1
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1

The coordination number of Al in the crystalline state of AlCl$$_3$$ is ___________.

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2
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1

The total number of cyclic structural as well as stereoisomers possible for a compound with the molecular formula C$$_5$$H$$_{10}$$ is ____________.

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3
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1
Let $$\left( {x,\,y,\,z} \right)$$ be points with integer coordinates satisfying the system of homogeneous equation: $$$\matrix{ {3x - y - z = 0} \cr { - 3x + z = 0} \cr { - 3x + 2y + z = 0} \cr } $$$

Then the number of such points for which $$x^2 + {y^2} + {z^2} \le 100$$ is

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4
IIT-JEE 2009 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
For $$0 < \theta < {\pi \over 2},$$ the solution (s) of $$$\sum\limits_{m = 1}^6 {\cos ec\,\left( {\theta + {{\left( {m - 1} \right)\pi } \over 4}} \right)\,\cos ec\,\left( {\theta + {{m\pi } \over 4}} \right) = 4\sqrt 2 } $$$ is (are)
A
$$\,{\pi \over 4}$$
B
$$\,{\pi \over 6 }$$
C
$$\,{\pi \over 12}$$
D
$$\,{5\pi \over 12}$$
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