overrightarrow{OY}$ is $\frac{3}{\sqrt{2}}$, then possible value(s) of $|\beta |$ is (are)

(D) Suppose that $F(\alpha )$ denotes the area of the region bounded by $x=0,x=2,y^2=4x$ and $y=|\alpha x-1|+|\alpha x-2|+\alpha x$, where $\alpha \in \{0,1\}$. Then the value(s) of $F(\alpha )+\frac{8}{3}\sqrt{2}$, when $\alpha =0$ and $\alpha =1$, is (are)

Column II

(P) 1

(Q) 2

(R) 3

(S) 5

(T) (not listed in source)

Column II
(P) 1
(Q) 2
(R) 3
(S) 5
(T) 6