JEE Advanced 2008 Paper-2

JEE Advanced 2008 Paper-2 - Question 1

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A particle P starts from the point $$z_0 = 1 + 2i$$, where $$i - \sqrt{-1}$$. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point $$z_1$$. From $$z_1$$ the particle moves $$\sqrt{2}$$ units in the direction of the vector $$\hat{i} + \hat{j}$$ and then it moves through an angle $$\frac{\pi}{2}$$ in anticlockwise direction on a circle with center at origin, to reach a point $$z_2$$. The point $$z_2$$ is given by

A

$$6 + 7i$$

B

$$-7 + 6i$$

C

$$7 + 6i$$

D

$$-6 + 7i$$

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JEE Advanced 2008 Paper-2 - Question 2

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Let the function $$g : (-\infty, \infty)\rightarrow \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$ be given by $$g(u) = 2 \tan^{-1}(e^u) - \frac{\pi}{2}$$. Then, g is

A

even and is strictly increasing in $$(0, \infty)$$

B

odd and is strictly decreasing in $$(-\infty, \infty)$$

C

odd and is strictly increasing in $$(-\infty, \infty)$$

D

neither even nor odd, but is strictly increasing in $$(-\infty, \infty)$$

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JEE Advanced 2008 Paper-2 - Question 3

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Consider a branch of the hyperbola
$$x^2 - 2y^2 - 2\sqrt{2}x - 4\sqrt{2}y - 6 = 0$$
with vertex at the point A. Let B be oneof the endpoints of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is

A

$$1 - \sqrt{\frac{2}{3}}$$

B

$$\sqrt{\frac{3}{2}} - 1$$

C

$$1 + \sqrt{\frac{2}{3}}$$

D

$$\sqrt{\frac{3}{2}} + 1$$

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JEE Advanced 2008 Paper-2 - Question 4

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The area of the region between the curves $$y = \sqrt{\frac{1 + \sin x}{\cos x}}$$ and $$y = \sqrt{\frac{1 - \sin x}{\cos x}}$$ bounded by the lines x = 0 and $$x = \frac{\pi}{4}$$ is

A

$$\int_{0}^{\sqrt{2}-1}\frac{t}{(1+t^2)\sqrt{1-t^2}}dt$$

B

$$\int_{0}^{\sqrt{2}-1}\frac{4t}{(1+t^2)\sqrt{1-t^2}}dt$$

C

$$\int_{0}^{\sqrt{2}+1}\frac{4t}{(1+t^2)\sqrt{1-t^2}}dt$$

D

$$\int_{0}^{\sqrt{2}+1}\frac{t}{(1+t^2)\sqrt{1-t^2}}dt$$

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JEE Advanced 2008 Paper-2 - Question 5

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Consider three points $$P = (-\sin (\beta - \alpha), -\cos \beta), Q = (\cos(\beta - \alpha), \sin \beta)$$ and $$R = (\cos(\beta - \alpha + \theta), \sin(\beta - \theta))$$, where $$0 < \alpha, \beta, \theta < \frac{\pi}{4}$$. Then,

A

P lies on the line segment RQ

B

Q lies on the line segment PR

C

R lies on the line segment QP

D

P, Q, R are non-collinear

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JEE Advanced 2008 Paper-2 - Question 6

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An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is

A

2, 4 or 8

B

3, 6 or 9

C

4 or 8

D

5 or 10

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JEE Advanced 2008 Paper-2 - Question 7

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Let two non-collinear unit vectors $$\hat{a}$$ and $$\hat{b}$$ form an acute angle. A point P moves so that at any time t the position vector $$\overrightarrow{OP}$$(where O is the origin) is given by $$\hat{a} \cos t + \hat{b} \sin t$$. When is farthest from origin O, let M be the length of $$\overrightarrow{OP}$$ and $$\hat{u}$$ be the unit vector along $$\overrightarrow{OP}$$ . Then

A

$$\hat{u} = \frac{\hat{a} + \hat{b}}{\mid \hat{a} + \hat{b} \mid}$$ and $$M = (1 + \hat{a}.\hat{b})^{\frac{1}{2}}$$

B

$$\hat{u} = \frac{\hat{a} - \hat{b}}{\mid \hat{a} - \hat{b} \mid}$$ and $$M = (1 + \hat{a}.\hat{b})^{\frac{1}{2}}$$

C

$$\hat{u} = \frac{\hat{a} + \hat{b}}{\mid \hat{a} + \hat{b} \mid}$$ and $$M = (1 + 2\hat{a}.\hat{b})^{\frac{1}{2}}$$

D

$$\hat{u} = \frac{\hat{a} - \hat{b}}{\mid \hat{a} - \hat{b} \mid}$$ and $$M = (1 + 2\hat{a}.\hat{b})^{\frac{1}{2}}$$

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JEE Advanced 2008 Paper-2 - Question 8

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Let
$$I = \int\frac{e^x}{e^{4x}+e^{2x}+1}dx, J = \int\frac{e^{-x}}{e^{-4x}+e^{-2x}+1}dx$$.
Then, for an arbitrary constant C, the value of J - I equals

A

$$\frac{1}{2}\log\left(\frac{e^{4x} - e^{2x} + 1}{e^{4x} + e^{2x} + 1}\right)+C$$

B

$$\frac{1}{2}\log\left(\frac{e^{2x} + e^{x} + 1}{e^{2x} - e^{x} + 1}\right)+C$$

C

$$\frac{1}{2}\log\left(\frac{e^{2x} - e^{x} + 1}{e^{2x} + e^{x} + 1}\right)+C$$

D

$$\frac{1}{2}\log\left(\frac{e^{4x} + e^{2x} + 1}{e^{4x} - e^{2x} + 1}\right)+C$$

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JEE Advanced 2008 Paper-2 - Question 9

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Let $$g(x) = \log f(x)$$ where $$f(x)$$ is a twice differentiable positive function on $$(0, \infty)$$ such that $$f(x + 1) = x f(x)$$. Then, for $$N = 1, 2, 3,...,$$
$$g''\left(N + \frac{1}{2}\right) - g''\left(\frac{1}{2}\right) =$$

A

$$-4\left\{1 + \frac{1}{9} + \frac{1}{25} + ... + \frac{1}{(2N - 1)^2}\right\}$$

B

$$4\left\{1 + \frac{1}{9} + \frac{1}{25} + ... + \frac{1}{(2N - 1)^2}\right\}$$

C

$$-4\left\{1 + \frac{1}{9} + \frac{1}{25} + ... + \frac{1}{(2N + 1)^2}\right\}$$

D

$$4\left\{1 + \frac{1}{9} + \frac{1}{25} + ... + \frac{1}{(2N + 1)^2}\right\}$$

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JEE Advanced 2008 Paper-2 - Question 10

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Suppose four distinct positive numbers $$a_1, a_2, a_3, a_4$$ are in G.P. Let $$b_1 = a_1, b_2 = b_1 + a_2, b_3 = b_2 + a_3$$ and $$b_4 = b_3 + a_4$$.
STATEMENT-1: The numbers $$b_1, b_2, b_3, b_4$$ are neither in A.P. nor in G.P.
and
STATEMENT-2: The numbers $$b_1, b_2, b_3, b_4$$ are in H.P.

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

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JEE Advanced 2008 Paper-2 - Question 11

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Let a, b, c, p, q be real numbers. Suppose $$\alpha, \beta$$ are the roots of the equation $$x^2 + 2px + q = 0$$ and $$\alpha, \frac{1}{\beta}$$ are the roots of the equation $$ax^2 + 2bx + c = 0$$, where $$\beta^2 \notin \left\{-1, 0, 1\right\}$$.
STATEMENT-1 : $$\left(p^2 - q\right)\left(b^2 - ac\right)\geq 0$$
and
STATEMENT-2 : $$b \neq pa$$ or $$c \neq qa$$

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

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JEE Advanced 2008 Paper-2 - Question 12

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Consider
$$L_1: 2x + 3y + p - 3 = 0$$
$$L_2: 2x + 3y + p + 3 = 0$$
where p is a real number, and $$C : x^2 + y^2 + 6x - 10y + 30 = 0$$.
STATEMENT-1: If line $$L_1$$ is a chord of circle C, then line $$L_2$$ is not always a diameter of circle C.
and
STATEMENT-2: If line $$L_1$$ is a diameterof circle C, then line $$L_2$$ is not a chord of circle C.

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

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JEE Advanced 2008 Paper-2 - Question 13

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Letasolution y = y(x) of the differential equation
$$x\sqrt{x^2 - 1} dy - y\sqrt{y^2 - 1}dx = 0$$ satisfy $$y(2) = \frac{2}{\sqrt{3}}$$
STATEMENT-1: $$y(x) = \sec\left(\sec^{-1}x - \frac{\pi}{6}\right)$$
STATEMENT-2: y(x) is given by $$\frac{1}{y} = \frac{2\sqrt{3}}{x} - \sqrt{1 - \frac{1}{x^2}}$$

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

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JEE Advanced 2008 Paper-2 - Question 14

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Which of the following is true?

A

$$(2 + a)^2f''(1) + (2 - a)^2f''(-1) = 0$$

B

$$(2 - a)^2f''(1) - (2 + a)^2f''(-1) = 0$$

C

$$f'(a)f''(-1) = (2 - a)^2$$

D

$$f'(a)f''(-1) = -(2 + a)^2$$

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JEE Advanced 2008 Paper-2 - Question 15

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Which of the following is true?

A

f(x) is decreasing on (—1, 1) and has a local minimum at x = 1

B

f(x) is increasing on (-1, 1) and has a local maximum at x = 1

C

f(x) is increasing on (—1, 1) but has neither a local maximum nor a local minimum at x = 1

D

f(x) is decreasing on (-1, 1) but has neither a local maximum nor a local minimum at x = 1

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JEE Advanced 2008 Paper-2 - Question 16

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Let
$$g(x) = \int_{0}^{e^x}\frac{f'(1)}{1 + t^2} dt$$.
Which of the following is true?

A

$$g'(x)$$ is positive on $$(-\infty, 0)$$ and negative on $$(0, \infty)$$

B

$$g'(x)$$ is negative on $$(-\infty, 0)$$ and positive on $$(0, \infty)$$

C

$$g'(x)$$ changes sign on both $$(-\infty, 0)$$ and $$(0, \infty)$$

D

$$g'(x)$$ does not change sign on $$(-\infty, \infty)$$

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JEE Advanced 2008 Paper-2 - Question 17

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The unit vector perpendicular to both $$L_1$$ and $$L_2$$ is

A

$$\frac{-\hat{i} + 7\hat{j} + 7\hat{k}}{\sqrt{99}}$$

B

$$\frac{-\hat{i} - 7\hat{j} + 5\hat{k}}{5\sqrt{3}}$$

C

$$\frac{-\hat{i} + 7\hat{j} + 5\hat{k}}{5\sqrt{3}}$$

D

$$\frac{7\hat{i} - 7\hat{j} - \hat{k}}{\sqrt{99}}$$

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JEE Advanced 2008 Paper-2 - Question 18

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The shortest distance between $$L_1$$ and $$L_2$$ is

A

0

B

$$\frac{17}{\sqrt{3}}$$

C

$$\frac{41}{5\sqrt{3}}$$

D

$$\frac{17}{5\sqrt{3}}$$

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JEE Advanced 2008 Paper-2 - Question 19

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The distance of the point (1,1, 1) from the plane passing through the point (-1, -2, -1) and whose normalis perpendicularto both the lines $$L_1$$ and $$L_2$$ is

A

$$\frac{2}{\sqrt{75}}$$

B

$$\frac{7}{\sqrt{75}}$$

C

$$\frac{13}{\sqrt{75}}$$

D

$$\frac{23}{\sqrt{75}}$$

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JEE Advanced 2008 Paper-2 - Question 20

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Consider the lines given by
$$L_1: x + 3y - 5 = 0$$
$$L_2: 3x - ky - 1 = 0$$
$$L_3: 5x + 2y - 12 = 0$$
Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

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JEE Advanced 2008 Paper-2 - Question 21

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Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

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JEE Advanced 2008 Paper-2 - Question 22

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Consider all possible permutations  of the letters of the word ENDEANOEL. Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

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JEE Advanced 2008 Paper-2 - Question 23

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Consider a system of three charges $$\frac{q}{3}, \frac{q}{3}$$ and $$-\frac{2q}{3}$$ placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle $$CAB = 60^\circ$$

A

The electric field at point O is $$\frac{q}{8 \pi \varepsilon_0 R^2}$$ directed along the negative x-axis

B

The potential energy of the system is zero

C

The magnitude of the force between the charges at C and B is $$\frac{q^2}{54 \pi \varepsilon_0 R^2}$$

D

The potential at point O is $$\frac{q}{12 \pi \varepsilon_0 R}$$

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JEE Advanced 2008 Paper-2 - Question 24

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A radioactive sample S1 having an activity of $$5 \mu Ci$$ has twice the number of nuclei as another sample S2 which has anactivity of $$10 \mu Ci$$. The half lives of S1 and S2
can be

A

20 years and 5 years, respectively

B

20 years and 10 years, respectively

C

10 years each

D

5 years each

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JEE Advanced 2008 Paper-2 - Question 25

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A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the waveis 0.5 m and its amplitude is 10 cm. At a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is

A

$$\frac{\sqrt{3}\pi}{50}\hat{j}$$ m/s

B

$$-\frac{\sqrt{3}\pi}{50}\hat{j}$$ m/s

C

$$\frac{\sqrt{3}\pi}{50}\hat{i}$$ m/s

D

$$-\frac{\sqrt{3}\pi}{50}\hat{i}$$ m/s

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JEE Advanced 2008 Paper-2 - Question 26

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A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k, respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio $$\frac{y}{x}$$ is

A

4

B

2

C

$$\frac{1}{2}$$

D

$$\frac{1}{4}$$

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JEE Advanced 2008 Paper-2 - Question 27

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A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle $$\theta$$ at which the speed of the bob is half of that at A, satisfies 

A

$$\theta = \frac{\pi}{4}$$

B

$$\frac{\pi}{4} < \theta < \frac{\pi}{2}$$

C

$$\frac{\pi}{2} < \theta < \frac{3 \pi}{4}$$

D

$$\frac{3 \pi}{4} < \theta < \pi$$

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JEE Advanced 2008 Paper-2 - Question 28

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A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,

A

air from end 1 flows towards end 2. No change in the volumeof the soap bubbles

B

air from end 1 flows towards end 2. Volumeof the soap bubble at end 1 decreases

C

no change occurs

D

air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increases

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JEE Advanced 2008 Paper-2 - Question 29

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A vibrating string of certain length l under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension ofthe string is slightly increased the numberof beats reduces to 2 per second. Assuming the velocity of soundin air to be 340 m/s, the frequency n of the tuning fork in Hz is

A

344

B

336

C

117.3

D

109.3

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JEE Advanced 2008 Paper-2 - Question 30

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A parallel plate capacitor C with plates of unit area and separation is filled with a liquid of dielectric constant K = 2. The level of liquid is $$\frac{d}{3}$$ initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is

A

$$\frac{6 \varepsilon_0 R}{5d + 3V t}$$

B

$$\frac{(15 d + 9V t) \varepsilon_0 R}{2d^2 - 3dV t - 9V^2t^2}$$

C

$$\frac{6 \varepsilon_0 R}{5d - 3V t}$$

D

$$\frac{(15 d - 9V t) \varepsilon_0 R}{2d^2 + 3dV t - 9V^2t^2}$$

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JEE Advanced 2008 Paper-2 - Question 31

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A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are $$n_0, \frac{n_0}{2}, \frac{n_0}{6}$$ and $$\frac{n_0}{8}$$, respectively. The angle of incidence $$\theta$$ for which the beam just misses entering Region IV is 

A

$$\sin^{-1}\left(\frac{3}{4}\right)$$

B

$$\sin^{-1}\left(\frac{1}{8}\right)$$

C

$$\sin^{-1}\left(\frac{1}{4}\right)$$

D

$$\sin^{-1}\left(\frac{1}{3}\right)$$

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JEE Advanced 2008 Paper-2 - Question 32

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STATEMENT-1
For an observer looking out through the window of a fast moving train, the nearby objects appear to movein the opposite direction to the train, while the distant objects appearto be stationary.
and
STATEMENT-2
If the observer and the object are moving at velocities $$\overrightarrow{V_1}$$ and $$\overrightarrow{V_2}$$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $$\overrightarrow{V_2} - \overrightarrow{V_1}$$.

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

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JEE Advanced 2008 Paper-2 - Question 33

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STATEMENT-1
It is easier to pull a heavy object than to pushit on a level ground.
and
STATEMENT-2
The magnitude of frictional force depends on the nature of the two surfaces in contact.

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

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JEE Advanced 2008 Paper-2 - Question 34

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STATEMENT-1
For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
and
STATEMENT-2
The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by $$\frac{Q}{4 \pi \varepsilon_0 R}$$.

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

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JEE Advanced 2008 Paper-2 - Question 35

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STATEMENT-1
The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.
and
STATEMENT-2
Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

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JEE Advanced 2008 Paper-2 - Question 36

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The electric field at r = R is

A

independent of a

B

directly proportional to a

C

directly proportional to $$a^2$$

D

inversely proportional to a

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JEE Advanced 2008 Paper-2 - Question 37

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For a = 0, the value of d (maximum value of $$\rho$$ as shown in the figure) is

A

$$\frac{3Ze}{4 \pi R^3}$$

B

$$\frac{3Ze}{\pi R^3}$$

C

$$\frac{4Ze}{3 \pi R^3}$$

D

$$\frac{Ze}{3 \pi R^3}$$

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JEE Advanced 2008 Paper-2 - Question 38

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The electric field within the nucleus is generally observed to be linearly dependent on r. This implies

A

a = 0

B

$$a = \frac{R}{2}$$

C

a = R

D

$$a = \frac{2R}{3}$$

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JEE Advanced 2008 Paper-2 - Question 39

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The net external force acting on the disk whenits centre of mass is at displacement x with respect to its equilibrium position is

A

-kx

B

-2kx

C

$$-\frac{2kx}{3}$$

D

$$-\frac{4kx}{3}$$

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JEE Advanced 2008 Paper-2 - Question 40

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The centre of mass of the disk undergoes simple harmonic motion with angular frequency $$\omega$$ equal to

A

$$\sqrt{\frac{k}{M}}$$

B

$$\sqrt{\frac{2k}{M}}$$

C

$$\sqrt{\frac{2k}{3M}}$$

D

$$\sqrt{\frac{4k}{3M}}$$

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JEE Advanced 2008 Paper-2 - Question 41

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The maximum value of $$V_0$$ for which the disk will roll without slipping is

A

$$\mu g \sqrt{\frac{M}{k}}$$

B

$$\mu g \sqrt{\frac{M}{2k}}$$

C

$$\mu g \sqrt{\frac{3M}{k}}$$

D

$$\mu g \sqrt{\frac{5M}{2k}}$$

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JEE Advanced 2008 Paper-2 - Question 42

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Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graphs given in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.

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JEE Advanced 2008 Paper-2 - Question 43

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An optical component and an object S placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.

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JEE Advanced 2008 Paper-2 - Question 44

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Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.

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JEE Advanced 2008 Paper-2 - Question 45

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The correct stability order for the following species is

A

(II) > (IV) > (I) > (III)

B

(I) > (II) > (III) > (IV)

C

(II) > (I) > (IV) > (III)

D

(I) > (III) > (II) > (IV)

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JEE Advanced 2008 Paper-2 - Question 46

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Cellulose upon acetylation with excess acetic anhydride/ $$H_2SO_4$$ (catalytic) gives cellulose triacetate whose structure is

A

B

C

D

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JEE Advanced 2008 Paper-2 - Question 47

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In the following reaction sequence, the correct structures of E, F and G are 

(* implies $$^{13}C$$ labelled carbon)

A

B

C

D

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JEE Advanced 2008 Paper-2 - Question 48

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Among the following, the coloured compound is

A

$$CuCl$$

B

$$K_3[Cu(CN)_4]$$

C

$$CuF_2$$

D

$$[Cu(CH_3CN)_4]BF_4$$

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JEE Advanced 2008 Paper-2 - Question 49

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Both $$[Ni(CO)_4]$$ and $$[Ni(CN)_4]^{2-}$$ are diamagnetic. The hybridisations of nickel in these complexes, respectively, are

A

$$sp^3, sp^3$$

B

$$sp^3, dsp^2$$

C

$$dsp^2, sp^3$$

D

$$dsp^2, dsp^2$$

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JEE Advanced 2008 Paper-2 - Question 50

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The IUPAC name of $$[Ni(NH_3)_4][NiCl_4]$$ is

A

Tetrachloronickel(II) - tetraamminenickel(II)

B

Tetraamminenickel(II) - tetrachloronickel (II)

C

Tetraamminenickel(II) - tetrachloronickelate (II)

D

Tetrachloronickel (II) - tetraamminenickelate (0)

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JEE Advanced 2008 Paper-2 - Question 51

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Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 milli ampere current. The time required to liberate 0.01 mol of H, gas at the cathode is (1 Faraday = 96500 C mol$$^{-1}$$)

A

$$9.65 \times 10^4$$ sec

B

$$19.3 \times 10^4$$ sec

C

$$28.95 \times 10^4$$ sec

D

$$38.6 \times 10^4$$ sec

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JEE Advanced 2008 Paper-2 - Question 52

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Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient conditions is

A

$$CH_3(CH_2)_{15}N^{+}(CH_3)_3 Br^{-}$$

B

$$CH_3(CH_2)_{11}OSO_{3}^{-} Na^{+}$$

C

$$CH_3(CH_2)_{6}COO^{-} Na^{+}$$

D

$$CH_3(CH_2)_{11}N^{+}(CH_3)_3 Br^{-}$$

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JEE Advanced 2008 Paper-2 - Question 53

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Solubility product constants $$(K_{sp})$$ of salts of types $$MX, MX_2$$ and $$M_3X$$ at temperature ‘T’ are $$4.0 \times 10^{-8}, 3.2 \times 10^{-14}$$ and $$2.7 \times 10^{-15}$$, respectively. Solubilities (mol dm$$^{-3}$$) of the salts at temperature 'T' are in the order

A

$$MX > MX_2 > M_3X$$

B

$$M_3X > MX_2 > MX$$

C

$$MX_2 > M_3X > MX$$

D

$$MX > M_3X > MX_2$$

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JEE Advanced 2008 Paper-2 - Question 54

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STATEMENT-1: Aniline on reaction with $$NaNO_2/HCl$$ at $$0^\circ C$$ followed by coupling with $$\beta$$ - naphthol gives a dark blue coloured precipitate.
and
STATEMENT-2: The colour of the compound formed in the reaction of aniline with $$NaNO_2/HCl$$ at $$0^\circ C$$ followed by coupling with $$\beta$$ - naphthol is due to the extended conjugation.

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

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JEE Advanced 2008 Paper-2 - Question 55

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STATEMENT-1: $$[Fe(H_2O)_5NO]SO_4$$ is paramagnetic.
and
STATEMENT-2: The Fe in $$[Fe(H_2O)_5NO]SO_4$$ has three unpaired electrons.

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

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JEE Advanced 2008 Paper-2 - Question 56

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STATEMENT-1: The geometrical isomers of the complex $$[M(NH_3)_4Cl_2]$$ are optically inactive.
and
STATEMENT-2: Both geometrical isomers of the complex $$[M(NH_3)_4Cl_2]$$ possess axis of symmetry.

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

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JEE Advanced 2008 Paper-2 - Question 57

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STATEMENT-1: There is a natural asymmetry between converting work to heat and converting heat to work.
and
STATEMENT-2: Noprocessis possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

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JEE Advanced 2008 Paper-2 - Question 58

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Compound H is formed by the reaction of 

A

Figure 1

B

Figure 2

C

Figure 3

D

Figure 4

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JEE Advanced 2008 Paper-2 - Question 59

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The structure of compound I is

A

B

C

D

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JEE Advanced 2008 Paper-2 - Question 60

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The structures of compounds J, K and L, respectively, are

A

$$PhCOCH_3, PhCH_2COCH_3$$ and $$PhCH_2COO^{-}K^{+}$$

B

$$PhCHO, PhCH_2CHO$$ and $$PhCOO^{-}K^{+}$$

C

$$PhCOCH_3, PhCH_2CHO$$ and $$CH_3COO^{-}K^{+}$$

D

$$PhCHO, PhCOCH_3$$ and $$PhCOO^{-}K^{+}$$

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JEE Advanced 2008 Paper-2 - Question 61

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The number of atoms in this HCP unitcell is

A

4

B

6

C

12

D

17

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JEE Advanced 2008 Paper-2 - Question 62

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The volume of this HCP unitcell is

A

$$24\sqrt{2} r^3$$

B

$$16\sqrt{2} r^3$$

C

$$12\sqrt{2} r^3$$

D

$$\frac{64}{3\sqrt{3}}r^3$$

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JEE Advanced 2008 Paper-2 - Question 63

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The emptyspace in this HCP unit cell is

A

74%

B

47.6%

C

32%

D

26%

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JEE Advanced 2008 Paper-2 - Question 64

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Match the compounds in Column I with their characteristic test(s)/reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.

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JEE Advanced 2008 Paper-2 - Question 65

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Match the conversions in Column I with the type(s) of reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS

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JEE Advanced 2008 Paper-2 - Question 66

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Match the entries in Column  I with the correctly related quantum number(s) in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS

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