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JEE Advanced 2015 Paper 1

Section: Mathematics

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Question : 60 of 60

Marks: +1, -0

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 Adv 2015 P1]

(A) → (P, R, S), (B) → (P), (C) → (P, Q), (D) → (S, T)
(A) → (P, S, T), (B) → (P), (C) → (P, Q), (D) → (S, T)
(A) → (P, Q, S), (B) → (P), (C) → (P, Q), (D) → (S, T)
(A) → (P, R, S), (B) → (Q), (C) → (P, Q), (D) → (S, T)

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