This practice test consists of IIT JEE 2008 question paper to help you practice for actual IIT JEE main examination. Solve previous year IIT JEE question papers to get good rank in IIT JEE 2011 exam.

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A particle P starts from the point , where . It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point . From the particle moves units in the direction of the vector ï€« and then it moves through an angle in anticlockwise direction on a circle with centre at origin, to reach a point . The point is given by

-7+6i

-6+7i

6+7i

7+6i

Let the function be given by Then g is

even and is strictly increasing in

neither even nor odd, but is strictly increasing in

odd and is strictly decreasing in

odd and is strictly increasing in

Section I

Consider a branch of the hyperbola 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

The area of the region between the curves bounded by the lines

Consider three points , Then

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

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

5 or 10

3, 6 or 9

2, 4 or 8

4 or 8

Let two non-collinear unit vectors and form an acute angle. A point P moves so that at any time t the position vector (where O is the origin) is given by . When P is farthest from origin O, let M be the length of and be the unit vector along . Then

Let Then, for an arbitrary constant C, the value of equals

This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Suppose four distinct positive numbers are in G.P. Let and STATEMENT-1: The numbers are neither in A.P. nor in G.P. and STATEMENT-2: The numbers are in H.P

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.

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

STATEMENT-1: and STATEMENT-2: y(x) is given by

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 defined by

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

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

f(x) is increasing on ï€¨(-1,1) but has neither a local maximum nor a local minimum at x = 1

f(x) is decreasing on ï€¨ (-1,1) and has a local minimum at x = 1

g’(x) does not change sign on

g’(x) is positive on and negative on

g’(x) changes sign on both and

g’(x) is negative on and positive on

Paragraph for Question Nos. 17 to 19

Consider the lines

The unit vector perpendicular to both and is

The shortest distance between and is

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 and is

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 Ã— 4 matrix should be as follows:

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 Ã— 4 matrix given in the ORS.

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 Ã— 4 matrix given in the ORS.

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

The electric field at point O is directed along the negative x-axis

The magnitude of the force between the charges at C and B is

The potential energy of the system is zero

The potential at point O is

5 years each

20 years and 5 years, respectively

10 years each

20 years and 10 years, respectively

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 is

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 at which the speed of the bob is half of that at A, satisfies

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,

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

344

117.3

109.3

336

A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant . The level of liquid is initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is

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 and respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is

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.

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

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.

directly proportional to

directly proportional to a

inversely proportional to a

independent of a

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 The coefficient of friction is

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:

(A) â€“ (Q); (B) â€“ (q),(s) ; (C) â€“ (q); (D) â€“ (q)

(A) â€“ (p); (B) â€“ (q),(s) ; (C) â€“ (s); (D) â€“ (q)

(A) â€“ (s); (B) â€“ (q),(s) ; (C) â€“ (p); (D) â€“ (q)

(A) â€“ (p); (B) â€“ (q),(s) ; (C) â€“ (s); (D) â€“ (p)

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