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IIT-JEE CLASSROOM CENTRE

WEEKLY NORTH INDIA COMPETITIVE EXAMINATION-2(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.Each of these questions has 4 choices: (a), (b), (c) & (d), out of which one or more than onechoice is correct.

9. Each subject of Section-B contains 2 questions of matrix match type. Each question hasfour statements (A, B, C and D) given in Column I and five statements (1, 2, 3, 4 and 5) inColumn II. 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 youhave darkened 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: ………………………………


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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. Four charges +2q, –2q, –3q and +3q are kept on the cornersof a square of side a. The net electric field at the centre O is,

(a) zero (b)2

04

22

a

q

πε

(c)2

04

2

a

q

πε

(d)2

04

210

a

q

πε

O

+2q – 2q

+3q – 3qa

2. Position of a particle moving on a straight line is given as 2123 ++−= t t x . Here x is inmeter and t is in second. Distance travelled by particle in starting 3 seconds is

(a) 9 m (b) 11 m (c) 23 m (d) 18 m

3. Seven point charges each of charge q is placed at the seven corners of a cube of side a (onecorner is empty). Find the magnitude of electric field at centre of cube.

(a) zero (b)2

04

1

a

q

πε (c)

2

03

1

a

q

πε (d)

2

0

7

4

1

a

q

πε

4. A positive charge particle q is placed at rest at the origin on smooth surface. The electric

field on the surface at a point is given as i x E ˆ=r

, here x is x-coordinate of the point and E isin N/C. Then

(a) particle will move along positive x-axis with increasing speed.

(b) particle will move along negative x-axis with decreasing speed.

(c) particle will oscillate about origin.

(d) particle will not move.


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5. If a positively charged pendulum is oscillating in a uniformelectric field as shown in figure. Its time period of SHM ascompared to that when it was uncharged. (mg > qE )

(a) will increase(b) will decrease(c) will not change(d) will first increase then decrease

E

6. The figure shows two point charges +2Q and – Q. Considerthree regions I, II and III, for the points on the line joining twocharges. Which of the following statements is correct?

(a) Region III has a local maxima of electric field

(b) Region I has a local minima of electric field

(c) Equilibrium position for a test charge lies in region I

+2Q

III II I

–Qr

(d) Equilibrium position for a test charge lies in region III

7. In the given figure, two semicircular wires of radius R areconnected which are in x- y and x- z plane respectively. Charge q0 isdistributed uniformly over it on each semicircular wire, then themagnitude of electric field intensity at the origin is

(a)2

0

0

R

q

πε (b)

20

204

R

q

πε

(c) 20

202 R

q

επ (d) 200

2 R

q

πε

++++

++++

+++++

++

x

z

y

R

R

8. A particle is projected with a velocity u, at an angle α, with the horizontal. Time at whichits vertical component of velocity becomes half of its net speed at the highest point will be

(a) g

u

2 (b) ( )α−α cossin

2 g

u

(c) ( )α−α sincos22 g

u (d) ( )α−α cossin2

2 g

u


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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. A point charge q is placed at origin. Let A E r

, B E r

and C E r

be the electric field at three points

A(1,2,3), B (1, 1, -1) and C (2, 2, 2) due to charge q. Then

(a) B A E E rr

⊥ (b) B A E E rr

|| (c) ||4|| C B E E rr

= (d) ||16|| C B E E rr

=

10. A positively charged thin metal ring of radius R is fixed in the xy plane, with its centre at theorigin O. A negatively charged particle P is released from rest at the pint (0, 0, z ), where z >0. Then the motion of P is

(a) periodic, for all values of z satisfying ∞


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12. A non conducting wheel having mass m has charges+q and – q on diametrically opposite points asshown in figure. It remains in equilibrium on a

rough non conducting incline plane in the presenceof uniform electric field of intensity E in verticallyupward direction. Neglecting the mass of charges incomparison to mass of wheel. Which of thefollowing statements is/are true?

–q

+q

θ

E

(a) The value of E isq

mg

2

(b) The value of E isq

mg

(c) The friction force on the wheel is mg sinθ

(d) The direction of friction force on the wheel is up the plane.

Reasoning Type

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

13. Statement-1: When charges are shared between two bodies, there occurs no loss of charge, but there does occur a loss of energy.

Statement-2: In case of sharing of charges, conservation of total energy fails.

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


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14. Statement-1: Horizontal range is same for angle of projection θ and (90 – θ)Statement-2: Horizontal range is independent of angle of projection.(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 question has 4 choices (a), (b), (c) and (d), out of which ONLYONE is correct.

Paragraph –1

A uniformly charged ring carrying charge +Q and of radius R is placed in y - z plane with its centre at origin. A long wire with

uniform linear charge density (– λ) is placed along y-axis, suchthat wire and ring does not touch each other. A particle withcharge +q and mass m is placed on x-axis, at a distance x fromthe origin as shown in figure. For x = 2 R the net force on the particle is zero. (Neglect gravity)

x x+q,m R

y

– λ

+Q

15. The value of R

Q

λ5

2is

(a) 3 (b) 5 (c) 4 (d) 18

16. For ,22 R x = the acceleration of the particle is

πε=

04

1k .

(a)mR

qk λ (b)

−

λλ

23

12

m

qk (c)

−

λ

23

82

mR

qk (d) none of these


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17. If another long wire with linear charge density +λ is also placed along z -axis withouttouching ring and the other infinite wire. The variation of net electric field intensity (due totwo long wires and ring) with x-coordinate on the points on x-axis (for 0 ≤ x ≤ ∞) is (takingfield intensity to be positive if it is along positive x-axis and vice-versa).

y

x

(a) E

x

E

x (b)

y

x

E

x (c)

x

y

(d) none of these

Paragraph –2

Due to charge on a large plate, a constant electric field of intensity E exist everywhere. Anobject of mass m and charge q is projected from the plate with velocity u at an angle θ withthe plate. It follows the path as shown with maximum height h above plate and range R (Neglect gravity).

+ + + + + + +

u

θ

R

h

E

E


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18. Which of the following is true concerning all objects that follow the path shown when projected with velocity u at an angle θ.(a) They must have same mass

(b) They must have same charge(c) They must have the same mass and the same charge

(d) Their mass to charge ratio must be same

19. If E = 100 N/C, m = 1 kg and q = –1C, u = 10 m/s and θ = 30o, then value of h and R arerespectively

(a)8

1m,

2

1m (b)

4

1m,

2

3m (c)

8

1m,

2

3m (d)

4

1m,

2

1m

20. Statement – 1: On decreasing q by a factor of 2 whileincreasing m by a factor of 2, the value of R increases.Statement – 2: If q is positive the particle will followthe path shown. Then

(a) statement-1 is true and statement-2 is false

(b) statement-1 is false and statement-2 is true + + + + + + +

(c) both are false(d) both are true


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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 to2 and 3 in the ORS.

1. The position ( x) of a particle varies with time as x = t 3 – 3t 2, where t is time in second. Match Column I with Column II.

Column I Column II

(A) Position of particle is zero at 1. t = 3 s

(B) Velocity of particle is zero at 2. t = 2 s

(C) Magnitude of acceleration of particle is non zero at 3. t = 0 s

(D) Magnitude of displacement is equal to distancetraveled by the particle at

4. t = 1 s

5. t = 4 s


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2. In the figure shown two identical small charged balls

having mass m and charge ‘q’ are suspended with the

help of two light inextensible silk strings each of length‘l ’. At equilibrium the angular separation between thestring is ‘θ’.

T

θ

m,q

T

m,q

Column I Column II

(A) If θ is very small then charge ‘q’ is proportional to 1. 2/3θ

(B) If T is tension in the string and θ is very smallthen (T – mg ) is proportional to

2. l

(C) If the system is taken in satellite then tension T is proportional to

3. π

(D) Angular separation between the charges (atequilibrium) in the satellite is 4.

2−

l

5.2/1

m

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. An infinite number of charges each equal to q are placed along the x-axis at x = 1, x = 2,

x = 4, x = 8…. and so on. The electric field at point x = 0 is 0πεnq

. Find the value of n.

2. Linear charge density on a rod is varying as

l

x0λ=λ , here λ0 is constant, l is length of rod and x

is distance from point P as shown in figure. Electric

field at point P on the axis of rod is ( )nlnl 0

0

8πελ

.

Find the value of n.

P

x

l

x0λ=λ

l l


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CHEMISTRYSECTION–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. Which one of the following is most stable free radical?

(a) (b) (c)

CH3

(d)

2. In benzyne intermediate, the triple bond consists of:

(a) one sp–sp sigma bond and two p–p pi bonds.(b) one sp2 –sp2 sigma bond and two p–p pi bonds.(c) two sp–sp sigma bonds and one p–p pi bond.(d) one sp2 –sp2 sigma bond, one sp2 –sp2 pi bond and one p–p pi bond.

3. In which of the following pair of carbocations, the first carbocation is more stable than thesecond?

(i) 22 HCCHCH

+

−= and 222 HC – CHCHCH+

−=

(ii) 23 HC NHCH+

−− and OHHC 2 −+

(iii) 223 HCCHOCH+

−−− and 23 HCOCH+

−−

(iv) 3223 CHCHCHHCCH −− +

and 3223 CHCHHCCHCH −− +

(a) (i), (ii) and (iii) (b) (i), (ii) and (iv)(c) (ii) and (iii) (d) (iii) and (iv)


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4. In which of the following compounds, allylic hydrogen is most acidic?

(a) CH3 –CH=CH2 (b) CH2=CH–CH2 –CH=CH2

(c)HH

(d)HH

5. The correct order of acidic strength is

(I)

COOH

NO2

(II)

COOH

NO2

CH3H3C(III)

COOH

NO2

CH3H3C

(a) (III) > (II) > (I)

(b) (II) > (III) > (I)(c) (I) > (II) > (III) (d) (II) > (I) > (III)

6. Which of the following intermediate is/are aromatic nature?

(a)

(Triplet)

(b)

(Singlet)

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

7. A. B. C.

Compare carbon-carbon bond rotation across A, B, and C

(a) A > B > C

(b) A > C > B(c) B > A > C (d) B > C > A


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8. In which of the following the first compound is more acidic than second?

(a)

OH

CH3

OH

CH3 (b)

OH

NO2

OH

Me

Me Me

Me

NO2

(c)

OH

OH

OH

OH

(d)

OH

OH

OH

NO2

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 compound(s) contain same number of linearly arranged carbon atomsin their respective molecules?

(a) H2C=CH–C≡CH (b) HC≡C–C≡CH(c) H2C=CH–CH=CH2 (d) CH3 –C≡C–CH3

10. Which of the following compound(s) have delocalized π –electrons?

(a)

.H

(b) CH3CH2 NHCH=CH–CH3

(c) CH3−C−CH2 –CH=CH2

CH3

⊕ (d) CH3CH=CH–CH2 –OCH3


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11. Which of the following species will be aromatic?

(a)

....

(b).

H

(c)....

(d)

12. Which of the following compounds exhibit tautomerism?

(a) CH=CHOH (b) OO

(c) O

O

(d) O

O

Reasoning Type





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

13. Statement 1 : cis-2-butene has higher melting point and trans-2-butene has higher boiling point.

Statement 2 : Geometrical isomers differ in their physical properties.

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


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17. What functional group classes are present in it?

N–C

CH3

NHN

OH5C2

H5C2

(a) 3° amide.(b) 2° and 3° amine.(c) aromatic ring and alkene (C=C bonds).(d) all of these.

Paragraph –2

The observed wavelengths in the line spectrum of hydrogen atom were first expressed interms of a series by Johan Jakob Balmer, a Swiss teacher.

Balmer's empirical formula is

−=λ 22H n

1

2

1R

1; n = 3, 4, 5, ..........

R H = 109678 cm –1 is the Rydberg constant.

Niel Bohr derived the expression theoretically in 1913. The formula is generalised to anyone electron atom/ion.

18. Calculate the longest wavelength in Å (1 Å = 10 –10 m) in the Balmer series of singly ionizedhelium He+. Select the correct answer. Ignore the nuclear motion in your calculation.

(a) 2651 Å (b) 1641.1 Å(c) 6569 Å (d) 3249 Å

19. How many lines in the spectrum will be observed when electron returns from 7th shell to 2ndshell of a Bohr atom?(a) 13 (b) 14(c) 15 (d) 16

20. In which region of electromagnetic spectrum does the Balmer series of Li2+ lie?(a) uv (b) visible(c) infrared (d) far infrared


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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 to2 and 3 in the ORS.

1.

Column I Column II

(A) Aromatic 1. CH3

N+

CH3

(B) Non-aromatic 2. B–H

(C) Anti aromatic 3.

4. N

(D) Non planar ring

5. +

+


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2.

Column – I Column –II

(A) O can exhibit1. Position Isomerism

(B) CH

CO

O

can exhibit

2. Chain Isomerism

(C) NO2 can exhibit

3. Metamerism

(D) CN can exhibit

4. Tautomerism

5. Functional

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. Determine the number of sp hybridized atoms in cyanogen, (CN)2.

2. Tropylium carbocation is aromatic in nature. How many resonating structures are

possible for this ion?


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MATHEMATICS

SECTION – A

Single Correct Choice Type

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. The number of real roots of the equation 0)3()2()1( 222 =−+−+− x x x is

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

2. If ),,(02 Rcbacbxax ∈=++ has two non-real roots and ,0


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7. The equation 022 =+− mmx x has two real roots if

(a) 10 ++ cb

12. The points which satisfy 23 +> x y , y > x, y > 0 is/ are

(a) (2, 1) (b) (–1, 0) (c) (1, 6) (d) (0, 5)


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Reasoning Type





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

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

13. Statement-1: If the equation 0168 234 =+++− cxbx x x (b, c ∈ R) has all positive realroots, then they are equal.

Statement-2: If 4321 ,,, αααα are positive real numbers, then ≥α+α+α+α

44321

4

1

4321 )( αααα and the equality occurs only if 4321 α=α=α=α .

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

14. Statement-1: 0)1()1( 22422 =−++−++ m xmm xmm )( Rm∈ has non-real roots.

Statement-2: Rmmm ∈∀>++ 012 .

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


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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

Consider the equation .012 22 =−+− mmx x

15. If both the roots of the equation lie between –2 and 4, then

(a) )4,0(∈m (b) )3,1(−∈m (c) )0,(−∞∈m (d) ),2( ∞∈m

16. If both the roots are of opposite signs, then

(a) )1,1(−∈m (b) )2,0(∈m (c) )0,2(−∈m (d) Rm∈

17. If both the roots of the equation are less than 5, then

(a) )5,0(∈m (b) )10,5(∈m (c) )6,1(∈m (d) )4,(−∞∈m

Paragraph – 2

Consider the equation .02 224 =−+− aaax x

18. The equation has four real distinct roots if(a) 0>a (b) 0a (d) 10 a (b) 0a (d) 10 a (b) 0a (d) 10


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SECTION – B

Matrix TypeThis 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 givenstatement 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 statementsgiven in 2 and 3, then for that particular question, against statement B, darken the bubblescorresponding to 2 and 3 in the ORS.

1.

Column I Column II

(A) Minimum value of )0(11

)(2

2 >+++= x x x

x x x f is 1. 1

(B) Minimum value of 84)( 2 +−= x x x f is 2. 2

(C) Minimum value of 413)( 2 ++−= x x x f is 3. 3

(D) If z y x ,, are real, then the minimum value of

4222222 ++++++ z y x z y x is

4. 4

5. none of these


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2.

Column I Column II

(A) If βα, are the roots of 0164 2 =+− c x x such that,321

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