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 (More than One Correct Answer)
+4
-2
Area of the region bounded by the curve $$y = {e^x}$$ and lines $$x=0$$ and $$y=e$$ is
A
$$e-1$$
B
$$\int\limits_1^e {\ln \left( {e + 1 - y} \right)dy} $$
C
$$e - \int\limits_0^1 {{e^x}dx} $$
D
$$\int\limits_1^e {\ln y\,dy} $$
3
IIT-JEE 2009 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
If $${{{{\sin }^4}x} \over 2} + {{{{\cos }^4}x} \over 3} = {1 \over 5},$$ then
A
$${\tan ^2}x = {2 \over 3}$$
B
$${{{{\sin }^8}x} \over 8} + {{{{\cos }^8}x} \over {27}} = {1 \over {125}}$$
C
$${\tan ^2}x = {1 \over 3}$$
D
$${{{{\sin }^8}x} \over 8} + {{{{\cos }^8}x} \over {27}} = {2 \over {125}}$$
4
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.

The conditional probability that $$X\ge6$$ given $$X>3$$ equals :

A
$${{125} \over {216}}$$
B
$${{25} \over {216}}$$
C
$${{5} \over {36}}$$
D
$${{25} \over {36}}$$

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