1
JEE Advanced 2016 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-0
Football teams $${T_1}$$ and $${T_2}$$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $${T_1}$$ winning, drawing and losing a game against $${T_2}$$ are $${1 \over 2},{1 \over 6}$$ and $${1 \over 3}$$ respectively. Each team gets $$3$$ points for a win, $$1$$ point for a draw and $$0$$ point for a loss in a game. Let $$X$$ and $$Y$$ denote the total points scored by teams $${T_1}$$ and $${T_2}$$ respectively after two games.

$$P\,\left( {X = Y} \right)$$ is

A
$${{11} \over {36}}$$
B
$${{1} \over {3}}$$
C
$${{13} \over {36}}$$
D
$${{1} \over {2}}$$
2
JEE Advanced 2016 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Let $$P$$ be the image of the point $$(3,1,7)$$ with respect to the plane $$x-y+z=3.$$ Then the equation of the plane passing through $$P$$ and containing the straight line $${x \over 1} = {y \over 2} = {z \over 1}$$ is
A
$$x+y-3z=0$$
B
$$3x+z=0$$
C
$$x-4y+7z=0$$
D
$$2x-y=0$$
3
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $$\widehat u = {u_1} \widehat i + {u_2}\widehat j + {u_3}\widehat k$$ be a unit vector in $${{R^3}}$$ and
$$\widehat w = {1 \over {\sqrt 6 }}\left( {\widehat i + \widehat j + 2\widehat k} \right).$$ Given that there exists a vector $${\overrightarrow v }$$ in $${{R^3}}$$ such that $$\left| {\widehat u \times \overrightarrow v } \right| = 1$$ and $$\widehat w.\left( {\widehat u \times \overrightarrow v } \right) = 1.$$ Which of the following statement(s) is (are) correct?
A
There is exactly one choice for such $${\overrightarrow v }$$
B
There are infinitely many choices for such $${\overrightarrow v }$$
C
If $$\widehat u$$ lies in the $$xy$$-plane then $$\left| {{u_1}} \right| = \left| {{u_2}} \right|$$
D
If $$\widehat u$$ lies in the $$xz$$-plane then $$2\left| {{u_1}} \right| = \left| {{u_3}} \right|$$
4
JEE Advanced 2016 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

Let $$P = \left[ {\matrix{ 1 & 0 & 0 \cr 4 & 1 & 0 \cr {16} & 4 & 1 \cr } } \right]$$ and I be the identity matrix of order 3. If $$Q = [{q_{ij}}]$$ is a matrix such that $${P^{50}} - Q = I$$ and $${{{q_{31}} + {q_{32}}} \over {{q_{21}}}}$$ equals

A
52
B
103
C
201
D
205
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