All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.

Column I	Column II
(A) (CH3)2SiCl2	(P) Hydrogen halide formation
(B) XeF4	(Q) Redox reaction
(C) Cl2	(R) Reacts with glass
(D) VCl5	(S) Polymerisation
	(T) O2 formation

Match the statement in Column-$$I$$ with the values in Column-$$II$$

$$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ Column-$$I$$
(A)$$\,\,\,\,$$ A line from the origin meets the lines $$\,{{x - 2} \over 1} = {{y - 1} \over { - 2}} = {{z + 1} \over 1}$$
and $${{x - {8 \over 3}} \over 2} = {{y + 3} \over { - 1}} = {{z - 1} \over 1}$$ at $$P$$ and $$Q$$ respectively. If length $$PQ=d,$$ then $${d^2}$$ is
(B)$$\,\,\,\,$$ The values of $$x$$ satisfying $${\tan ^{ - 1}}\left( {x + 3} \right) - {\tan ^{ - 1}}\left( {x - 3} \right) = {\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ are
(C)$$\,\,\,\,$$ Non-zero vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c \,\,$$ satisfy $$\overrightarrow a \,.\,\overrightarrow b \, = 0.$$
$$\left( {\overrightarrow b - \overrightarrow a } \right).\left( {\overrightarrow b + \overrightarrow c } \right) = 0$$ and $$2\left| {\overrightarrow b + \overrightarrow c } \right| = \left| {\overrightarrow b - \overrightarrow a } \right|.$$
If $$\overrightarrow a = \mu \overrightarrow b + 4\overrightarrow c \,\,,$$ then the possible values of $$\mu $$ are
(D)$$\,\,\,\,$$ Let $$f$$ be the function on $$\left[ { - \pi ,\pi } \right]$$ given by $$f(0)=9$$
and $$f\left( x \right) = \sin \left( {{{9x} \over 2}} \right)/\sin \left( {{x \over 2}} \right)$$ for $$x \ne 0$$
The value of $${2 \over \pi }\int_{ - \pi }^\pi {f\left( x \right)dx} $$ is

$$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$Column-$$II$$
(p)$$\,\,\,\,$$ $$-4$$
(q)$$\,\,\,\,$$ $$0$$
(r)$$\,\,\,\,$$ $$4$$
(s)$$\,\,\,\,$$ $$5$$
(t)$$\,\,\,\,$$ $$6$$

Match the statements in Column I with those in Column II.

[Note : Here z takes value in the complex plane and Im z and Re z denotes, respectively, the imaginary part and the real part of z.]

Column I

(A) The set of points z satisfying $$\left| {z - i} \right|\left. {z\,} \right\|\,\, = \left| {z + i} \right|\left. {\,z} \right\|$$ is contained in or equal to
(B) The set of points z satisfying $$\left| {z + 4} \right| + \,\left| {z - 4} \right| = 10$$ is contained in or equal to
(C) If $$\left| w \right|$$= 2, then the set of points $$z = w - {1 \over w}$$ is contained in or equal to
(D) If $$\left| w \right|$$ = 1, then the set of points $$z = w + {1 \over w}$$ is contained in or equal to.

Column II

(p) an ellipse with eccentricity $${4 \over 5}$$
(q) the set of points z satisfying Im z = 0
(r) the set of points z satisfying $$\left| {{\rm{Im }}\,{\rm{z }}} \right| \le 1$$
(s) the set of points z satisfying $$\,\left| {{\mathop{\rm Re}\nolimits} \,\,z} \right| < 2$$
(t) the set of points z satisfying $$\left| {\,z} \right| \le 3$$

Consider a triangle $$ABC$$ and let $$a, b$$ and $$c$$ denote the lengths of the sides opposit to vertices $$A, B$$ and $$C$$ respectively. Suppose $$a = 6,b = 10$$ and the area of the triangle is $$15\sqrt 3 $$, if $$\angle ACB$$ is obtuse and if $$r$$ denotes the radius of the incircle of the triangle, then r² is equal to :