1
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

Match each of the compounds in Column I with its characteristic reaction(s) in Column II.

Column I Column II
(A) $$C{H_3}C{H_2}C{H_2}CN$$ (P) Reduction with $$Pd - C/{H_2}$$
(B) $$C{H_3}C{H_2}OCOC{H_3}$$ (Q) Reduction with $$SnC{l_2}/HCl$$
(C) $$C{H_3} - CH = CH - C{H_2}OH$$ (R) Development of foul smell on treatment with chloroform and alcoholic KOH
(D) $$C{H_3}C{H_2}C{H_2}C{H_2}N{H_2}$$ (S) Reduction with diisobutylaluminium hydride (DIBAL-H)
(T) Alkaline hydrolysis

A
$$\mathrm{(A)\to(P),(Q),(S),(T);(B)\to(Q),(T);(C)\to(P);(D)\to(S)}$$
B
$$\mathrm{(A)\to(Q), (R), (S),(T);(B)\to(S),(T);(C)\to(P);(D)\to(R)}$$
C
$$\mathrm{(A)\to(P),(R),(S),(T);(B)\to(S),(T);(C)\to(P);(D)\to(R), (T)}$$
D
$$\mathrm{(A)\to(P),(Q),(S),(T);(B)\to(S),(T);(C)\to(P);(D)\to(R)}$$
2
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

Let $$z = x + iy$$ be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation $$\overline z {z^3} + z{\overline z ^3} = 350$$ is

A
48
B
32
C
40
D
80
3
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Let $$z = \,\cos \,\theta \, + i\,\sin \,\theta $$ . Then the value of $$\sum\limits_{m = 1}^{15} {{\mathop{\rm Im}\nolimits} } ({z^{2m - 1}})\,at\,\theta \, = {2^ \circ }$$ is
A
$${1 \over {\sin \,{2^ \circ }}}$$
B
$${1 \over {3\sin \,{2^ \circ }}}$$
C
$${1 \over {2\sin \,{2^ \circ }}}$$
D
$${1 \over {4\sin \,{2^ \circ }}}$$
4
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$P(3,2,6)$$ be a point in space and $$Q$$ be a point on the line $$$\widehat r = \left( {\widehat i - \widehat j + 2\widehat k} \right) + \mu \left( { - 3\widehat i + \widehat j + 5\widehat k} \right)$$$

Then the value of $$\mu $$ for which the vector $${\overrightarrow {PQ} }$$ is parallel to the plane $$x - 4y + 3z = 1$$ is :

A
$${1 \over 4}$$
B
$$-{1 \over 4}$$
C
$${1 \over 8}$$
D
$$-{1 \over 8}$$
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