Fiitjee: Mock Test–3

FIITJEE MOCK TEST–3 IIT – JEE 2011 PAPER – I Time: 3 hours

Maximum Marks: 240

INSTRUCTIONS: A. Genera Generall

1. This booklet booklet is your your Question Question Paper containing 60 questions. questions. 2. Blank papers, papers, clipboards, log tables, slide rules, rules, calculators, cellular cellular phones, pagers pagers and electronic gadgets in any form are not allowed to be carried inside the examination hall. 3. Fill in the boxes provided for Name and Enrolment Enrolment No. 4. The answer sheet, a machine-readable Objective Response (ORS), is provided separately. 5. DO NOT TAMPER WITH / MULTILATE THE ORS OR THE BOOKLET. B. Filling Filling in the OMR:

6. The instructions instructions for the OMR sheet are given on the OMR itself. C. Marking Marking Scheme: Scheme:

7. For each each question question in Section I, you will be awarded 3 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. 8. For each each question question in Section II, you will be awarded 4 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. 9. For each each question question in Section III, you will be awarded 4 marks if you darken only the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. 10.For each question in Section IV: you will be awarded 2 marks for each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of 8 marks. There is No negative marks awarded for incorrect answer(s) in this section. Don’t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the exam. NAME: ENROLLMENT NO.:

PAPER – I

MOCK TEST-2011-P(I)-PMC-(VSB)-2

PART I: PHYSICS SECTION – I Single Correct Choice Type This section contains 8 multiple choice questions . Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

1.

Two boats, A and B, start off simultaneously from the same point from the bank of a river. A moves with a uniform velocity of 4 m/s relative to water perpendicular to the bank, and B starts from rest with an acceleration of 5 m/s2 w.r.t. water in the direction shown in figure. If the speed of water current be u = 2 m/s, then find the separation between the boats at the moment when they are at equal distance from the bank. Assume sufficient width of the river. (A) 4 m (B) 9 m (C) 8 m

2.

(D) 6 m

Consider the circuit shown in figure; r is the winding resistance of each of the two coils. If switch S is closed at t = 0, effective resistance in the circuit at t = 0 is R (A) 4

(C) R

R (B) 2

(D) 4 R

3.

A smooth sphere of radius R is made to translate in a straight line with a constant acceleration ‘a’. A particle kept on top of the sphere is released from there with zero velocity with respect to the sphere. The speed of the particle with respect to the sphere as a function of the angle  it slides, when  is small, is given by (given: R = 1/2 m; a = 1 m/s2) (A) v   (B) v  5 (C) v  7 (D) v  11

4.

A 500  resistor and a capacitor C are connected in series across 50 Hz ac supply mains. The r.m.s. potential difference recorded on high impedance voltmeters are V1 = 120 V (across resistor) and V2 = 160 V (across capacitor). What is the power taken from the supply mains? (A) 48 W (B) 200 W (C) 28.8 W (D) 14.4 W Space for rough work


5.

A string is wound on a cylinder of unit mass and radius R. One end of the string is continuously pulled vertically upwards such that as the string unwinds, the cylinder spins, but its axis remains horizontal at the same level. Tension in the vertical portion of the string is (A) 2g (B) 3g (C) 6g (D) g

6.

A double slit of separation 1.5 mm is illuminated by white light (4000 – 8000 Å). On a screen 120 cm away, coloured interference pattern is formed. If a pinhole is made on this screen at a distance of 3 mm from the central white fringe, some wavelengths will be absent in the transmitted light. Find the second longest wavelength (in Å) which will be absent in the transmitted light. (A) 6818 (B) 5769 (C) 5800 (D) 4421

7.

A solid cone of height H and base radius H/2 floats in a liquid of density . It is hanging from the ceiling with the help of a string. The force by the fluid on the curved surface of the cone is (P0: atmospheric pressure)

 P  gH   P  gH  H2  0  H2  0    3  (B) 6  4 4 (A) H2  P0 H2    gH P0   gH    (D) 4 (C) 4  4 8.

The electron in a hydrogen atom makes a transition n1  n2 where n1 and n2 are the principle quantum numbers of the two states. Assume Bohr model is valid in this case. The frequency of the orbital motion of the electron in the initial state is 1/27 of that in the final state. The possible values of n1 and n2 are (A) n1 = 6, n2 = 3 (B) n1 = 4, n2 = 2 (C) n1 = 8, n2 = 1 (D) n1 = 3, n2 = 1 Space for rough work


SECTION–II Multiple Correct Choice Type This section contains 4 multiple choice questions . Each question has 4 choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.

9.

Suppose two particles 1 and 2 are projected in vertical plane simultaneously. Their angles of projection are 30° and , respectively, with the horizontal. Suppose they collide after a time t in air. Then 4   sin1    5  and they will have the same speed just before the collision (A) 4   sin1    5  and they will have different speeds just before the collision (B)

(C) x < 1280 3 – 960m (D) it is possible that the particles collide when both of them are at their highest point. 10.

Energy liberated in the de-excitation of hydrogen atom from third level to first level falls on a photocathode. Later when the same photo-cathode is exposed to a spectrum of some unknown hydrogenlike gas, excited to second energy level, it is found that the de Broglie wavelength of the fastest photoelectrons now ejected has decreased by a factor of 3. For this new gas, difference of energies of second Lyman line and first Balmer line is found to be three times the ionization potential of the hydrogen atom. Select the correct statement(s): (A) The gas is lithium (B) The gas is helium (C) The work function of photo—cathode is 8.5 eV (D) The work function of photo—cathode is 5.5 eV

11.

A smooth hemispherical bowl 30 cm in diameter rotates with angular speed  about an axis of symmetry. A particle P of weight 0.5 kgf is observed to remain at rest relative to the bowl at a height of 10 cm above the base. If N is the force extended by the particle on the bowl, then (A) w = 4.5 rad/s (B) N = 1.5 kgf (C) When w is increased to 9 rad/s, N becomes 3.0 kgf (D) When w is increased to 9 rad/s, N becomes 0.5 kgf Space for rough work


12.

An electron and a proton travel at equal speeds around circular orbits in the same uniform magnetic field as indicated (not to scale) in the following diagram. The field is into the page on the diagram. The electron travels _______ around the __________ circle and the proton travels _________ around the ________ circle. (A) clockwise, smaller, counterclockwise, larger (B) counterclockwise, larger, counterclockwise, smaller (C) clockwise, larger, counterclockwise, smaller (D) counterclockwise, larger, clockwise, smaller SECTION – III Paragraph Type

This section contains 2 paragraphs. Based upon each of the paragraph 3 multiple choice questions have to be answered. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Paragraph for Question Nos. 13 to 15

Inside a uniform spherical shell of mass 4m and radius 4R, a solid sphere of mass 2m and radius R is kept. The solid sphere is of uniform density. The centre of the solid sphere is displaced by 2R w.r.t. the centre of shell. 13.

What is the ratio of gravitational field intensity at the centre of the shell to that at the surface of solid sphere? (A) 1/2 (B) 2 (C) 1/4 (D) 4

14.

What is the ratio of gravitational field potential at the centre of the shell to that at the centre of solid sphere? (A) 1/2 (B) 2 (C) 1/4 (D) 4

15.

A particle of very small mass m0 is shifted from centre of shell to any point on the surface of the solid sphere. What is the work done by gravitational forces in this process?

 Gmm0    (A) –  R 

 Gmm0    (B)  R 

 Gmm0    (C) 2  R 

Space for rough work

 Gmm0    (D) –2  R 


Paragraph for Question Nos. 16 to 18

The singly ionised helium gas in Geissler tube is excited to the state of potential energy of – 1.7 eV. The radiations from the tube are made to illuminate a clean metal surface of work function 8 eV. [Radiations are almost of same intensity irrespective of their wavelengths] 16.

The number of monochromatic radiations that induce photoelectron emission is (A) six (B) five (C) four (D) three

17.

The de Broglie wavelength of photoelectrons lies in the range (A) 1.8 Å    8.24 Å (B) 3.8 Å    4.3 Å (C) 1.33 Å    1.8 Å (D) 8.24 Å    4.3 Å

18.

A schematic graph of applied voltage V versus photoelectric current I is as follows:

(A)

(B)

(C)

(D)

SECTION – IV Matrix–Match Type This section contains 2 questions. Each question has four statements (A, B, C and D) given Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II. For example, if for a given question, statement B matches

will the statements given in q and r, then for that particular question, against statement B, darken the bubbles corresponding to q and r in the ORS. Space for rough work


19.

E is the total energy (KE + PE) of a satellite orbiting around the earth. Match the columns: Column – I

20.

Column – II

(A)

E>0

(p)

elliptical or circular orbit of satellite

(B)

E<0

(q)

escapes from the gravitational pull of earth

(C)

E varies

(r)

orbit of variable radius

(D)

E=0

(s)

may or may not have constant speed

(t)

orbit of constant radius

Match column-I of properties with column-Il of reactions: Column – I

(A)

Mass of products formed is less than the original mass of the system in

Column – II

(p)

 –decay

(B)

Binding energy per nucleon increase in

(q)

 –decay

(C)

Mass number is conserved in

(r)

nuclear fission

(D)

Charge number is conserved in

(s)

nuclear fusion

(t)

 –decay



PART II: MATHEMATICS SECTION – I Single Correct Choice Type This section contains 8 multiple choice questions . Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

21.

f is function defined on the interval [–1, 1] such that f(sin 2x) = sin x + cos x.

  ,     Statement 1: If x   4 4  , then f(tan2x) = sec x Statement 2: f(x) = 1  x ,  x  [–1, 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 22.

In a triangle ABC,  A = 30, BC = 2 + 5 , then the distance of the vertex A from the orthocenter of the triangle is

2  5  (A) 1

(B) y2

23.

c

The determinant a

b

c

is equal to

cx  by

(A) bx  a y c x  b y

ax  by

ax  by

(C) bx  c y a x  b y 24.

(D)

2 2

1 2

 xy x2 b

bx  cy



3 1

(C)

a bx  ay



3

(B) ax  by bx  c y ax  by

bx  cy bx  cy

(D) ax  by b x  c y

A line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB. If d1 and d2 are the distances of the tangent to the circle at the origin O from the points A and B, respectively, the diameter of the circle is d1d 2  d1  d2   d1  2d2  2 (A) d1d 2 (B) (C) d + d (D)  d1  d2  1

2



25.

26.

The number of 3 digits in which the digit at hundredth’s place is greater than the other two digits is (A) 285 (B) 281 (C) 240 (D) 204

1   1 1  1  A 2       1   2   1 0 . The sum of the elements of A, is A is a 2  2 matrix such that     and (A) –1

27.

28.

(B) 0

(C) 2

(D) 5

The value of 20C0 + 20C1 + 20C2 + 20C3 + 20C4 + 20C12 + 20C13 + 20C14 + 20C15 equals to

  20 C10  20 C9     2    (A) 219 – 

  20 C10  2  20 C9     2    (B) 219 – 

 219  20 C10    2  (C) 

(D) none of these

Which of the following conditions imply that the real number x is rational ? I. x 1/2 is rational II. x2 and x5 are rational III. x2 and x4 are rational (A) I and II only (B) I and III only (C) II and III only (D) I, II and III

SECTION–II Multiple Correct Choice Type This section contains 4 multiple choice questions . Each question has 4 choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct. 1

29.

The function f is continuous and has the property f(f(x)) = 1 – x for all x  [0, 1] and J = Then which of the following is/are true ?

 1 3    f   (A)  4   4  = 1  1  2 f    f   3 3 (C)     = 1 f

30.

 f(x) 0

1 (B) the value of J equal to 2 /2 sinx dx

(D)



0

3

 sinx  cosx  has the same value of J

In triangle ABC, if sin A + sin B + sin C  1, then (A) at least one of A, B, C must exceed 150 (B) at least one of A, B, C must be less than 30 (C) sum of at least two angles must be less than 30 (D) all three angles are acute Space for rough work

dx.


31.

→ → Let unit vectors a and b be perpendicular and unit vector c be inclined at an angle  to both a and b

. If

→ → → →→ c  a  b   a  b

(A)  =  32.



 , then (B) 1 – 2 =  2

2

1  cos 2 (C)  = 2 2

(D) 2 – 2 = 2

A continuous function f(x) on R  R satisfies the relation f(x) + f(2x + y) + 5xy = f(3x – y) + 2x2 + 1 for  x, y  R, then which of the following hold(s) good (A) f is many-one (B) f has no minima (C) f is neither odd nor even (D) f is bounded SECTION – III Paragraph Type


A player tosses a coin and scores one point for every head and two points for every tail that turns up. He plays on until his score reaches or passes n. Pn denotes the probability of getting a score of exactly n. 33. The value of Pn is equal to 1 (A) 2 [Pn – 1 + Pn – 2 ]

34.

35.

1 (B) 2 [2Pn – 1 + Pn – 2 ]

1 The value of Pn + 2 Pn – 1 is equal to 1 2 (A) 2 (B) 3

1 (C) 2 [Pn – 1 + 2Pn – 2 ]

(D) none of these

(C) 1

(D) none of these

2 (C) P100, P 101 > 3

(D) none of these

Which of the following is not true ? 2 (A) P100 > 3

2 (B) P101 < 3




Suppose a cubic polynomial f(x) = x3 + px2 + qx + 72 is divisible by both x2 + ax + b and x2 + bx + a (where a, b, p, q are constants and a  b) 36. 37. 38.

The value of p is (A) –1

(B) 1

(C) 2

(D) none of these

The value of q is (A) 70

(B) 55

(C) –73

(D) –101

The sum of square of roots of the equation f(x) = 0 is (A) 150 (B) 146 (C) 251

(D) 300


will the statements given in q and r, then for that particular question, against statement B, darken the bubbles corresponding to q and r in the ORS. 39.

Match the following Column I

(A)

Column II

a  R, then number of distinct real solutions of x – |x| + a = 0 can be 2

a1  b1x

a1 x  b1

c1

(B)

 b2 x a2 x  b2 c2 If x  R, ai, b i, c i  R for i = 1, 2, 3 and a3  b3 x a3 x  b3 c3 = 0  x =

(C)

Let (1 + x ) (1 + x) =  

p. q.

1 2

r.

3

s.

4

t.

–1

a2

n 4

(D)

40.

ak xk

. If a1, a 2 and a3 are in arithmetic progression, then possible value/values of n is/are The value of x for which sin  + 3 cos  = 6x – x2 – 11, 0    4, x  R holds 2 2

n

k 0

 x 2   y2   2  2  The tangents drawn from a point P to the ellipse  a   b  = 1 make angle  and  with the major axis. Column I

(A) (B) (C) (D)

Column II

c If  +  = 2 (c  N)

p.

circle

If tan  tan  = c [where c  R], then locus of P can be If + tan {where cc  R}, locus then locus of Pbe can be  +  R}, If tan cot  cot  == cc {where of P can

q. r. s.

ellipse hyperbola pair of straight lines

t.

rectangular hyperbola



PART III: CHEMISTRY SECTION – I Single Correct Choice Type This section contains 8 multiple choice questions . Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

41.

Which of the following has the maximum value of angle strain ? (A) cyclopropane (B) cyclopentane (C) cyclobutane

(D) cyclohexane

42.

The maximum difference in covalent radii is for the following pairs of elements : (A) Zr and Hf (B) Mo and W (C) La and Y (D) Pd and Pt

43.

The packing fraction for a particular unit cell is given by the following equation : 8 3 r 3

 64  3  3 3   r   Identify the type of the unit cell (A) bcc (B) fcc 44. 45.

(C) simple cubic

In the most stable elements, the number of protons and neutrons are (A) odd–odd (B) even–even (C) odd–even

(D) none of these (D) even–odd

For hydrocarbons, heat of cracking is defined as H at 298.15 K and 101.325 kPa for the following process. m  CnHm   2n   H2  g  nCH4  g 2  Heat of cracking for ethane is –65.2 kJ and for propane is –87.4 kJ. Calculate H for the following reaction : CH4(g) + C3H8(g)  2C2H6(g) (A) + 43 kJ (B) –22.2 kJ (C) –44.4 kJ (D) –21.5 kJ Space for rough work


46.

25 mL of a mixture of sodium hydroxide and sodium carbonate requires 25 mL of HCl when titrated with N/10 HCl using phenolphthalein as indicator. The same volume of the mixture when titrated with same HCl using methyl orange as indicator required 30 mL of HCl. Calculate the amount of sodium hydroxide in half litre of this mixture. (A) 3.2 g (B) 1.6g (C) 4.8g (D) 6.4g

47.

What is the product formed when benzene is reduced with lithium in liquid ammonia ? (A)

48.

(B)

(C)

(D)

Nef Carbonyl Synthesis is applicable to the following : (A) Amines (B) nitro compounds (C) isocyanides

no reaction

(D) cyanides

SECTION–II Multiple Correct Choice Type This section contains 4 multiple choice questions . Each question has 4 choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.

49.

Which of the following statement/s are correct for an electron that has n = 4 and m = –2 ? (A) Electron may be in d–orbital (B) Electron is in 4th principle shell (C) Electron may be in p–orbital (D) Electron must have spin quantum number +1/2.

50. The ether

(A)

51. 52.

O

CH2I

(B)

CH2

when treated with HI produces

CH2OH

(C)

The compound which has zero dipole moment is/are (A) CH2Cl2 (B) BF3 (C) NF3

I

(D)

OH

(D) PF2Cl3

An aqueous solution of phosphoric acid (H3PO4) being titrated has molarity equal to 0.25 M. Which of the following could be normality of this solution ? (A) 0.25 N (B) 0.50 N (C) 0.75 N (D) 1.00 N Space for rough work


SECTION – III Paragraph Type


The carbon–metal bond in carbonyls may be represented as the donation of an electron pair from carbon to the metal M  C O. This original  bond is weak. A stronger second bond is formed by back bonding, sometimes called dative  bonding. This arises from sideways overlap of a full dxy orbital one the metal with the empty anti–bonding *2y orbital of the carbon, thus forming a  M  C bond. The total bonding is thus M=C=O. The drift of  electron density from M to C makes the ligand more negative, which in turn enhances its  donating power. Thus CO forms weak bonds to Lewis acids (electron pair acceptors) such as BF3 as only  bonding is involved. In contract, CO forms strong bonds to transition metals where both  and  bonding can occur. Other  acceptor ligands include CN –, RNC and NO+. Comparing these ligands, the strengths of the  bonds are in the order CN – > RNC > CO > NO+, whilst their  acceptor properties are in the reverse order. 53.

In carbon monoxide molecule, the atom which has a lone pair of electrons is (A) carbon atom (B) oxygen atom (C) both of them (D) none of them

54.

Carbon monoxide forms metal carbonyl compounds with the following metal/s : (A) manganese (B) iron (C) nickel (D) all of these

55.

Which of the following is not a consequence of back–bonding in metal carbonyls ? (A) Bond length in CO increases (B) Bond order of CO decreases. (C) New electron enters the anti–bonding orbital. (D) Electron density increases on the metal. Space for rough work



The trend of metallic properties is less obvious in group 17. Increasing stability of positive ions shows an increasing tendency to basic or metallic character. Fluorine is the most electronegative element and has no basic properties. Iodine dissolve in oleum and other strongly oxidizing solvents forming bright blue (paramagnetic) solutions containing [I2]+. [Br 2]+ is also formed in oleum and is bright red coloured and paramagnetic . [Cl2]+ has been spectroscopically in discharge tubes. Many crystalline compounds containing [I2]+ or [Br 2]+ have been prepared. Many other compounds containing cations like [Cl3]+, [Br 3]+ and [I3]+ have been prepared. 56.

57.

58.

Which of the following halogens is the most basic in nature ? (A) fluroine (B) iodine (C) bromine 

(D) chlorine



The shapes of I3  and I3  , respectively, are (A) linear, bent (B) bent, bent (C) linear, linear 

0

(D) bent, linear 0

The bond length in Br 2  cation is 2.15 A as compared with the bond length in Br 2, which is 2.27 A . This definitely shows that (A) The electron is removed from a bonding orbital (B) The electron is removed from an anti–bonding orbital. (C) The electron is shifted from a bonding orbital to an anti–bonding orbital. (D) The electron is shifted from an anti–bonding orbital to a bonding orbital. Space for rough work



will the statements given in q and r, then for that particular question, against statement B, darken the bubbles corresponding to q and r in the ORS. 59.

Match the following Column – I

(A) (B) (C) (D) 60.

Column – II

106g sodium carbonate 66g H3PO2 126 g of crystalline oxalic acid 158g of Na2S2O3 in reaction with I2

(p) (q) (r) (s) (t)

1 mole 2g equivalents 2 moles 4g equivalents 1 g equivalent

Match the following Column – I

Column – II

Cl

(A)

(p)

More reactive than benzene towards ES reactions

(q)

Less reactive than benzene towards ES reaction

OH

(B) OCH3

(C)

(r)

Doesn’t have acidic nature

(s)

Gives o– and p–products in ES

(t)

Gives m–products in ES

CHO

(D)



FIITJEE MOCK TEST–3 IIT – JEE 2011 PAPER – I ANSWERS PHYSICS

1.

D

2.

C

3.

A

4.

C

5.

D

6.

A

7.

B

8.

D

B,C,D

10.

B,C

11.

A,B

12.

A

13.

C

14.

A

15.

B

16.

C

17.

A

18.

C

19.

A – q, B – p,s, C – r, D – q

20.

A – p,q,r,s, B – p,q,r,s, C – p,q,r,s, D – p,q,r,s,

21.

C

22.

B

23.

D

24.

C

25.

A

26.

D

27.

B

28.

A

29.

A, B, D

30.

A, C

31.

B, C

32.

A, B

33.

A

34.

C

35.

C

36.

D

37.

C

38.

B

39.

A

q, r, s; B

p, t; C

40.

A

r, s, t; B

p, q, r, s, t; C

9.

MATHS

q, r, s; D

r

r, s; D

r, s

CHEMISTRY

41.

A

42.

C

43.

A

44.

B

45.

A

46.

B

47.

C

48.

B

49.

A, B

50.

A, D

51.

B, D

52.

A, B, C

53.

C

54.

D

55.

D

56.

B

57.

A

58.

B

59.

A

p, q; B

60.

A

q, r, s ; B

p, t ; C p, s; C

p, q ; D

p, t

p, r, s ; D

q, r, t

Fiitjee: Mock Test–3

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