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

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1

IIT-JEE 2009 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-0

Match the conics in Column I with the statements/expressions in Column II :

	Column I		Column II
(A)	Circle	(P)	The locus of the point ($$h,k$$) for which the line $$hx+ky=1$$ touches the circle $$x^2+y^2=4$$.
(B)	Parabola	(Q)	Points z in the complex plane satisfying $$\|z+2\|-\|z-2\|=\pm3$$.
(C)	Ellipse	(R)	Points of the conic have parametric representation $$x = \sqrt 3 \left( {{{1 - {t^2}} \over {1 + {t^2}}}} \right),y = {{2t} \over {1 + {t^2}}}$$
(D)	Hyperbola	(S)	The eccentricity of the conic lies in the interval $$1 \le x \le \infty $$.
		(T)	Points z in the complex plane satisfying $${\mathop{\rm Re}\nolimits} {(z + 1)^2} = \|z{\|^2} + 1$$.

A

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

B

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

C

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

D

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

2

IIT-JEE 2009 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

Let $$f$$ be a non-negative function defined on the interval $$[0,1]$$.

If $$\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}dt} = \int\limits_0^x {f(t)dt,0 \le x \le 1} } $$, and $$f(0) = 0$$, then

A

$$f\left( {{1 \over 2}} \right) < {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) > {1 \over 3}$$

B

$$f\left( {{1 \over 2}} \right) > {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) > {1 \over 3}$$

C

$$f\left( {{1 \over 2}} \right) < {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) < {1 \over 3}$$

D

$$f\left( {{1 \over 2}} \right) > {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) < {1 \over 3}$$

3

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

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

4

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)

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