Iit Jee 2010 Part 2

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Space for Rough Work

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CHEMISTRY

SECTION – I Single Correct Choice Type

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

1. Which of the following compounds was the starting material for the oxidation shown below?

?KMnO /H4

+

O

HO OH + CO2OH

O

O

(A)

(B)

(C)

(D)

2. Pick out the incorrect statement.

(A) trans-2-butene reacts with singlet :CH2 to give meso form of cis 1, 2-dimethyl cyclopropane. (B) trans -2-butene reacts with triplet carbene : CH2 to give racemic mixture of trans 1, 2-dimethyl

cyclopropane. (C) singlet can be generated by decomposition of diazomethane (D) Triplet is obtained by a special photochemical method using photosensitizer. 3. (X) + K2CO3 + Air heat (Y) (Y) + Cl2 (Z) Pink Which of the following is correct? (A) X = black, MnO2, Y = Blue, K2CrO4, Z = KMnO4 (B) X = green, Cr2O3, Y = Yellow, K2CrO4, Z = K2Cr2O7 (C) X = black, MnO2, Y = green, K2MnO4, Z = KMnO4 (D) X = black, Bi2O3, Y = colourless, KbiO2, Z = KbiO3

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4. In a recently conducted experiment, VO2 could be disproportionated, in presence of concentrated

aqueous solution of NaOH and CsOH, into two different compounds Cs4Na(HV10O28) and Na[V(OH)2]. What is the number of moles of Cs4Na(HV10O28) formed when number of moles of Na V(OH)2 formed is 0.5.

(A) 0.167 (B) 0.15 (C) 0.05 (D) 0.2

SECTION – II Multiple Correct Choice Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct. 5. In which of the following cases rate is dependent upon concentration of nucleophile? (A)

CH3

Ph

ClCH3F/SO2 (liquid)

(Specific rotation = 0)Product

(B)

H

CH3

C6H13

I (Specific rotation = 0)NaI/ acetoneProduct

(C)

Product

NO2

Cl

NO2

NaOH/

(D) Product AgIPhCl

DH(mixture of stereoisomers)

6. Consider the given reaction: In the above reaction which of the given ring will not undergo

reduction? (A) ring A (B) ring B (C) ring C (D) ring D

Pd / C23H Pr oduct

C

A

B D

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7. Which of the following statement (s) is/are incorrect?

(A) In 2CoBrCl en

geometrical isomerism exists, while optical isomerism does not exist

(B) Potassium aquadicyanosuperoxoperoxochromate (III) is IUPAC name 2 2 2 22

K Cr N O O H O (C) There are 3 geometrical and 15 stereoisomers possible for

2 3 2Pt NO NH NH OH py

and 2 3PtBrClI NO NH py respectively (D) cis and trans forms are not diastereomers to each other.

8. An acid–base indicator has a Ka of 3.0 10–5. The acid form of the indicator is red and the basic form is blue. Then:

(A) pH is 4.05 when indicator is 75% red (B) pH is 5.00 when indicator is 75% blue (C) pH is 5.00 when indicator is 75% red (D) pH is 4.05 when indicator is 75% blue 9. Which of the following statements is/are not correct :

(A) Physical adsorption is directly related to the critical temperature of the gas (adsorbate) (B) One gram of charcoal at 25°C will always adsorb the same amount of particular gas at a

particular pressure (C) At particular temperature, adsorption always increases with increase of pressure (D) In adsorption, the concentration of adsorbate is always greater at the surface of the adsorbent

SECTION – III Matrix-Match Type

This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example: If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s and t; then the correct darkening of bubbles will look like the following.

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10. Match Column I with Column II

Column I Column II (A) XeF2 (p) Square pyramidal (B) PCl5 (q) Linear shape (C) XeOF4 (r) sp3d hybridization (D) XeF4 (s) sp3d2

11. Match the particle in column I with their effects in column II Column – I (Particle)

Column – II (Effect)

(A) Alpha particle emission (p) Number of proton increases

(B) Beta particle emission (q) Number of proton decreases

(C) Positron emission (r) Number of neutron increases

(D) Electron capture (s) Number of neutron decreases

SECTION – IV Integer Answer Type

This section contains 8 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the following.

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12. (C H N )4 12 2O /Zn H /KMnO 2 mole of sodamide Alkaline3 4

H O NaNH Bro min e2 2C H O C H O (C H O N )7 12 2 6 10 4 6 12 2 2 Br NaOH2

A B C D

CH3

C7H12

prop 2 enal conc. H SO2 4C H (C H O )C H O 4 6 4 10 27 10

G F E

2NaNO HCl

How many type of functional group are present in compound G. 13. The number of water molecules present as water of crystallization in Borax Na2B4O7.10H2O. 14. Enthalpy neutralization of H3PO3 is –106.68 kJ/mol using NaOH. If enthalpy of neutralization of HCl

by NaOH is –55.84 kJ/mol. H ionization of H3PO3 into its ions is x kJ/mol. Find the value of x. 15. The maximum possible number of hydrogen bonds a water molecule can form in ice is…

16. 10% sites of catalyst bed have adsorbed by H2. On heating H2 gas is evolved from sites and collected at 0.03 atm and 300 K in a small vessel of 2.46 cm3. Number of sites available is 6.0 × 1015 per cm2 and surface area is 1000 cm2. Find out the no. of surface sites occupied per molecule of H2. (Given NA = 6 × 1023)

17. What is the value of i for Ca3(PO4)2 assuming complete ionisation ?

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18. Haemoglobin contains 0.25% iron by weight. The molecular weight of haemoglobin is 89600. Calculate the number of iron atom per molecule of haemoglobin.

19. Freon-12 is used as a refrigerant in central home air conditioners. The rate of effusion of Freon-12 to Freon-11 (molar mass =137.4 g/mol) is 1.07 : 1. The formula of Freon-12 is one of the following : CF4, CF3 Cl, CF2Cl2, CFCl3, or CCl4. Find the number of fluorine atoms in a molecules of Freon-12.

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MATHEMATICS SECTION – I

Single Correct Choice Type


20. Let f(x) = (x + 1) (x + 2) (x + 3) . . . (x + 100) and g(x) = f(x). 2f (x) f (x) , then g(x) = 0, has (A) no solution (B) exactly one solution (C) exactly two solutions (D) minimum three solutions

21. If g(x) be a continuous function for all real values of x and satisfies x 82

2

3 x

xg(t)dt t g(t)dt,2

then

1

1/ 2

g(x)dx is equal to

(A) 5ln8

(B) 82 ln5

(C) 1 8ln2 5

(D) 1 5ln2 8

22. If |z – 3i| = 3 and amp z 0,2

then

6cot(amp z)z

is equal to

(A) i (B) 1 (C) – 1 (D) –i 23. If line y = x + 2 do not intersect any member of family of parabola y2 = ax, (aR+) at two distinct

point, then maximum value of latus rectum of parabola is (A) 4 (B) 8 (C) 16 (D) 32


This section contains 5 multiple correct answer(s) type questions Each question has 4 choices (A), (B), (C) and (D), out of which MORE THAN ONE is/are correct.

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24. The values of ‘a’ for which the integral 2

0

x a dx 1 is satisfied are

(A) [2, ) (B) (– , 0] (C) (0, 2) (D) none of these 25. Let the algebraic sum of the perpendicular distances from the points A(2, 0), B(0, 2), C(1, 1) to a

variable line be zero. Then all such lines (A) are concurrent (B) passes through a fixed point (1, 2) (C) touches some fixed circle (D) passes through a fixed point (1, 1) 26. Sum to m terms of the series S = 12 + 2(2)2 + 32 + 2(4)2 + (5)2 + 2(6)2 + ……. is

(A) 14

m2(m + 2) ; m is odd (B) 12

m2(m + 1) ; m is odd

(C) 12

m(m + 1)2 ; m is even (D) 14

m(m + 2)2 ; m is even

27. The eccentric angles of the extremities of a chord of an ellipse 2 2

2 2x y 1a b

are and . If this

chord passes through the focus, then

(A) 1 etan tan 02 2 1 e

(B)

sin sinesin( )

(C) cos e cos2 2

(D)

e 1cot cot2 2 e 1

28. The value of 7 14

k 0 r k

7r 14k

14 k rk

, where nr

denotes nrC , is

(A) 67 (B) greater than 76 (C) 87 (D) greater than 78

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29. Let y(x) be the solution of differential equation dydx

= –2x (y– 1) with y(0) = 1

g(x) = min{|x|, x2, y(x)} and h(x) = ex, p(x) = 3 ln x Column I Column II (A) y(x) equals (p) 4 (B) If area bounded by p(x) = 3 lnx, y (x) and the

y–axis is e1/3, then equals (q) 3

(C) If area bounded by the curves y(x); g(x), x = 0, x = 2 and x–axis is /3, then equals

(r) 1

(D) If h(x) = y(x), then x equals (s) 0 30. Match Column I with Column II

Column – I Column – II (A) P(A/B) + P(A/B) (p) P(A) – P(A B) (B) P(A) . P(B/A) + P(A) . P(B/A) (q) 1 (C) P(A – B) (r) P(B) (D) P(A B) – P(A B) (s) P(B) – P(A B) (t) P(A B) + P(A B)

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31. The number of common tangents that can be drawn to the circle x2 + y2 – 4x – 6y – 3 = 0 and x2 + y2 + 2x + 2y + 1 = 0 is

32. The area of the region in the x–y plane defined by [x]2 + [y]2 = 5 is ________ sq. units. 33. Four lines x = a, y = a forms a square in x-y plane. A point P is moving in such a way that its

distance from any of these sides of square is greater than its distance from the centre of the square. Then number of curves bounding the above region is

34. The equation of an ellipse is 10x2 + 6y2 = 15, then the distance between the directrices is

35. On a chess-board if two squares are chosen, the probability that they have a side in common is 1

2P then P will be…..

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36. If 3 2iz z z i 0 , then |z| equals

37. If 1 2 31 2 3

1 1 1| z | | z | | z | 1z z z

then 1 2 3| z z z | is equal to ….

38. If A is a square matrix of order n such that |adj (adj A)| = |A|9, then the value of n can be

PHYSICS SECTION – I

Single Correct Choice Type


39. A sphere of mass M and radius R is placed at rest on a smooth horizontal surface. It is given a horizontal impulse F at a height h above the centre of mass. Identify the correct statement :

(A) the centre of mass moves with velocity, 0FVM

Fh

smooth

(B) it rotates with an angular velocity, 0 2

5 Fh2 MR

(C) the sphere will start rolling motion if 2h R5

(D) all of these 40. Two identical blocks P and Q have mass m each. They are attached to two identical springs initially

unstretched. Now the left spring (along with P) is compressed by A/2 and the right spring (along with Q) is compressed by A. Both the blocks are released simultaneously. They collide perfectly inelastically. The time period of both the blocks oscillating independently on there respective springs is T. The time period of oscillation of combined mass is

(A) T2

(B) 2 T (C) T (D) T2

AP Q

2A

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41. A wedge of mass m, lying on a rough horizontal plane, is acted

upon by a horizontal force F1 and another force F2, inclined at an angle to the vertical. The block is in equilibrium, then minimum coefficient of friction between it and the surface is

(A) (F2 sin ) / (mg + F2 cos ) F1

F2

(B) (F1 cos + F2) / (mg F2 sin ) (C) (F1 + F2 sin ) / (mg + F2 cos ) (D) (F1 sin F2) / (mg F2 cos )

42. A uniform conducting rectangular loop of sides , b and mass m carrying current i is hanging horizontally with the help of two vertical strings. There exists a uniform horizontal magnetic field B which is parallel to the longer side of loop. The value of tension which is least is

(A) mg Bb

2

(B) mg Bb

2

b

B

(C) mg 2iBb

2

(D) mg 2Bb

2

43. The wavelengths of K X-rays from lead isotopes Pb204, Pb206 and Pb208 are 1, 2, and 3 respectively. Choose the correct alternative

(A) 1 < 2 < 3 (B) 1 > 2 > 3 (C) 1 = 2 = 3 (D) none of these


This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct.

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44. A long block A is at rest on a smooth horizontal surface. A small block B, whose mass is half of A, is placed on A at one end and projected along A with some velocity u. The coefficient of friction between the blocks is

BA

v

(A) the blocks will reach a final common velocity u3

(B) the work done against friction is two-thirds of the initial kinetic energy of B

(C) before the blocks reach a common velocity, the acceleration of A relative to B is 2 g3

(D) before the blocks reach a common velocity, the acceleration of A relative to B is 3 g2

45. A particle is dropped from a height equal to the radius of the earth above the tunnel dug through the earth as shown in the figure.

R : Radius of earth. M : Mass of earth. (A) Particle will oscillate through the earth to a height R on both

sides (B) Particle will execute simple harmonic motion (C) Motion of the particle is periodic

(D) Particle passes the centre of earth with a speed = RGM2

R

C

46. A charged particle of unit mass and unit charge moves with velocity of v = ˆ ˆ8 6i jms

in a

magnetic field of B

= 2 k̂ T. Then choose the correct statement. (A) The path of the particle may be x2 + y2 – 4x – 21 = 0 (B) The path of the

particle may be x2 + y2 = 25 (C) The path of the particle may be x2 + z2 = 25 (D) The time period of the

particle will be 3.14 s 47. A thin paper of thickness 0.02 mm having refractive index 1.45 is pasted across one of the slit in a

Young’s double slit experiment. The paper transmits 4/9 of light falling on it. (light = 600 nm). (A) Amplitude of light wave transmitted through the paper will be 2/3 time of incident wave. (B) The ratio of maximum and minimum intensity in the fringe pattern will be 25.

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(C) The total number of fringe crossing the centre if an identical paper is pasted on the other slit is 15.

(D) The ratio of maximum and minimum intensity in the pattern will be 5. 48. X ray from a tube with a target A of atomic number Z shows strong K lines for target A and weak K

lines for impurities. The wavelength of K lines is z for target A and 1 and 2 for two impurities.

z z

1 2

14 and4

.

Screening constant of K lines to be unity. Select the correct statement(s) (A) The atomic number of first impurity is 2z – 1. (B)The atomic number of first impurity is 2z

+ 1.

(C) The atomic number of second impurity is (z 1)2 (D) The atomic number of

second impurity is z 12

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49. In the circuit shown in the figure, switch S is closed at t = 0.

Column – I Column – II

(A) Ratio of the charge in capacitor 2C and C at any time t is

(p) 1 : 2

(B) Time constants of both the capacitor are in the ratio of

(q) 1 : 1

(C) Steady state charge in C and 2C are in the ratio of

(r) 2ln 2 : 1

(D) Ratio of t

when the current in the C is 14

th

of the maximum current in it

(s) 2 : 1

50. The diagrams in Column I show transverse sinusoidal standing/travelling waveforms on stretched

strings. In each case, the string is oscillating in a particular mode, and, its shape and other characteristics are shown at time t = 0. The maximum amplitude (in all the cases) is A, the velocity of the waveform on the string is e, the mass per unit length of the string is and the frequency of vibration is f (angular frequency = ).

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The kinetic energy of the string (of length L) is represented by the functions in Column II. Match the correct entries in Column II.

Column I Column II

(A)

A

L

Fixedend

Fixedend

(p)

2 229 c A

4 L

(B)

A

L

Fixedend

Freeend

(q)

2 22 29 c A sin t

4 L

(C)

A

L

Freeend

Freeend

A

(r)

2 22 29 c A sin t

16 L

(D) A

LTravelling wave

(s)

2 22 2c A sin t

4 L

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51. A particle is projected at 60° to the horizontal with a kinetic energy K. The kinetic energy at the

highest point is kn

. What is the value of n?

52. Two uniform spheres shown in figure rotate separately on parallel axis. The upper sphere has angular speed 0 and lower sphere is at rest. Now the two spheres are moved together so that their surfaces touch. After a short time the two spheres now in contact are rotating without slipping.

Find the final rate of rotation of upper sphere in rad/s. [given moment of inertia of upper sphere I1 = 4 kg m2,

moment of inertia of lower sphere I2 = 2 kg m2, a = 2 m, b = 1 m, 0 = 12 rad/s].

R=a

a

0

R=bb

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53. A U-tube is partially filled with a liquid. The horizontal part of the tube is 2 m. The tube is accelerated horizontally with a constant acceleration of 5 m/s2. What is the difference in the heights of the liquid in the two arms of the U-tube?

54. Two containers A and B are connected by a conducting solid cylindrical rod of length 2427

cm and

radius 8.3 cm. Thermal conductivity of the rod is 693 watt/mole–K. The container A contains two mole of oxygen gas and the container B contains four mole of helium gas. At time t = 0 temperature difference of the containers is 50ºC. After what time (in seconds) temperature difference between them will be 25ºC. Transfer of heat takes place through the rod only. Neglect radiation loss. Take R

= 8.3 J/mole–K and 227

.

A B

O2 He

55. There are two uniformly charged solid spheres having radius a and 2a. They contain charges Q and 16Q respectively. Distance between their centres is 10 a. The distance of a point P from the center of smaller sphere, on the line joining the centers of two spheres, such that point has minimum potential, is

a 2a

10a

56. A ring of mass 4 kg is uniformly charged with = 4 c/m and kept on rough horizontal surface with friction coefficient

4

. A time varying magnetic field B = B0t2 is applied in a

circular region of radius a (a < r) perpendicular to the plane of ring as shown in figure. Find out the time when ring just starts to rotate on surface. (take a = 5 cm and g = 10 m/s2 0 = 125 SI Unit).

++ + + +

++

+++++++

B

ar

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57. A convex lens of focal length 15 cm is split into two halves and the two halves are placed at a

separation of 120 cm. Between the two halves of convex lens a plane mirror is placed horizontally and at a distance of 4 mm below the principal axis of the lens halves. An object AB of length 2 mm is placed at a distance of 20 cm from one half lens as shown in figure. The final image of the point A is formed at a distance of n/3 mm from the principle axis. Determine the value of n.

f=15 cm

4 mm20 cm

2 mm

120 cm

f=15 cm

A

B

Hydrogen atoms absorbs radiation of wavelength 0 and consequently emit radiations of 6 different wavelengths of which two wavelengths are shorter than 0. The final excited state of the atoms is n =

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Answers (chemistry)

1. (c) 2. (a) 3. (c) 4. (b) 5. (b, c) 6. (b, c, d) 7. (a, b, c, d)

8. (a, b) 9. (b, c, d) 10. (a-q,r; b-r; c-p, s; d-s) 11. (a-q, s; b-p, s; c-q, r; d-

q, r)

12. (2) 13. (8) 14. (d) 15. (4) 16. (3) 17. (5) 18. (4) 19. (2)

(Mathematics)

20. (a) 21. (c) 22. (a) 23. (b) 24. (a, b, c) 25. (a, d) 26. (b, c)

27. (a, b, c, d) 28. (a, b) 29. (A-r; B-q; C-p; D-s) 30. (A-q; B-r; C-p; D-t)

31. (3) 32. (8) 33. (4) 34. (5) 35. (9) 36. (1) 37. (1) 38. (4)

(Physics)

39. (d) 40. (c) 41. (c) 42. (c) 43. (a, b, d) 44. (a, c, d) 45. (a, b, d)

46. (a, b, c) 47. (a, c) 48. (A-s; B-q; C-p; D-r) 49. (A-q; B-r; C-s; D-p)

50. (4) 51. (4) 52. (1) 53. (3) 54. (2) 55. (4) 56. (8) 57. (4)

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Iit Jee 2010 Part 2

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Transcript of Iit Jee 2010 Part 2