This practice test consists of IIT JEE 2008 question paper to help you practice for actual IIT JEE main examination.

IIT JEE 2008 Question Paper

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Question

Section I

Q1. 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 centre at origin, to reach a point z_2 . The point z_2 is given by

Possible Answers

Selected	Possible Answer
	-7+6i
	-6+7i
	6+7i
	7+6i

Question

Section I

Q2. Let the function $g: \Big( - \infty, \infty \Big )$ $\rightarrow \Big( - \cfrac {\pi}{2}$ $, \cfrac {\pi}{2} \Big)$ be given by $g (u)=2 tan^{-1} (e^{\mu} ) -\cfrac {\pi}{2}$ Then g is

Possible Answers

Selected	Possible Answer
	even and is strictly increasing in $(0, \infty)$
	neither even nor odd, but is strictly increasing in $(- \infty , \infty)$
	odd and is strictly decreasing in $(- \infty , \infty)$
	odd and is strictly increasing in $(- \infty , \infty)$

Question

Section I

Q.3. 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 one of the end points 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

Possible Answers

Selected	Possible Answer
	$\sqrt{\cfrac {3}{2}}+1$
	$\sqrt{\cfrac {3}{2}}-1$
	$1-\sqrt{\cfrac {2}{3}}$
	$1+ \sqrt {\cfrac {2}{3}}$

Question

Section I

Q4. The area of the region between the curves $y =\sqrt {\cfrac {1+\sin x }{\cos x}}$ $\, and \,$ $y =\sqrt {\cfrac {1-\sin x }{\cos x}}$ bounded by the lines $x =0 \, and \, x = \cfrac {\pi}{4} \, \, is$

Possible Answers

Selected	Possible Answer
	$\overset {\sqrt{2}+1}{\underset {o}{\int}}$ $\frac {t}{\sqrt {(1+t^2)\sqrt {1-t^2}}}dt$
	$\overset {\sqrt{2}-1}{\underset {o}{\int}}$ $\frac {4t}{\sqrt {(1+t^2)\sqrt {1-t^2}}}dt$
	$\overset {\sqrt{2}-1}{\underset {o}{\int}}$ $\frac {t}{\sqrt {(1+t^2)\sqrt {1-t^2}}}dt$
	$\overset {\sqrt{2}+1}{\underset {o}{\int}}$ $\frac {4t}{\sqrt {(1+t^2)\sqrt {1-t^2}}}dt$

Question

Section I

Q5. Consider three points $p=(-sin(\beta-\alpha),- cos \beta)$ $, Q =(cos (\beta -\alpha), sin \beta ) \, and \,$ $R=(cos (\beta-\alpha+\theta),$ $sin(\beta-\theta))$ $\, where \, 0<\alpha, \beta ,$ $\theta < \cfrac {\pi}{4}$ , Then

Possible Answers

Selected	Possible Answer
	P, Q, R are non-collinear
	Q lies on the line segment PR
	P lies on the line segment RQ
	R lies on the line segment QP

Question

Section I

Q6. 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

Possible Answers

Selected	Possible Answer
	5 or 10
	3, 6 or 9
	2, 4 or 8
	4 or 8

Question

Section I

Q7. 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 $\overset {\rightarrow}{OP}$ (where O is the origin) is given by $\hat a\; cost+\hat b\; sin\; t$ . When P is farthest from origin O, let M be the length of $\overset {\rightarrow}{OP}$ and $\hat {u}$ be the unit vector along $\overset {\rightarrow}{OP}$ . Then

Possible Answers

Selected	Possible Answer
	$\hat {u}=\cfrac {\hat a+\hat b}{\|\hat a+\hat b\|}$ and $M=(1+2 \hat a. \hat b)^{1/2}$
	$\hat {u}=\cfrac {\hat a+\hat b}{\|\hat a+\hat b\|}$ and $M=(1+\hat a. \hat b)^{1/2}$
	$\hat {u}=\cfrac {\hat a-\hat b}{\|\hat a-\hat b\|}$ and $M=(1+2 \hat a. \hat b)^{1/2}$
	$\hat {u}=\cfrac {\hat a-\hat b}{\|\hat a-\hat b\|}$ and $M=(1+\hat a. \hat b)^{1/2}$

Question

Section I

Q8. Let $I=\int \cfrac {e^x}{e^{4x}+e^{2x}+1}dx$ $,\, J=\int \cfrac {e^-x}{e^{-4x}+e^{-2x}+1}dx$ Then, for an arbitrary constant C, the value of J-I equals

Possible Answers

Selected	Possible Answer
	$\cfrac{1}{2}log\Bigg(\cfrac {e^{2x}-e^{x}+1}{e^{2x}+e^{x}+1}\Bigg)+C$
	$\cfrac{1}{2}log\Bigg(\cfrac {e^{4x}+e^{2x}+1}{e^{4x}-e^{2x}+1}\Bigg)+C$
	$\cfrac{1}{2}log\Bigg(\cfrac {e^{4x}-e^{2x}+1}{e^{4x}+e^{2x}+1}\Bigg)+C$
	$\cfrac{1}{2}log\Bigg(\cfrac {e^{2x}-e^{x}+1}{e^{2x}-e^{x}+1}\Bigg)+C$

Question

Section I

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,......

$g"\Bigg(N+\cfrac{1}{2}\Bigg)$ $-g" \Bigg( \cfrac{1}{2}\Bigg ) =$

Possible Answers

Selected	Possible Answer
	$-4 \{ 1+\frac {1}{9}+$ $\frac {1}{25}+....\frac {1}{(2N+1)^2}\}$
	$4 \{ 1+\frac {1}{9}+$ $\frac {1}{25}+....\frac {1}{(2N+1)^2}\}$
	$-4 \{ 1+\frac {1}{9}+$ $\frac {1}{25}+....\frac {1}{(2N-1)^2}\}$
	$4 \{ 1+\frac {1}{9}+$ $\frac {1}{25}+....\frac {1}{(2N-1)^2}\}$

Question

Section II

Reasoning Type

This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
Q10. 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 are in H.P

Possible Answers

Selected	Possible Answer
	STATEMENT-1 is True, STATEMENT-2 is False.
	STATEMENT-1 is False, STATEMENT-2 is True.
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.

Question

Section II

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 $\beta^2 \not \in \{-1,0,1\}$

STATEMENT-1: $(p^2-q)(b^2-ac) \geq 0$

and

STATEMENT-2: $b \not = pa \, or \, c \not = qa$

Possible Answers

Selected	Possible Answer
	STATEMENT-1 is False, STATEMENT-2 is True.
	STATEMEN-1 is True, STATEMENT-2 is True; STATEMEN-2 is NOT a correct explanation for STATEMENT-1.
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMEN-2 is a correct explanation for STATEMENT-1.
	STATEMENT-1 is True, STATEMENT-2 is False.

Question

Section II

Consider

, 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 diameter of circle C, then line L_2

is not a chord of circle C.

Possible Answers

Selected	Possible Answer
	STATEMENT-1 is True, STATEMENT-2 is False.
	STATEMENT-1 is False, STATEMENT-2 is True.
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.

Question

Section II

Let a solution 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: $y(x)=sec \Big (sec^{-1}x -\cfrac {\pi}{6}\Big )$

and

STATEMENT-2: y(x) is given by $\cfrac {1}{y}=\cfrac {2 \sqrt{3}}{x}$ $-\sqrt{1-\cfrac {1}{x^2}}$

Possible Answers

Selected	Possible Answer
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
	STATEMENT-1 is True, STATEMENT-2 is False.
	STATEMENT-1 is False, STATEMENT-2 is True.
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.

Question

Section III

Linked Comprehension Type

This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question no 14 to 16 questions

Consider the function $f: (- \infty, \infty)\rightarrow (- \infty, \infty)$ defined by $f(x)=\cfrac {x^2-ax+1}{x^2+ax+1},0<a < 2$

Which of the following is true?

Possible Answers

Selected	Possible Answer

Question

Section III

Which of the following is true?

Possible Answers

Selected	Possible Answer
	f(x) is increasing on (-1,1) and has a local maximum at x = 1
	f(x) is decreasing on (-1,1) but has neither a local maximum nor a local minimum at x = 1
	f(x) is increasing on (-1,1) but has neither a local maximum nor a local minimum at x = 1
	f(x) is decreasing on  (-1,1) and has a local minimum at x = 1

Question

Section III

Let $g(x)=\overset {e^x}{\underset {0}{\int}}$ $\cfrac {f'(t)}{1+t^2}dt$ Which of the following is true?

Possible Answers

Selected	Possible Answer
	g’(x) does not change sign on $(- \infty, \infty)$
	g’(x) is positive on $(- \infty, 0)$ and negative on $(0, \infty)$
	g’(x) changes sign on both $(- \infty, 0)$ and $(0, \infty)$
	g’(x) is negative on $(- \infty, 0)$ and positive on $(0, \infty)$

Question

Section III

Paragraph for Question Nos. 17 to 19

Consider the lines $L_1: \cfrac {x+1}{3}=\cfrac {y+2}{1}=\cfrac {z+1}{2}; \quad \quad L_2 : \cfrac {x-2}{1}=\cfrac {y+2}{2}=\cfrac {z-3}{3}$

Q17. The unit vector perpendicular to both L_1 and L_2 is

Possible Answers

Selected	Possible Answer
	$\cfrac {\hat {i}+7 \hat {j}+5 \hat {k}}{5 \sqrt{3}}$
	$\cfrac {\hat {i}-7 \hat {j}+5 \hat {k}}{5 \sqrt{3}}$
	$\cfrac {\hat {i}+7 \hat {j}+7 \hat {k}}{\sqrt{99}}$
	$\cfrac {7 \hat {i}-7 \hat {j}- \hat {k}}{\sqrt{99}}$

Question

Section III

Q18. The shortest distance between L_1 and L_2 is

Possible Answers

Selected	Possible Answer
	$\cfrac {17}{\sqrt{3}}$

	$\cfrac {41}{5 \sqrt{3}}$
	$\cfrac {17}{5 \sqrt{3}}$

Question

Section III

Q19. The distance of the point (1,1,1) from the plane passing through the point (-1,-2,-1) and whose normal is perpendicular to both the lines L_1 and L_2 is

Possible Answers

Selected	Possible Answer
	$\cfrac {23}{\sqrt{75}}$
	$\cfrac {7}{\sqrt{75}}$
	$\cfrac {2}{\sqrt{75}}$
	$\cfrac {13}{\sqrt{75}}$

Question

Section IV

Matrix-Match Type

This section contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements in Column I are labeled as A, B, C and D whereas statements in Column II are labeled as p, q, r, and s. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-q, A-r, B-s, C-r, C-s and D-q, then the correctly bubbled 4 × 4 matrix should be as follows:

Consider the lines given by $L_1: x+3y-5=0; \quad L_2:3x-ky-1=0 \,\quad and\quad L_3:5x +2y-12=0$
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 × 4 matrix given in the ORS.

Column I	Column II
(A) are concurrent, if	(p) k=-9
(B) One of are parallel to at least one of the other two, if	(Q) $k=-\cfrac {6}{5}$
(C) form a triangle, if	(r) $k =\cfrac {5}{6}$
(D) do not form a triangle, if	(s) k=5

Possible Answers

Selected	Possible Answer
	$A \rightarrow (r), B \rightarrow (p,q), C \rightarrow (s), D \rightarrow (p,q,s)$
	$A \rightarrow (s), B \rightarrow (p,q), C \rightarrow (r), D \rightarrow (p,q,s)$
	$A \rightarrow (p,q,s), B \rightarrow (p,q), C \rightarrow (r), D \rightarrow (s)$
	$A \rightarrow (s), B \rightarrow (r), C \rightarrow (p.q), D \rightarrow (p,q,s)$

Question

Section IV

Q21. Match the Statement/ Expressions in Column I with the Statement/ Expression in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I	Column II
(A) The minimum value of $\cfrac {x^2+2x+4}{x+2} \, is$	(p) 0
(B) Let A and B be 3 * 3 matrices of real numbers, where A is symmetric, B is skew-symmetric, and if where is the transpose of the matrix AB, then the possible values of k are	(q) 1
(C) Let $a= log_3 \; log_3 2$ . An integer k satisfying $1<2^{(-k+3^{-a})}<2$ must be less than	(r) 2
(D) if $sin \theta =cos \phi$ then the possible values of $\cfrac {1}{\pi} \Big( \theta \pm \phi -\cfrac {\pi}{2} \Big)$ are	(s) 3

Possible Answers

Selected	Possible Answer
	$A-(p,r) \rightarrow , B-(q) \rightarrow , C-(s) \rightarrow , D-(p,r)$
	$A-(p) \rightarrow , B-(q,s) \rightarrow , C-(r,s) \rightarrow , D-(p,r)$
	$A-(p,r) \rightarrow , B-(s) \rightarrow , C-(r,s) \rightarrow , D-(r)$
	$A-(p) \rightarrow , B-(r,s) \rightarrow , C-(q,s) \rightarrow , D-(p,r)$

Question

Section IV

Q22. Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statement/ Expressions in Column I with the Statement/ Expression in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.

coloum I	coloum II
(A) The number of permutations containing the word ENDEA is	(p) 5 !
(B) The number of permutations in which the letter E occurs in the first and the last positions is	(q) 2 × 5 !
(C) The number of permutations in which none of the letters D, L, N occurs in the last five positions is	(r) 7 × 5 !
(D) The number of permutations in which the letters A, E, O occur only in odd positions is	(s) 21 × 5 !

Possible Answers

Selected	Possible Answer
	$A-(p) \rightarrow , B-(s,q) \rightarrow , C-(q) \rightarrow , D-(q)$
	$A-(q) \rightarrow , B-(s) \rightarrow , C-(q) \rightarrow , D-(p)$
	$A-(p) \rightarrow , B-(q) \rightarrow , C-(s) \rightarrow , D-(q)$
	$A-(p) \rightarrow , B-(s) \rightarrow , C-(q) \rightarrow , D-(q)$

Question

Section I

Straight Objective Type

This section contains 9 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Consider a system of three charges $\cfrac {q}{3},$ $\cfrac {q}{3} \, and \, - \cfrac {2q}{3}$ 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 $CAB=60^{\circ}$

Possible Answers

Selected	Possible Answer
	The electric field at point O is $\cfrac {q}{8 \pi \epsilon_0 R^2}$ directed along the negative x-axis
	The magnitude of the force between the charges at C and B is $\cfrac {q^2}{54 \pi \epsilon_0 R^2}$
	The potential energy of the system is zero
	The potential at point O is $\cfrac {q}{12 \pi \epsilon _0 R^2}$

Question

Section I

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

Possible Answers

Selected	Possible Answer
	5 years each
	20 years and 5 years, respectively
	10 years each
	20 years and 10 years, respectively

Question

Section I

A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 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

Possible Answers

Selected	Possible Answer
	$\cfrac {\sqrt{3}\pi}{50} \hat {i} \, m/s$
	$\cfrac {\sqrt{3}\pi}{50} \hat {j} \, m/s$
	$- \cfrac {\sqrt{3}\pi}{50} \hat {i} \, m/s$
	$- \cfrac {\sqrt{3}\pi}{50} \hat {j} \, m/s$

Question

Section I

A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4 k, 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 $\cfrac {y}{x}$ is

Possible Answers

Selected	Possible Answer


	$\cfrac {1}{4}$
	$\cfrac {1}{2}$

Question

Section I

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

Possible Answers

Selected	Possible Answer
	$\cfrac {3 \pi}{4} < \theta < \pi$
	$\cfrac {\pi}{4} < \theta < \cfrac {\pi}{2}$
	$\cfrac {\pi}{2} < \theta < \cfrac {3 \pi}{4}$
	$\theta =\cfrac {\pi}{4}$

Question

Section I

Q28. 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,

Possible Answers

Selected	Possible Answer
	no change occurs
	air from end 1 flows towards end 2. No change in the volume of the soap bubbles
	air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases
	air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increases

Question

Section I

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 of the string is slightly increased the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is

Possible Answers

Selected	Possible Answer
	344
	117.3
	109.3
	336

Question

Section I

Q30. A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2 . The level of liquid is $\cfrac{d}{3}$ initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is

Possible Answers

Selected	Possible Answer
	$\cfrac{6 \epsilon_0 R}{5d+3Vt}$
	$\cfrac{(15d - 9Vt)\epsilon_0 R}{2d^2 + 3dVt-9V^2t^2}$
	$\cfrac{(15d + 9Vt)\epsilon_0 R}{2d^2 - 3dVt-9V^2t^2}$
	$\cfrac{6 \epsilon_0 R}{5d-3Vt}$

Question

Section I

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

Possible Answers

Selected	Possible Answer
	$\sin^{-1} \Big( \frac{1}{8}\Big)$
	$\sin^{-1} \Big( \frac{3}{4}\Big)$
	$\sin^{-1} \Big( \frac{1}{3}\Big)$
	$\sin^{-1} \Big( \frac{1}{4}\Big)$

Question

Section II

This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

STATEMENT-1 For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

and

STATEMENT-2
If the observer and the object are moving at velocities $\overset{\rightarrow}{V_1}$ and $\overset{\rightarrow}{V_2}$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $\overset{\rightarrow}{V_2}-\overset{\rightarrow}{V_1}$

Possible Answers

Selected	Possible Answer
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
	STATEMENT-1 is False, STATEMENT-2 is True.
	STATEMENT-1 is True, STATEMENT-2 is False.

Question

Section II

STATEMENT-1 It is easier to pull a heavy object than to push it on a level ground.

and

STATEMENT-2 The magnitude of frictional force depends on the nature of the two surfaces in contact.

Possible Answers

Selected	Possible Answer
	STATEMENT-1 is True, STATEMENT-2 is False.
	STATEMENT-1 is False, STATEMENT-2 is True.
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.

Question

Section II

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 $\cfrac{Q}{4 \pi \epsilon_0 R}$

Possible Answers

Selected	Possible Answer
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
	STATEMENT-1 is True, STATEMENT-2 is False.
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
	STATEMENT-1 is False, STATEMENT-2 is True.

Question

Section II

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.

Possible Answers

Selected	Possible Answer
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
	STATEMENT-1 is True, STATEMENT-2 is False.
	STATEMENT-1 is False, STATEMENT-2 is True.
	STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.

Question

Section III

This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $\rho (r)$ [charge per unit volume] is dependent only on the radial distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction

The electric field at r = R is

Possible Answers

Selected	Possible Answer
	directly proportional to
	directly proportional to a
	inversely proportional to a
	independent of a

Question

Section III

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

Possible Answers

Selected	Possible Answer
	$\cfrac{Ze}{3\pi R^3}$
	$\cfrac{3Ze}{\pi R^3}$
	$\cfrac{4Ze}{3\pi R^3}$
	$\cfrac{3Ze}{4\pi R^3}$

Question

Section III

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

Possible Answers

Selected	Possible Answer

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

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

Question

Section III

Paragraph for Question Nos. 39 to 41.

A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of the each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $\overset{\rightarrow}{V_0}=V_0 \hat{i}$ The coefficient of friction is $\mu$

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

Possible Answers

Selected	Possible Answer
	$-\cfrac{2kx}{3}$
	$\cfrac{-4kx}{3}$

Question

Section III

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

Possible Answers

Selected	Possible Answer
	$\sqrt{\cfrac{k}{M}}$
	$\sqrt{\cfrac{2k}{3M}}$
	$\sqrt{\cfrac{2k}{M}}$
	$\sqrt{\cfrac{4k}{3M}}$

Question

Section III

The maximum value of V_0

for which the disk will roll without slipping is

Possible Answers

Selected	Possible Answer
	$\mu g \sqrt \frac{M}{2k}$
	$\mu g \sqrt \frac{3M}{k}$
	$\mu g \sqrt \frac{5M}{2k}$
	$\mu g \sqrt \frac{M}{k}$

Question

Section III

MAtrix – Match Type

This section contains 3 questions. Each question contains statements given in two columns, which have to be matched. Statements in Column I are labelled as A, B, C and D whereas statements in Column II are labelled as p,q. r and s. The answers to these questions have to be appropriately bubbled as illustrated in the following example.

If the correct matches are A-q, A-r, B-p, B-s, C-r, C-s and D-q, then the correctly bubbled matrix will look like the following:

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 * 4

matrix given in the ORS.

Possible Answers

Selected	Possible Answer
	(A) – (Q); (B) – (q),(s) ; (C) – (q); (D) – (q)
	(A) – (p); (B) – (q),(s) ; (C) – (s); (D) – (q)
	(A) – (s); (B) – (q),(s) ; (C) – (p); (D) – (q)
	(A) – (p); (B) – (q),(s) ; (C) – (s); (D) – (p)

Question

Section III

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 * 4

matrix given in the ORS.

Possible Answers

Selected	Possible Answer
	$(A) \rightarrow (p),(q),(r),(s); (B) \rightarrow (q) ; (C) \rightarrow (p), (q), (r); (D) \rightarrow (p),(q),(r),(s)$
	$(A) \rightarrow (p),(q),(s); (B) \rightarrow (q) ; (C) \rightarrow (p), (q), (r), (s); (D) \rightarrow (p),(q),(r),(s)$
	$(A) \rightarrow (p),(q),(r),(s); (B) \rightarrow (q) ; (C) \rightarrow (p), (q), (r), (s); (D) \rightarrow (p),(q),(r),(s)$
	$(A) \rightarrow (p),(q),(r),(s); (B) \rightarrow (q) ; (C) \rightarrow (p), (q), (r), (s); (D) \rightarrow (p),(q),(r)$

Question

Section III

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 * 4

matrix given in the ORS.

Possible Answers

Selected	Possible Answer
	$(A) \rightarrow (q); (B) \rightarrow (p),(r) ; (C) \rightarrow (p), (s) \rightarrow (q), (s)$
	$(A) \rightarrow (q); (B) \rightarrow (p),(r) ; (C) \rightarrow (p), (s); (D) \rightarrow (q), (s)$
	$(A) \rightarrow (p); (B) \rightarrow (q),(r) ; (C) \rightarrow (p), (s); (D) \rightarrow (q), (s)$
	$(A) \rightarrow (q); (B) \rightarrow (p),(r) ; (C) \rightarrow (p), (s); (D) \rightarrow (q)$

Prev Next

Selected	Possible Answer
	$\hat {u}=\cfrac {\hat a+\hat b}{\|\hat a+\hat b\|}$ and $M=(1+2 \hat a. \hat b)^{1/2}$
	$\hat {u}=\cfrac {\hat a+\hat b}{\|\hat a+\hat b\|}$ and $M=(1+\hat a. \hat b)^{1/2}$
	$\hat {u}=\cfrac {\hat a-\hat b}{\|\hat a-\hat b\|}$ and $M=(1+2 \hat a. \hat b)^{1/2}$
	$\hat {u}=\cfrac {\hat a-\hat b}{\|\hat a-\hat b\|}$ and $M=(1+\hat a. \hat b)^{1/2}$

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