Column I Column II (A) In a triangle XYZ, let a,b\;{and}\;c be the length of the sides opposite to the angles X,Y\;{and}\;Z, respectively. If 2(a²-b²)=c² {and}\; λ=(X-Y)/ Z ,then possible values of n for which (nπ λ)=0 is (are) (P) 1 (B) In a triangle XYZ,let a,b\;{and}\;c be the length of the sides opposite to the anglesX,Y\;{and}\;Z,respectively.If 1+ 2X-2 2Y=2 X, Y,then possible value(s) of a/b is (are) (Q) 2 (C) In {R}³,let {{3i}} + {j}, {i} + {{3j}} \;{and}\; β{i} + (1-β){j} be the position vectors of X, Y {and} Z with respect of the origin, respectively. If the distance of Z from the bisector of the acute angle of {OX}\;{with}\;{OY}\;{is}\;{3}{{2}}. then the possible value(s)of |β| is (are) (R) 3 (D) Suppose that F(α) denotes the area of the region bounded by x=0,x-2,y²=4x\;{and}\;y=|α x-1|=|α x-2|+α x,{where} α\{0,1\}.Then the value(s) of F(α)+{8}{3{2}}.where α=0 and α=1 is (are) (S) 5 (T) 6 [JEE Adv 2015 P1]

Question

Examsnet · Accepted Answer

Correct Answer is : (A) → (P, R, S), (B) → (P), (C) → (P, Q), (D) → (S, T)

Column I		Column II
(A)	In a triangle $\triangle XYZ$ , let $a,b\;\text{and}\;c$ be the length of the sides opposite to the angles $X,Y\;\text{and}\;Z$ , respectively. If $2(a^2-b^2)=c^2 \text{and}\; \lambda=\frac{\sin(X-Y)}{\sin Z}$ ,then possible values of $n$ for which $\cos(n\pi \lambda)=0$ is (are)	(P)	1
(B)	In a triangle $\triangle XYZ$ ,let $a,b\;\text{and}\;c$ be the length of the sides opposite to the angles $X,Y\;\text{and}\;Z$ ,respectively.If $1+\cos 2X-2\cos 2Y=2\sin X,\sin Y$ ,then possible value(s) of $\frac{a}{b}$ is (are)	(Q)	2
(C)	In $\mathbb{R}^3$ ,let $\sqrt{\hat{3i}} + \hat{j}, \hat{i} + \sqrt{\hat{3j}} \;\text{and}\; \beta\hat{i} + (1-\beta)\hat{j}$ be the position vectors of $X, Y \text{and} Z$ with respect of the origin, respectively. If the distance of Z from the bisector of the acute angle of $\overrightarrow{OX}\;\text{with}\;\overrightarrow{OY}\;\text{is}\;\frac{3}{\sqrt{2}}$ . then the possible value(s)of \|β\| is (are)	(R)	3
(D)	Suppose that $F(\alpha)$ denotes the area of the region bounded by $x=0,x-2,y^2=4x\;\text{and}\;y=\|\alpha x-1\|=\|\alpha x-2\|+\alpha x,\text{where} \alpha\in\{0,1\}$ .Then the value(s) of $F(\alpha)+\frac{8}{3\sqrt{2}}$ .where $\alpha=0$ and $\alpha=1$ is (are)	(S)	5
		(T)	6

JEE Advanced 2015 Paper 1