jee-advanced 2009 Q29

jee-advanced · India · paper2 Vectors: Cross Product & Distances
Match the statements/expressions given in Column I with the values given in Column II.
Column I
(A) Root(s) of the equation $$2\sin^{2}\theta+\sin^{2}2\theta=2$$ (B) Points of discontinuity of the function $$f(x)=\left[\frac{6x}{\pi}\right]\cos\left[\frac{3x}{\pi}\right],$$ where $[y]$ denotes the largest integer less than or equal to $y$
(C) Volume of the parallelopiped with its edges represented by the vectors $$\hat{i}+\hat{j},\quad\hat{i}+2\hat{j}\text{ and }\hat{i}+\hat{j}+\pi\hat{k}$$ (D) Angle between vectors $\vec{a}$ and $\vec{b}$ where $\vec{a},\vec{b}$ and $\vec{c}$ are unit vectors satisfying $$\vec{a}+\vec{b}+\sqrt{3}\vec{c}=\overrightarrow{0}$$
Column II
(p) $\frac{\pi}{6}$
(q) $\frac{\pi}{4}$
(r) $\frac{\pi}{3}$
(s) $\frac{\pi}{2}$
(t) $\pi$
A-(q,s), B-(p,r,s,t), C-(t), D-(r)
Match the statements/expressions given in Column I with the values given in Column II.

\textbf{Column I}\\
(A) Root(s) of the equation
$$2\sin^{2}\theta+\sin^{2}2\theta=2$$
(B) Points of discontinuity of the function
$$f(x)=\left[\frac{6x}{\pi}\right]\cos\left[\frac{3x}{\pi}\right],$$
where $[y]$ denotes the largest integer less than or equal to $y$\\
(C) Volume of the parallelopiped with its edges represented by the vectors
$$\hat{i}+\hat{j},\quad\hat{i}+2\hat{j}\text{ and }\hat{i}+\hat{j}+\pi\hat{k}$$
(D) Angle between vectors $\vec{a}$ and $\vec{b}$ where $\vec{a},\vec{b}$ and $\vec{c}$ are unit vectors satisfying
$$\vec{a}+\vec{b}+\sqrt{3}\vec{c}=\overrightarrow{0}$$

\textbf{Column II}\\
(p) $\frac{\pi}{6}$\\
(q) $\frac{\pi}{4}$\\
(r) $\frac{\pi}{3}$\\
(s) $\frac{\pi}{2}$\\
(t) $\pi$