JEE Advanced 2015 · Paper 1, Mathematics question 60

Column I

• A
  In a triangle $\Delta XYZ$, let $a$, $b$ and $c$ be the lengths of the sides opposite to the angles $X$, $Y$ and $Z$, respectively. If $2(a^2-b^2)=c^2$ and $\lambda=\dfrac{\sin(X-Y)}{\sin Z}$, then possible values of $n$ for which $\cos(n\pi\lambda)=0$ is (are)
• B
  In a triangle $\Delta XYZ$, let $a$, $b$ and $c$ be the lengths of the sides opposite to the angles $X$, $Y$ and $Z$, respectively. If $1+\cos2X-2\cos2Y=2\sin X\sin Y$, then possible value(s) of $\dfrac ab$ is (are)
• C
  In $\mathbb R^2$, let $\sqrt3\hat i+\hat j$, $\hat i+\sqrt3\hat j$ 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 $\dfrac3{\sqrt2}$, 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 $F(\alpha)+\dfrac83\sqrt2$, when $\alpha=0$ and $\alpha=1$, is (are)

Column II

• P
  1
• Q
  2
• R
  3
• S
  5
• T
  6