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IIT-JEE CLASSROOM CENTRE

WEEKLY NORTH INDIA COMPETITIVE EXAMINATION-3(WNICE)ALL RESHUFFLED BATCHES

Time: 3 Hours Maximum Marks: 264

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

INSTRUCTIONS:

A. GENERAL

1. This booklet is your Question Paper containing 72 questions. The booklet has 24 pages.

2. No additional sheets will be provided for rough work.

3. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers &

electronic gadgets in any form are not allowed to be carried inside the examination hall.4. Write your Name and Enrollment No. in the space provided below.5. The answer sheet, a machine-readable Objective Response Sheet (ORS), is provided separately.

B. Filling the ORS

6. On the upper part of the ORS, write in ink, your name, enrollment number and batch numberin the space provided. Do not write these anywhere else.

C. Question paper format:

7. This question paper has 3 sections: Section-A, B & C. Section-A has 60 questionsof physics, chemistry & mathematics (20 per subject), Section-B has 6 questions of

matrix match type (2 per subject) & Section-C has 6 questions of single integer type(2 per subject).

8. Each subject of Section-A contains 8 questions of single correct choice type,2 reasoning type, 2 set of paragraph type questions. The paragraph is followed by3 questions. Each of these questions has 4 choices: (a), (b), (c) & (d), out of which only onechoice is correct. Each subject also contains 4 questions of multiple correct choice type. Eachof these questions has 4 choices: (a), (b), (c) & (d), out of which one or more than one choice iscorrect.

9. Each subject of Section-B contains 2 questions of matrix match type. Each question has fourstatements (A, B, C and D) given in Column I and five statements (1, 2, 3, 4 and 5) in ColumnII. Any given statement in Column I can have correct matching with one or more statement(s)given in Column II.

10. Each subject of Section-C contains 2 questions of integer answer type ranging from0 to 9. The answer will have to be appropriately bubbled in the ORS as per the instructionsgiven at the beginning of the section.

D. Marking Scheme:

11. In Section-A, for single correct choice type questions, you will be awarded 3 marks if you havedarkened only the bubble corresponding to the correct answer and zero mark if no bubble is

darkened. In all other cases, minus one (–1) mark will be awarded.12. In Section-A, for multiple correct choice type questions, you will be awarded

4 marks if you darken only the bubble(s) corresponding to the correct answer and zero mark if

no bubbles are darkened. No negative marks will be awarded.13. In Section-A, for reasoning type and paragraph type questions, you will be awarded

3 marks if you darken only the bubble corresponding to the correct answer and zero mark ifno bubbles are darkened. In all other cases, minus one (–1) mark will be awarded.

14. For each question in Section-B, you will be awarded 8 marks if you have darkened ALL thebubbles corresponding ONLY to the correct answer or awarded 2 marks each for correctbubbling of answer in any row. No negative mark will be awarded foran incorrectly bubbled answer.

15. For each question in Section-C, you will be awarded 4 marks if you darken the bubblecorresponding to the correct answer and zero mark if no bubble is darkened.No negative marks will be awarded in this Section.

Name: ………………………………………… Enrollment No.:

Batch number: ………………………………



Brilliant Tutorials QUESTIONS WNICE-3/RB/090511/PCM 2

Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

Space for rough work

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PHYSICSSECTION–A

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. A long string with uniform linear charge density λ , is passing through an imaginary cube of

edge length a. The maximum flux of the electric field through the cube will be

(a)0

3

ελa

(b)0

2

ελa

(c)0

26

ελa

(d)0ελa

2. Two infinitely long parallel thin conducting sheets having surface charge densities +σ and – σ respectively, are separated by a small distance. The medium between the sheets is

vacuum. If ε0 is the permittivity of vacuum, then the electric field in the region between the

sheets is

(a)02ε

σvolt/meter (b)

0εσ

volt/meter (c)0

2

εσ

volt/meter (d) zero

3. A point charge q is placed at a height a from the vertex of the

square surface of side a as shown. The electric flux through the

square surface is

(a)024ε

q (b)0ε

q

(c)06ε

q (d) zero

a

a

a

a

a

q

4. An electric field given by j yi E ˆ)2(3ˆ4 2 ++=r

pierces Gaussian cube of side 1m placed at

origin such that its three sides represents x, y and z axes. The net charge enclosed within the

cube is

(a) 04ε (b) 03ε (c) 05ε (d) zero






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5. For spherical charge distribution, the volume charge density is given as

>=ρ

≤

−ρ=ρ

3when,0

3when,

3

10

r

r r

(where r is the distance from the centre of spherical charge distribution)

The electric field intensity is maximum at

(a) 5.1=r (b) 2=r (c) 5.4=r (d) at infinity

6. A body moves with velocity v = ln ( x) m/s, where x is its position in metre. The net force

acting on body is zero at x equal to

(a) 0 m (b) e2m (c) e m (d) 1 m

7. A block of mass 1 kg just remains in equilibrium with the

vertical wall of a cart accelerating uniformly with 20 m/s2 as

shown. The co-efficient of friction between block and wall

is ( g = 10 m/s2)

(a) 0.1 (b) 0.2

(c) 0.5 (d) 1

1 kg

a=20m/s2

8. A solid metallic sphere is placed in a uniform electric field.

Which of the lines A, B, C and D shows the correct path?

(a) A (b) B

(c) C (d) D

A B

C

D

E








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12. If the flux of the electric field through a closed surface is zero.

(a) the electric field must be zero every where on the surface.

(b) the electric field may be zero every where on the surface.

(c) the net charge inside the surface must be zero.

(d) the charge in the vicinity of the surface must be zero.

Reasoning Type

This section contains 2 reasoning type questions. Each question contains Statement-1 and

Statement-2. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE is

correct.

Directions: Read the following questions and choose

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation forStatement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation forStatement-1.

(C) Statement-1 is True, Statement-2 is False.(D) Statement-1 is False, Statement-2 is True.

13. Statement-1: Electrostatic electric lines of force can never be closed loops.

Statement-2: The number of electric lines of force originating or terminating on a charge is

proportional to the magnitude of charge.(a) A (b) B (c) C (d) D

14. Statement-1: Electric field at any point on the Gaussian surface is due to charges enclosed

by the Gaussian surface.

Statement-2: The flux of electric field through a closed surface due to all charges is equal

to the flux due to the charges enclosed by the surface.

(a) A (b) B (c) C (d) D








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Paragraph –2

A charged particle is suspended at the centre of two thin concentric spherical charged shells,

made of non conducting material. Figure A shows cross section of the arrangement. Figure

B gives the net flux φ through a Gaussian spherical surface centered on the particle, as a

function of the radius r of the spherical surface. (ε0 = 8.85 × 10 –12

C2/N-m

2)

Shell A

Or A

r B

Charged particle

Shell B

Figure ( A)

r

Figure ( B)

0

6 × 105

φ(N-m2/C)

r A r B

–5 × 105

18. The charge on central particle is

(a) 0.2µ C (b) 2 µC (c) 1.77 µC (d) 3.4 µC

19. The charge on shell A is

(a) 5.31µC (b) –5.31µC (c) –3.54 µC (d) –1.77 µC

20. In which range of the values of r , the electric field intensity is zero?

(a) 0 to r A (b) r A to r B

(c) for r B < r < ∞ (d) for no range of r , electric field intensity is zero.






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SECTION B

Matrix Type

This section contains 2 questions. Each question has four statements (A, B, C and D) givenin Column I and five statements (1, 2, 3, 4 and 5) in Column II. Any given statement inColumn 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 with the statements given in 2 and3, then for that particular question, against statement B, darken the bubbles corresponding to

2 and 3 in the ORS.

1. Consider an imaginary closed cylindrical surface of

length 3 R and radius R. A point charge q is placedat the axis of cylinder at a distance of 2 R from

plane circular face F 2 and at R from plane circular

face F 1.

F 2

q

R

F 1

2 R

R

Column I Column II

(A) Electric flux through face F 1 is1.

+

ε 5

1

22

1

0

q

(B) Electric flux through face F 2 is2.

0ε

q

(C) Electric flux through curved surface of cylinder is3.

−

ε 2

11

20

q

(D) Total flux through the cylinder is4.

−

ε 5

21

20

q

5. Positive






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2. A man of mass M is standing on a platform of mass m1 and holding a string passing over a system of ideal

pulleys. Another mass m2 is hanging as shown.(m2= 20kg, m1 = 10 kg, g = 10 m/s2). Initially the

system is in equilibrium.m1

m2 M

Column –I Column -II

(A) Weight of man is 1. 100 N

(B) Force exerted by man on string to accelerate himself

upwards2. 150 N

(C) Force exerted by man on string to accelerate

himself downwards

3. 500 N

(D) Normal reaction of plank on man in equilibrium 4. 600 N

5. 700 N

SECTION – C

Integer Type

This section contains TWO questions. The answer to each question is a single-digit integer,ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.

1. The intensity of an electric field depends only on the co-ordinates x and y as follows.

( )( )22

ˆˆ

y x

j yi x E

++=

r

, where x and y are in meter and i and j are the unit vectors of the x and

y-axis. The flux associated with sphere of radius 0.5m with the centre at the origin is nπ.

Find the value of n.

2. A point charge q is placed on the apex of a cone of semi-vertex angle 530. The electric flux

through the base of the cone is0εn

q. Find the value of n.






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CHEMISTRYSECTION–A


This section contains 8 multiple choice questions. Each question has 4 choices (a), (b), (c)

and (d), out of which ONLY ONE is correct.

Atomic numbers: H = 1, C = 6, N = 7, O = 8, P = 15, Sn =50, Xe = 54

1. Identify the most stable and least stable resonating structure of nitroethene from the

following.

CH2=CH− NO

(I)

+

O – CH2 –CH− N

+ – + O

O –

(II)

CH2 –CH− N – + + O

O –

(III)

CH2 –CH=N+ + O

–

O –

(IV)

(a) Most stable: (I) (b) Most stable: (I)

Least stable: (III) Least stable: (II)

(c) Most stable: (IV) (d) Most stable: (IV)

Least stable: (III) Least stable: (II)

2. How many isomers, including open chain, cyclic and stereoisomers of C4H8 are possible?

(a) 4 (b) 5

(c) 6 (d) 7

3. Which one of the following is the weakest acid?

(a)

NH3 +

(b)

+ NH3

OCH3

(c)

+ NH3

OCH3

(d)

+ NH3

OCH3






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4. In which of the following compounds the homolytic bond dissociation energy of the bond

between C-atom and labelled H-atom is the lowest?

H

(I)

H

(II)

NO2

H(III)

H3CC6H5

H

(IV)

(a) (II) (b) (IV)

(c) (I) (d) (III)

5. Which one of the following compounds will show geometrical isomerism?

(a) CHClCl (b) CH2

Cl

(c) CCl2

Cl

(d) CHCl

Cl

6. The linear structure is assumed by

(a) SnCl2 (b) NCO−

(c) CS2 (d) (b) and (c) both

7. Which of the following compounds has the maximum s−character in its central atom?

(a) CH4 (b) XeO3

(c) H3PO4 (d) all the above

8. Which of the following options represents

the correct order of dipole moment of the

compounds drawn?

(a) (I) = (II) = (III)

(b) (I) < (II) < (III)

(c) (II) < (III) < (I)

(d) (III) < (II) < (I)

CH3

(I) (II) (III)

NO2

CH3

NO2

CH3

NO2






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Multiple Correct Choice Type

This section contains 4 multiple correct questions. Each question has 4 choices: (a), (b), (c)

and (d) for its answer, out of which ONE OR MORE may be correct.

9. Which of the following will show optical activity?

(a)

CH3

H

H

H OH

H

(b)

CH3

H

H

H

H3C

OH

(c)

CH3

H

H

HO

H

CH3

(d)

CH3

H

HO

H

CH3

HO

10. Which of the following statement(s) is/are true for the given compound?

Me H

Me H

(a) It is a meso compound. (b) It will show geometrical isomerism.

(c) It is a chiral molecule. (d) It has two stereo centres.

11. The percentage of enol form of CH3−C−C−CH3

O O

can be increased by using

(a) high temperature. (b) low temperature.

(c) n-heptane solvent. (d) ethanolic solvent.

12. CH3CH2−C−CH3 can show

O

(a) Tautomerism (b) Functional isomerism(c) Geometrical isomerism (d) Position isomerism








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Paragraph Type

This section contains 2 paragraphs. Based upon the paragraph 3 multiple choice questions

have to be answered. Each question has 4 choices (a), (b), (c) and (d), out of which ONLYONE is correct.

Paragraph –1

A compound with delocalised π-electrons is said to have resonance. The approximate

structure using localized electrons is called a resonance contributor, a resonance structure, or

a contributing resonance structure. The actual structure, drawn using delocalised electrons is

called a resonance hybrid. All resonance contributors do not necessarily contribute equally to

the resonance hybrid. The degree to which each resonance contributor contributes depends onits predicted stability. Because the resonance contributors are not real, their stability can’t be

measured. Therefore, stabilities of resonance contributors have to be predicted on the basis of

molecular features that are found in real molecules.

15. Compare the relative stability of following resonating structures.

CH3 –C− NCH3

CH3 O–H⊕

(1)

CH3 –C− NCH3

CH3

OH

⊕

(2)

CH3 –C=NCH3

CH3

OH⊕

(3)

(a) (1) > (2) > (3) (b) (3) > (2) > (1)

(c) (2) > (1) > (3) (d) (3) > (1) > (2)

16. Which one of the following compound is most basic?

(a) CH3−C− NH2

O

(b) CH3−C− NH2

CH2

(c) CH3−C− NH2

S

(d) CH3−C− NH2

NH






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17. O

The most stable canonical structure of the given molecule is

(a)O⊕ (b)

⊕

O

(c)O⊕ (d)

⊕ O⊕

Paragraph –2

Isomerism is a phenomenon by which two or more compounds have same molecular formula

but different properties. If the difference in properties is due to difference in their structuralformulae, it is called structural isomerism. If the difference in properties is due to difference in

arrangement of atoms or groups in space, it is called stereoisomerism. The different compounds arecalled isomers.

Structural isomers mainly differ in the length of carbon chain (chain isomers) or the position

of substituents/functional groups on same carbon skeleton (position isomers) or functional groups

(functional isomers).Stereoisomers are of two types: conformational (due to rotation about C–C single bond or ring

flipping) and configurational (having different configurations obtained by the switching oftwo groups on a stereocentre). Configurational is further of two types: geometrical

(due to restricted rotation about double bonded atoms or single bonds in cyclic compounds) and

optical (due to presence of chirality or non-superimposability condition).

18. The number of structural isomers possible for a compound with molecular formula C4H8O are

(excluding cyclic isomers)

(a) 8 (b) 9 (c) 10 (d) 11






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19. Which one of the following conformational isomer is the most stable for isopentane

(Me2CHCH2CH3) when rotation is done about C2 –C3 bond?

(a)

H3C

CH3H

H

HH3C

(b)

CH3

H

H

H

H3C

CH3

(c)

H3C

CH3H H

CH3

H(d)

CH3

H

H

H CH3

CH3

20. Which one of the following structure is chiral?

(a)CH3

CH3

CH3 H

H CH3

(b)CH3

H

CH3

H

(c)

Cl

H

CH3

CH3

H

Cl (d)

CH3

CH3

CH3

H

H CH3








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2. Match the Column I with Column II

Column I Column II

(A) CH2 = CH – NH3 +

1. Resonance

(B)+

2. Hyperconjugation

(C)CCl3 3. Inductive effect

(D)OO 4. Aromatic

5. Non aromatic

SECTION – C

Integer Type

This section contains TWO questions. The answer to each question is a single-digit integer,ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.

1. The total number of isomers that are possible with trisubstituted C6H3Br 2Cl is ----------.

2. Give the total number of stereoisomeric pairs i.e., pair of enantiomers and pair of

diastereomers present in the given compound. 2,4-dibromo-3-hydroxy pentane-1,5-dioic acid.






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MATHEMATICS

SECTION – A


This Section contains 8 multiple choice questions. Each question has four choices (a), (b),

(c) and (d) out of which ONLY ONE is correct.

1. If ,109483log42log39log x=+ then x =

(a) 3 (b) 7 (c) 5 (d) 10

2. If ,1> x the least value of 01.0loglog2 10 x x − is

(a) 10 (b) 2 (c) 0.1 (d) 4

3. The number of solutions of 05loglog 57 =++ x x is

(a) 0 (b) 1 (c) 2 (d) more than 2

4. The number of values of x such that ( )

−−2

72log,52log,2log 333

x x are in A.P. is

(a) 0 (b) 1 (c) 2 (d) 3

5. If the difference between the roots of the equation 012 =++ ax x is less than 5 then ∈a

(a) (–3, ∞) (b) (3, ∞) (c) (– ∞, –3) (d) (–3, 3)

6. Let cba ,, be distinct real numbers. If they are in G.P. and ,bxcba =++ then ∈ x (a) (0, ∞) (b) (– ∞, 0) (c) R – (–1, 3) (d) (–1, 3)

7. In a triangle ,2

, π=∠ R PQR if

2tan

P and

2tan

Q are the roots of the equation

02 =++ cbxax , then

(a) cba += (b) acb += (c) bac += (d) cb =

8. If ( ) 0122 =+−+ a xa x has two real roots and 1 lies between the two roots then ∈a

(a) (0, 1) (b) (–1, 0) (c) ),1()0,( ∞∪−∞ (d) ),0()1,( ∞∪−−∞






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Multiple Correct Choice Type

This section contains 4 multiple choice questions. Each question has four choices (a), (b),

(c) and (d) out of which ONE OR MORE may be correct.

9. ( ) ( )1log1log 09.03.0 −<− x x then, x may lie in the interval

(a) (1, 2) (b) (2, 10) (c) (2, 3) (d) (6, 8)

10. If ,254log2 <− x then, x may lie in the interval

(a)

4

5,0 (b)

5

4,0 (c)

5

8,0 (d)

5

8,

5

4

11. If ,11log 2.0 ≥+ x

x then x may lie in the interval

(a) (–1.2, 0) (b) (–1.1, –1) (c) [–1.25, –1.2] (d) (–1.2, –1.1]

12. If ( ( a xax x ++≥++ 4log1log12

5

2

5 for all R x∈ then a may lie in the interval

(a) (2, 3) (b) (1, 2) (c) (0, 3) (d) (2.5, 3]

Reasoning Type

This section contains 2 reasoning type questions. Each question contains Statement-1 and

Statement-2. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE iscorrect.

Directions: Read the following questions and choose

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation forStatement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation forStatement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.






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13. Statement 1 : ( ) 3log2log1log321log ++=++ .

Statement 2 : If ,0>i

a then ( )

∑∑ ==

=

n

i i

n

i i

aa11

loglog .

(a) A (b) B (c) C (d) D

14. Statement 1 : If 10 << x then x

r

r x

−=

∑∞

=

+

1

110 0

2110

log

Statement 2 : If ,10 << x then ∑∞

= −=

0 1

1

r

r

x x .

(a) A (b) B (c) C (d) D

Paragraph Type

This section contains 2 paragraphs. Based upon the paragraph 3 multiple choice

questions have to be answered. Each of these questions has four choices (a), (b), (c) and (d)

out of which ONLY ONE is correct.

Paragraph -1

Let z be a non zero complex number and r z = ( ) π≤θ<π−θ+θ ,sincos i (where z r =

and =θ principal arg( z )). Then ( ) z log is called principal logarithm of z and it is defined by

( ) ( ) θ+= ir z loglog

15. If ( ) iB Ai +=log ( ) R B A ∈,thatsuch then 22 B A + is equal to

(a) 1 (b)2π (c)

4

2π (d)

2

2π

16. Which of the following statement is false

(a) ( )4

52log1log)log(

π+=+−+ iii (b) ( ) ( ) 2log1loglogRe =+−+ ii

(c) ( ) ( )( )iiii +−=+−+ 1log1log)log( (d) ( ) ( )4

2loglog1log π

+=−+− iii






®

17. If ( )2

0,cossinlog π

<θ<θ−θ= i z . Then ( ) z arg is equal to

(a) θ (b) – θ (c) θ−π2 (d) 2

π−

Paragraph – 2

If n is a natural number and [ ]nk 10log= where [.] denotes the greatest integer function,

then the total number of digits in n is 1+k

18. If 477.03log10 = then the number of digits in 403 is

(a) 18 (b) 19

(c) 20 (d) 21

19. If 8451.07log10 = , then the least integral value of n for whichn7 has 11 digits, is

(a) 10 (b) 11

(c) 12 (d) 13

20. If ,3010.02log10 = then the number of digits in405 is

(a) 25 (b) 26

(c) 27 (d) 28






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SECTION – B

Matrix Type

This section contains 2 questions. Each question has four statements (A, B, C and D)given in Column I and five statements (1, 2, 3, 4 and 5) 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 with the statements

given in 2 and 3, then for that particular question, against statement B, darken the bubbles

corresponding to 2 and 3 in the ORS.

1. Match the Column I with Column II.

Column I Column II

(A) 0,0, >>≠ baba such that ( ) ( ) x

ab x

ba ba loglog = then x is equal to 1. 1

(B) ( ) ( ) ( ) )3logcoslog2sinlog 1.0101.0 =+ x x , then xcos is equal to 2. 2

1

(C) If ,26loglog5 =+ y x x y and ,64= xy then60

y x − is equal to 3.

2

3

(D) If cba acb log,log,log are in G.P. and 222 ,, abc are in A.P.

then cabcab

cba

++++ 222

is equal to

4. 1

5. 2






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2. Match the Column I with Column II.

Column I Column II

(A) The family of straight lines ( ) ( ) 011 =−+++− y xb y xa where

a, b are arbitrary constants passes through a fixed point ( )βα, .

Then β+α is equal to

1. 0

(B) A line passes through (2, 2) and perpendicular to the line

33 =+ y x . Then its y-intercept is2. 1

(C) If, ( )βα, be the foot of perpendicular drawn from (0, 5) to the

line 0543 =−− y x , then β−α is equal to3. 2

(D) If (0, 1), (1, 1), (1, 0) be the middle points of sides of a triangleand ( )βα, be its incentre then ( )β−α is equal to

4. 3

4

5. 3

SECTION – C

Integer Type

This section contains TWO questions. The answer to each question is a single-digit integer,

ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.

1. The number of integral value/s of x for which ( ) 05log2

2

5 <−

+

x x

is/are

2. If Rcba ∈,, cba ≠≠ , and the lines ,0=++ cbyax ,0=++ acybx 0=++ baycx are

con current then cba ++ is equal to

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