JEE (Advanced) 2007 Paper-2

The structure of the intermediate I is

Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.

Match the compounds/ions in Column I with their properties/reactions in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.

Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.

Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

If $$\mid z \mid = 1$$ and $$z \neq \pm 1$$, then all the values of $$\frac{z}{1 - z^2}$$ lie on

Let $$E^c$$ denote the complement of an event E. Let E, F, G be pairwise independent events with $$P(G) > 0$$ and $$P(E \cap F \cap G) = 0$$. Then $$P(E^c \cap F^c \mid G)$$ equals

$$\frac{d^2x}{dy^2}$$ equals

The differential equation $$\frac{dy}{dx} = \frac{\sqrt{1 - y^2}}{y}$$ determines a family of circles with

Let $$\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$$ be unit vectors such that $$\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} = \overrightarrow{0}$$. Which one of the following is correct?