IIT-JEE 2009 Paper 1 Offline | JEE Advanced Year Wise Previous Years Questions - ExamSIDE.Com

Joint Entrance Examination

Medical

Graduate Aptitude Test in Engineering

CBSE

1

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

$$\int\limits_1^e {\ln y\,dy} $$

2

IIT-JEE 2009 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-0

Match the statements/expressions in Column I with the open intervals in Column II :

	Column I		Column II
(A)	Interval contained in the domain of definition of non-zero solutions of the differential equation $${(x - 3)^2}y' + y = 0$$	(P)	$$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$
(B)	Interval containing the value of the integral $$\int\limits_1^5 {(x - 1)(x - 2)(x - 3)(x - 4)(x - 5)dx} $$	(Q)	$$\left( {0,{\pi \over 2}} \right)$$
(C)	Interval in which at least one of the points of local maximum of $${\cos ^2}x + \sin x$$ lies	(R)	$$\left( {{\pi \over 8},{{5\pi } \over 4}} \right)$$
(D)	Interval in which $${\tan ^{ - 1}}(\sin x + \cos x)$$ is increasing	(S)	$$\left( {0,{\pi \over 8}} \right)$$
		(T)	$$( - \pi ,\pi )$$

A

(A)$$\to$$(P), (Q), (S); (B)$$\to$$(P), (T), (S); (C)$$\to$$(P), (Q), (R), (T); (D)$$\to$$(S)

B

(A)$$\to$$(P), (Q), (S); (B)$$\to$$(P), (T), (R); (C)$$\to$$(P), (Q), (R), (T); (D)$$\to$$(R)

C

(A)$$\to$$(P), (Q), (S); (B)$$\to$$(P), (T), (S); (C)$$\to$$(S), (Q), (R), (T); (D)$$\to$$(S)

D

(A)$$\to$$(P), (T), (S); (B)$$\to$$(P), (T), (S); (C)$$\to$$(P), (Q), (R), (T); (D)$$\to$$(S)

3

IIT-JEE 2009 Paper 1 Offline

MCQ (Single Correct Answer)

+4

-1

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

The probability that X = 3 equals

A

$${{25} \over {216}}$$

B

$${{25} \over {36}}$$

C

$${{5} \over {36}}$$

D

$${{125} \over {216}}$$

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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