iitjee paper 1 solutions

8/2/2019 IITJEE PAPER 1 Solutions

1/168

Sri Chaitanya IIT Academy., A.P.

IIT-JEE 2012Paper - 1 along with Key

& Solutions

Admin Off : Plot No : 304, Kasetty Heights.

Ayyappa Society - Madhapur , Pin : 500081


2/168

INSTRUCTIONS

A. General

1. This booklet is your Question Paper. Do not break the seals of this boolket before being instructed to do so by the

invigilators.

2. The question paper CODE is printed on the right hand top corner of this page and on the back page (Page No. 28)

of this booklet.

3. Blank spaces and blank pages are provided in this booklet for your rough work. No additional sheets will be

provided for rough work.4. Blank papers, clipboards , log tables, slide rules, calculators, cameras, cellular phones, pagers and electronic

gadgets are NOT allowed inside the examination hall.

5. Answer to the questions and personal details are to be filled on a two-part carbon-less paper, which is provided

separately. You should not separate these parts. The invigilator will separate them at the end of examination. The

upper sheet is a machine-gradable Ob jective Response Sheet (ORS) which will be taken back up the invigilator.

You will be allowed to take away the bottom sheet at the end of the examination.

6. Using a black ball point pen, darken the bubbles on the upper original sheet. Apply sufficinet pressure so that the

impression is created on the bottom sheet.

7. DO NOT TAMPER WITH / MUTILATE THE ORS OR THE BOOKLET.

8. On breaking the seals of the booklet check that it contains 28 pages and all the 60 questions and corr es pond-

ing answer choices are legible. Read carefully the instructions printed at the beginining of each section.

B. Filling the Right Part of the ORS

9. The ORS has CODES printed on its left and right parts.

10. Check that the same CODE is printed on the ORS and on this boolet. IF IT NOT THEN ASK FOR A CHANGE OF THE

BOOKLET. Sign at the place provided on the ORS affirming that you have verified that all the codes are same.

11. Write your name , Registration Number and the name of examination centre and sign with pen in the boxes provided

on the right part of the ORS. Do not write any of this information anywhere else. Darken the appropriate bubble

UNDER each digit of your Registration Number in such a way that the impression is created on the bottom sheet. Also

darken the paper CODE given on the right side of ORS (R4)

C Question Paper Format

The questions paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consist of three sections.

12. Section I contains 10 multiple choice questions. Each question has four choices. (A), (B), (C) and (D) out of

which ONLY ONE is correct.

13. Section II contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which

ONE or MORE are correct.

14. Section III contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both

inclusive).

D.Marking Scheme

15. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding to the correct

answer ONLY and zero marks if no bubbles are darkened. In all ohter cases, minus one (1) mark will be awarded

in this section.

16. For each question in Section II, you will be awareded 4 marks if you darken ALL the bubble(s) corresponding to the

correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for

incorrect answers in this section.

17. For each question in Section III, you will be awarded 4 marks if you darken the bubble corresponding to the correct

answer ONLY. In all other cases zero (0) will be awarded. No negative marks will be awarded for incorrect answers

in this section.


3/168

Sri Chaitanya IIT Academy PAPER-1 KEY & SOLUTIONS

Sri Chaitanya IIT AcademyAdmin Off : Plot No : 304, Kasetty Heights.Ayyappa Society - Madhapur , Pin : 500081

# 3

Sri Chaitanya IIT Academy

PHYSICSSECTION I

( SINGLE CORRECT CHOICE TYPE )

This section conta ins 10 multi p le choicse questions. Each question has 4 choices (A), (B), (C) and (D) fo r it s

answer, out of which ONLY ONE is correct

1. A small block is connected to one end of massless spring of unstretched length 4.9 m. The

other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless

surface. The block is stretched by 0.2 m and released from rest at t= 0. It then executes

simple harmonic motion with angular frequency /3

rad s

. Simultaneously at t= 0, a

small pebble is projected with speed v from point P at an angle of 450 as shown in the figure.

Point P is at a horizontal distance to 10 m from O. If the pebble hits the block at t= 1s, the

value ofv is (take g = 10 m/s2)

a) 50 /m s b) 51 /m s c) 52 /m s d) 53 /m s

Ans : A

Equation of SHM cosy A t

At 1t 0.2cos (1) 0.2cos 0.13

y m

Block is at a distance 5m

Range of pebble is R =5m

22sin90 50

10

VR V

50 /V m s


4/168



# 4


2. In the determination of Youngs modulus 24MLg

Yld

by using Searles method, a wire of

length L = 2 m and diameter d= 0.5 mm is used. For a load M= 2.5 kg, an extension

l = 0.25 mm in the length of the wire is observed. Quantities dand l are measured using a

screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The num-

ber of divisions on their circular scale is 100. The contributions to the maximum probable

error of the Ymeasurement.

a) due to the errors in the measurements ofdand l are the same

b) due to the error in the measurement ofdis twice that due to the error in the measurement ofl.

c) due to the error in the measurement ofl is twice that due to the error in the measurement ofd.

d) due to the error in the measurement ofdis four times that due to the error in the measure-

ment ofl.Ans :A

2

2 2 4d d

dd v

40.25

l ll

l

3. A small mass m is attached to a massless string whose other end is fixed at P as shown in the

figure. The mass is undergoing circular motion in thexy plane with centre at O and constant

angular speed . If the angular momentum of the system, calculated about O and P are de-

noted by0L

andPL

respectively, then


5/168



# 5


a)0L

andPL

do not vary with time

b)0L

varies with time whilePL

remains constant

c)0L

remains constant whilePL

varies with time

d) 0L

and PL

both vary with time

Ans :C

Torque about O is zero angular momentum will be constant about O. Torque about P is non

zero. Angular momentum about P varies with time.

0L m r v

PL m OP v

direction ofPL

changes with OP and PL OP

4. Youngs double slit experiment is carried out by using green, red and blue light, one color at

a time. The fringe widths recorded are ,G R and B , respectively. Then

a) G B R b) B G R c) R B G d) R G B

Ans :D

D

d

R G B

R G B


6/168



# 6


5. Consider a thin spherical shell of radiusR with its centre at the origin, carrying uniform

positive surface charge density. The variation of the magnitude of the electric field E r

and the electric potential V(r) with the distance rfrom the centre, is best represented by

which graph ?

a) b)

c) d)

Ans : D

From centre to surface E = 0, then1

Er

From centre to surface V = k, then1

V

r

6. A biconvex lens is formed with two thin planoconvex lenses as shown in the figure. Re-

fractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both the curved

surfaces are of the same radius of curvatureR = 14 cm. For this biconvex lens, for an object

distance of 40 cm, the image distance will be

a) 280. 0 cm b) 40.0 cm c) 21. 5 cm d) 13.3 cm


7/168



# 7


Ans :B

1 2

1 1 1

F f f =

1 21 1

R

=

0.5 0.2 0.7 1

14 14 20

20F cm

40R cm

1 1 1 1 1 1 1 1 1 2 1 1

20 40 20 40 40 40F v u v v

40v cm

7. Two large vertical and parallel metal plates having as separation of 1 cm are connected to a

DC voltage source of potential differenceX. A proton is released at rest midway between the

two plates. It is found to move at 450 to the vertical JUST after release. ThenXis nearly

a) 51 10 V b) 71 10 V c) 91 10 V d) 101 10 V

Ans :C

mg Eq

45

mg

EqpVq

d

910mgd

V V approxq

8. Three very large plates of same area are kept parallel and close to each other. They are con-

sidered as ideal black surfaces and have very high thermal conductivity. The first and third

plates are maintained at temperatures 2Tand 3Trespectively. The temperature of the middle

(i.e. second) plate under steady state condition is

a)

1

465

2T

b)

1

497

4T

c)

1

497

2T

d) 1

497 T

Ans : C

4 4 4 41 2 2 3A T T A T T

1

44 44 4

2 2 2

972 3

2T T T T T T


8/168



# 8


9. A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular

speed , as shown in the figure. At time t= 0, a small insect starts from O and moves with

constant speed v with respect to the rod towards the other end. It reaches the end of the rod at

t= T and stops. The angular speed of the system remains throughout. The magnitude of the

torque of the torque

on the system about O, as a function of time is best represented by

which plot ?

a) b)

c) d)

Ans :B

dL d dI

Idt dt dt

constantrod

I

2

red

dI mr

dt = 0 2

drm r

dt

v

r = vt

22 2mr v m v t

t

when the insect reaches the end it stops v = 0

0


9/168



# 9


10. A mixture of 2 moles of helium gas (atomic mass = 4amu) and 1 mole of argon gas (atomic

mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds

helium

argon

rms

rms

v

v

is

a) 0.32 b) 0.45 c) 2.24 d) 3.16

Ans : D

rms

TV

M

1 2

2 1

4010

4

He

Ar

VV M

V V M

SECTION II( MULTIPLE CORRECT ANSWER TYPE)

This section contains 5 multip le choicse q uestions. Each question has 4 choi ces (A), (B), (C) and (D) for its answer,

out of w hich O NE or More a re correct.

11. A small block of mass of 0.1 kg lies on a fixed inclined plane PQ which makes an angle with the horizontal. A horizontal force of 1 N acts on the block through its center of mass as

shown in the figure. The block remains stationary if (take 210 /g m s )

a) 045

b) 045 and a frictional force acts on the block towards P.

c) 045 and a frictional force acts on the block towards Q.

d) 045 and a frictional force acts on the block towards Q.

Ans : A (or) AC


10/168



# 10


1cos sinmg

45

when 45

friction force is upwards

If friction force sufficient block will be in state of rest

12. Consider the motion of a positive point charge in a region where there are simulataneous

uniform electric and magnetic fields0E E j

and0B B j

. At time t= 0 , this charge has

velcoity v

in thex y plane, making an angle with thex axis. Which of the following

option(s) is(are) correct for time t> 0 ?

a) If 00 , the charge moves in a circular path in thex z plane

b) If 00 , the charge undergoes helical motion with constant pitch along they axis.

c) If 010 , the charge undergoes helical motion with its pitch increasing with time, along they axis

d) If 090 , the charge undergoes linear but accelerated motion along theyaxis

Ans :C,D

when 90

0mF

when 10

path is helical and with increasing pitch.


11/168



# 11


13. For the resistance network shown in the figure, choose the correct option(s).

a) The current through PQ is zero b) 1 3I A

c) The potential at S is less than that at Q. d) 2 2I A

Ans : A,B,C,D

1

123

4I

2

123

18I 2A

P QV V

S QalsoV V

14. A person blows into open end of a long pipe. A s a result, a high pressure pulse of air

travels down the pipe.When this pulse reaches the other end of the pipe,

a) a high pressure pulse starts travelling up the pipe, if the other end of the pipe is open

b) a low pressure pulse starts travelling up the pipe, if the other end of the pipe is open

c) a low pressure pulse starts travelling up the pipe, if the other end of the pipe is closed

d) a high pressure pulse starts travelling up the pipe, if the other end of the pipe is closed

Ans : B, D


12/168



# 12


Reflected pressure pulse

Incident pressure pulse

Open end

At open end pressure should not change pressure wave will get phase change as



Closed end

At enclosed end pressure wave will get reflected without phase change

15. A cubical region of side a has its centre at the origin. It encloses three fixed point charges,

q at 0, / 4,0 , 3a q at (0, 0, 0) and q at 0, / 4,0a . Choose the correctoption(s).

a) The net electric flux crossing the plane / 2x a is equal to the net electric flux crossing

the plane / 2x a

b) The net electric flux crossing the plane / 2y a is more than the net electric flux crossing

the plane / 2y a .

c) The net electric flux crossing the entire region is0

q

.

d) The net electric flux crossing the plane / 2z a is equal to the net electric flux crossing

the plane / 2x a


13/168



# 13


Ans : ACD

Net flux passing the plane2

ax and

2

ax is same

Net flux through cube is0

q

Flux through plane2az and

2ax is same

SECTION III( INTEGER ANSWER TYPE)

This section conta ins 5 questions. The answe r to ea ch question is a single digit integer, ranging from 0 to 9

(both inclusive).

16. A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform

mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina

about axes passing through O and P is0

I andP

I , respectively. Both these axes are perpen-

dicular to the plane of the lamina. The ratio0

PII

to the nearest integer is

Ans :3

2 2 2 2 2 2

0

1 12 2

2 2I R R R R R R

4 4382

R R

4 213 13

2 2R MR

2 2 2 21 14 2 4 2 5

2 2

PI M R M R MR M R

2 2 2118 16

2MR MR MR

2 211 3724

2 2MR MR


14/168



# 14


17. A circular wire loop of radius R is placed in the x - y plane centered at the origin O. A square

loop of side a a R having two turns is placed with its center at 3z R along the axis of

the circular wire loop, as shown in figure. The plane of the square loop makes an angle of

45with respect to the z - axis. If the mutual inductance between the loops is given by2

0

/ 22pa

R

,

then the value of p is

Ans : 7

220

3/22

2

2 1

4 23

iRB a

iR R

(n = 2)

22 20 0

9/21

2 22aM R a

18. A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the

figure. Both the cylinder and the cavity are infinetely long. A uniform current density J flows

along the length. If the magnitude of the magnetic field at the point P is given by 012

NaJ ,

then the value of N is


15/168



# 15


Ans : 5

01

2

jaB

2

20

02

2

3 1222

aj

jaB

a a

1 2 0

1 1

2 12B B ja

0 5

12

ja

19. A proton is fired from very far away towards a nucleus with charge 120Q e , where e is the

electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wave-

length (in units of fm) of the proton at its start is:

(take the proton mass, 275 / 3 10 ;pm kg 15/ 4.2 10 . /H e j S c ;

9

0

19 10 / ;

4m F

151 10fm m )

Ans :7

2 29

15

1209 10

10 10 2 p

e P

m

9 2 27

2

15

59 10 120 2 10

3

10 10

e

P

17

15

3 2 10 3 2

10 10

e eP

154.2 10

6

10

h

p


16/168



# 16


20. An infinitely long solid cylinder of radius R has a uniform volume charge density . It has a

spherical cavity of radiusR/2 with its centre on the axis on the cylinder, as shown in the

figure. The magnitude of the electric field at the point P, which is at the distance 2R from the

axis of the cylinder, is given by the expression0

23

16

R

k

. The value ofkis

Ans: 6

3

2

2

4

2 3 8

2 2p

RK

k RE

R R

4 11

3 32pE k R

0

1 114 24

R

0

23

4 24p

RE

24 46

16K


17/168



# 17


CHEMISRYSECTION I


This section conta ins 1 0 multi p le cho icse questions. Each question has 4 choices (A), (B), (C) and (D) for i ts


21. The number of aldol reaction(s) that occurs in the given transformation is

. .

34

conc aq NaOHCH CHO CHO

OH

OHHO

OH

a) 1 b) 2 c) 3 d) 4

Ans : C

3 2

OHCH CHO CH CHO

2 2 2H C H CH CHO O CH CH CHO

O

H

2 2

OHCH CHO HO CH CH CHO H - C - H

OH

'HCHO Cannizaro s

NaOH reactionCH CH

CHO

OH

OHCHO

HO

OH

OH OH OH

OHHO

Number of aldol reaction = 3


18/168



# 18


22. A compound MPX

Phas cubic close packing (ccp) arrangement of X. Its unit cell structure is

shown below. The empirical formula of the compound is

a) MX b) MX2

c) M2X d) M

5X

14

Ans : B

Corner

Face center 16 32

18 1

8

4

X :

Edge centre

Body center 1 1 1

14 1

4

2

M :

4 2X M

4 2X M 2MX

23. The carbonyl functional group (COOH) is present in

a) picric acid b) barbituric acid c) ascorbic acid d) aspirin

Ans : DAcetyle salicylic acid = Asprin

COOH

OCOCH3


19/168



# 19


24. The colour of light absorbed by an aqueous solution of CuSO4is :

a) organe-red b) blue-green c) yellow d) violet

Ans : A

Orange - red is absorbed

Based up on Munshell wagon wheel

V

B

G

O

R

Y

25. The number of optically active products obtained from the complete ozonolysis of the

given compound is :

CH3 - CH = CH - C - CH = CH - C - CH = CH - CH 3

HCH3

H CH3

a) 0 b) 1 c) 2 d) 4

Ans : A

As the ozonolysis products do not have chiral centres, number of optically active products = 0

26. As per IUPAC nomenclautre, the name of the complex 2 3 34 2Co H O NH Cl is

a) Tetraaqudiaminecobalt (III) chloride b) Tetraaquadiamminecobalt (III) chloride

c) Diammineteraaquacobalt (III) chloride d) Diamminetetraaquacobalt (III) chloride

Ans : D

2 3 34 2Co H O NH Cl

Diammineteraaquacobalt (III) chloride

27. Which ordering of compound is according to the decreasing order of the oxidation state ofnitrogen ?

a) 3 4 2, , ,HNO NO NH Cl N b) 3 2 4, , ,HNO NO N NH Cl

c) 3 4 2, , ,HNO NH Cl NO N d) 3 4 2, , ,NO HNO NH Cl N


20/168



# 20


Ans : B

35HNO

2NO

2 0N

43NH Cl

Decreasing order of

O -S =3 2 4, , ,HNO NO N NH Cl

28. For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs. I/V plot is shown

below. The value of the van der Waals constant a (atm. liter2 mol2) is

a) 1.0 b) 4.5 c) 1.5 d) 3.0

Ans : C

2

2

n aP v nb nRT

v

n = 1, b = 0

2q

p v b RTv

apv RT

v

apv RT

v

2 221.6 20.1

1.5 .3 2

y c mx m a slop atm t mole


21/168



# 21


29. In allene 3 4C H , the type(s) of hybridisation of the carbon atoms is (are)

a) sp and sp3 b) sp and sp2 c) only sp2 d) sp2 and sp3

Ans : B

2 2H C C CH

2 2sp sp sp

30. The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [a0is Bohr

radius]

a)

2

2 2

04

h

mab)

2

2 2

016

h

mac)

2

2 2

032

h

mad)

2

2 2

064

h

ma

Ans : C

mvr=2

nh

v=2

nh

mr

for second Bohrs orbit

2r=4 0a

V=04

h

ma

22

2 2 2

016

hV

m a

K.E

22

2 2

0

1

2 32

hmv

ma


22/168



# 22





31. Which of the following molecules, in prue form, is (are) unstable at room temperature ?

a) b) c)

O

d)

O

Ans : BC

cyclobutadiene and cyclopentadien are anti aromatic.

32. Which of the following hydrogen halides react(s) with 3AgNO aq to give a precipitate that

dissolves in 2 2 3Na S O aq ?

a) HCl b) HF c) HBr d) HI

Ans : ACD

3 3AgNO HX AgX HNO aq aq

2 2 3 3 2 3 22AgX Na S O Na Ag S O NaX aq

aqs

AgF is soluble

33. Choose the correct reason(s) for the stability of the lyophobic colloidal particles >

a) Preferential adsorption of ions on their surface from the solution

b) Preferential adsorption of solvent of their surface the solution

c) Attraction between different particles having opposite charges on their surface

d) Potential difference between the fixed layer and the diffused layer of opposite chargesaround the coolidal particles

Ans : AD


23/168



# 23


34. For an ideal gas, consider only P-V work in going from an

i ni ti al state X to the fi nal state Z. T he can be reached by

either of the two paths shown in the figure. Which of the

following choice(s) is (are) correct ? [Take S as change

in entropy and w as work done]

a) x z x y y zS S S b) x z x y y zW w w

c) x y z x yw w d) x y z x yS S

Ans : AC

Based up on the given graph

x y x y y zS S S

x y z x yW W

35. Identify the binary mixtrue(s) that can be separated into individual compounds, by differen-

tial extraction,a s shown in the given scheme.

a)6 5 6 5

C H OH and C H COOH b)6 5 6 5 2

C H COOH and C H CH OH

c) 6 5 2 6 5C H CH OH and C H OH d) 6 5 2 6 5 2C H CH OH and C H CH COOH

Ans : BD

Benzyl alcohol is insoluble in both NaOH and 3NaHCO ,


24/168



# 24




(both inclusive).

36. When the following aldohexose exists in its B-configuration, the total numberC

CH2

CHOH

CHOH

CHO

CH2OH

OHH

of stereoisomrs in its pyranose form is :

Ans : 8

As the configration at C-5 is fixed, (D-configration), then only 4 stero isomers are possible

solution

37. 29.2% (w/w) HCl stock solution has a densityh of 1.25 g mL1. The molecular weight of HCl

is 36.5 g mol1

. The volume (mL) of stock solution required to prepare a 200 mL solution of

0.4 M HCl is :

Ans : 8

Molarity of stock solution =10 d x

GMW

=10 1.25 29.2

36.5

=10M

1 1 2 2

1

1

10 200 0.4

8 ( )

V M V M

V

V ML approx

38. The periodic table consists of 18 groups. An isotope of copper, on bombardment with pro-

tons, undergoes a nuclear reaction yielding element X as shown below. To which

group,element X belongs int he periodic table ?

Ans : 8

63 1 1 4 1 52

29 1 0 2 1 266 2CU H n He H X

26Fe 8 th group


25/168



# 25


39. An organic compound undergoes first-order decomposition. The time taken for its decom-

position to 1/8 and 1/10 of its initial concentration are t1/8

and t1/10

respectively. What is the

Ans : 9

1

8

1

10

2.303log

8

2.303log

10

at

ak

at

ak

1

8

1

10

log8

log10

t

t

1

8

1

10

3log2t

t

1

8

1

10

10 9

t

t

40. The substituents R1and R

2for nine peptides are listed in the table given below. How many of

these peptides are positively charged at pH = 7.0 ?

Ans : 4

At pH below pI(Isoelectric point) Aminoacid exist as Cation. As BasicAminoacids of pH

around 9-8, these are expected to exists as cation of pH=7IV,VI,VIII,IX.


26/168



# 26


MATHEMATICSSECTION I


This section conta ins 10 multip le choice q uestions. Ea ch question has 4 choices (A), (B), (C) and (D) fo r it sa nswer, out of which ON LY O NE is correct

41. Let z be a complex number such that the imaginary part of z is nonzero and and 2 1a z z

is real. Then a connot take the value

a) 1 b)1

3c)

1

2d)

3

4

Ans. D

Let Z x iy 0y

21a z z becomes

2 1a x iy x iy

2 2 1 2 0x y x i xy y a i

Comparing real & imaginary parts

2 2 1x y x a (1)

2 0xy y (2)

From (2) 12

x as 0y

Put value of x in (1)

2

21 1 12 2

y a

21 1

4 2y a

2 30

4y a

3

4a


27/168



# 27


42. If

2 1lim 4

1x

x xax b

x

, then

a) a = 1, b = 4 b) a = 1, b = 4 c) a = 2, b = 3 d) a = 2, b = 3

Ans. B

2 1

lim 41x

x x

ax bx

2 1 1 14

1x

x a x a b blim

x

For existense of limit coefficient of 2 0x

1 a = 0

a = 1

1 1lim 4

1x

x a b b

x

1 4a b

b = 4

43. Let ijP a be a 3 3 matrix and let ijQ b , where 2i j

ij ijb a for 1 , 3i j . If the deter-

minant of P is 2, then the determinant of the matrix Q is

a) 210

b) 211

c) 212

d) 213

Ans. D

as 2i jij ijb a

11 11 12 12 13 134 , 8 , 16b a b a b a

21 2 22 22 23 238 , 16 , 32b a b a b a

31 31 32 32 33 3316 , 32 , 64b a b a b a

11 12 13

21 22 23

31 32 33

2

a a a

A a a a

a a a


28/168



# 28


11 12 13

21 22 23

31 32 33

4 8 16

8 16 32

16 32 64

a a a

B a a a

a a a

11 12 13

21 22 23

31 32 33

4 8 16 2 2 2

4 4 4

a a a

a a a

a a a

11 12 13

21 22 23

31 32 33

4 8 16 2 4

a a a

a a a

a a a

4 8 16 2 4 2

132B

44. The ellipse2 2

1 : 19 4

x yE is inscribed in a rectangle R whose sides are parallel to the coor-

dinates axes. Another ellipse E2

passing through the point (0, 4) circumscribes the rectangle

R. The eccentricity of the ellipse E2

is

a)2

2b)

3

2c)

1

2d)

3

4

Ans. C

Given Ellipse2 2

19 4

x y

As ellipse is bounded by &x a y b

Sides of rectangle are

3 & 2x y

3,2 , 3,2C D

D(0,2)

(3,0)

(0,-2)

(-3,0)

A B

C

3, 2 , 3, 2A B

As new ellipse

Circumscribe the rectangle & passes through (0 ,4).


29/168



# 29


Let new ellipse is2 2

2 21

x y

a b

Passes through 2216

0,4 1 16bb

Passes through 3,2 29 4

1

16a

212a

So, Vertical ellipse2 2

112 16

x y

2 2 21a b e

212 16 1 e

2 12 1116 4

e

1

2e

45. The function : 0,3 1, 29f , defined by 3 22 15 36 1f x x x x is

a) one-one and onto b) onto but not one-one

c) one-one but not onto d) neither one-one nor onto

Ans. B

: 0,3 1, 29f

3 22 15 36 1f x x x x

' 26 30 36f x x x

6 2 3x x

'' 6 2 5f x x

2x is pt of maxima.


30/168



# 30


3x is pt of minima.

& 2 29 0f

3 0f

so curve is

nf is not one one

2 3Min value 0 1f

Max value 2 29f

so nf is Onto.

46. The locus of the mid-point of the chord of contact of tangents drawn from points lying on

the straight line 4 5 20x y to the circle2 2

9x y is

a) 2 220 36 45 0x y x y b) 2 220 36 45 0x y x y

c) 2 236 20 45 0x y x y d) 2 236 20 45 0x y x y

Ans. A

Let 1 1, & ,P h k Q x y

As P lies of4x-5y=20

4 20,

5

hP h

P

A

B

Q

Equation of chord of contact

1 0AB S

4 209

5

hxh y

5 4 20 45xh y h ------------------(1)

Equation of chordAB whose mid point is 1 1,Q x y


31/168



# 31


2 2

1 1 1 1xx yy x y ---------------(2)

Compare (1) & (2)

2 2

1 1 1 1

5 4 20 45h h

x y x y

1 1

2 2 2 2

1 1 1 1

9 45&4 20x yh hx y x y

On eliminating h

1 1

2 2 2 2

1 1 1 1

49 4520

x y

x y x y

2 21 1 1 120 36 45x y x y

Locus is

2 220 36 45 0x y x y

47. The point P is the intersection of the straight line joining the points Q (2, 3, 5) and

R (1, 1, 4) with the plane 5 4 1x y z . If S is the foot of the perpendicular drawn from the

point T (2, 1, 4) to QR, then the length of the line segement PS is

a)1

2b) 2 c) 2 d) 2 2

Ans. A

Equation of1 1 4

1 4 1

x y zQR

Drs of 1,4,1QR

Co-ordinates of 1 , 1 4 , 4P

As P is point of Intersection of QR & given plane, so

5 1 4 1 4 4 1

1

3

T(2,1,4)

Q S R


32/168



# 32


4 1 13, ,

3 3 3P

Let 1 , 1 4 ,4S

Drs of 1, 4 2,TS

TS QR So,

1 1 4 4 2 0

1

2

3 9,1,

2 2S

2 2 24 3 1 13 9

13 2 3 3 2PS

1

2

48. Let 2 cos , 0

0, 0

x xf x x

x

, x IR , then f is

a) differentiable both at x = 0 and at x = 2

b) differentiable at x = 0 but not differentiable at x = 2

c) not differentiable at x = 0 but differentiable at x = 2

d) differentiable neither at x = 0 nor at x = 2

Ans. B

2 cos ; 0

0 ; 0

x xf x

xx

Atx=0


33/168



# 33


2

0 0

cos 00 0lim limh h

hf h f hRHDh h

0lim cos 0h

hh

2

0 0

cos 00 0

lim limh h

hf h f h

LHDh h

0lim cos 0h

hh

Differentiable atx=0

Atx=2

2

0 0

2 cos 4 cos2 2 2 2

lim limh h

hf h f h

RHDh h

2

0 0

2 cos 4 cos2 2 2 2

lim limh h

hf h f h

LHDh h

Not Differentiable atx=2.49. The total number of ways in which 5 balls of different colours can be distributed among 3

persons so that each person gets at least one ball is

a) 75 b) 150 c) 210 d) 243

Ans. B

5 Balls to 3 persons, so that all persons get atleast one ball.

Case-I

Total ways 2 2 1

2 1 2

1 2 2

5 3 12 2 1 3C C C


34/168



# 34


10 3 1 3 90

Case-II

Total ways

5 2 13 1 1 3C C C

11

1

13

3

1

3110 2 1 3 60

Total ways = 90 + 60 = 150.

50. The integral

2

9/ 2

sec

sec tan

xdx

x x equals (for some arbitrary constant K)

a) 2

11/2

1 1 1sec tan11 7sec tan

x x Kx x

b)

2

11/2

1 1 1sec tan

11 7sec tanx x K

x x

c)

2

11/ 2

1 1 1sec tan

11 7sec tanx x K

x x

d)

2

11/2

1 1 1sec tan

11 7sec tanx x K

x x

Ans. C

9

2

sec

sec tan

xdx

x x

Let sec tanx x t -------------(1)

So, 2sec tan secx x x dx dt

secdt

x dxt

------------(2)


35/168



# 35


1sec tanx x

t ----------(3)

From (1) & (3)

1 1sec

2x t

t

So, Integral becomes

9

2

sec .sec

sec tan

x xdx

x x

92

1 1

2dtt

tt

t

2

132

1 1

2

tdt

t

9 13

2 21

2t dt t dt

7 112 21

7 11222

t tK

7 112 2

7 11

t t

K

7 11

22

1 1

11 sec tan7 sec tan x xx x

2

112

1 1 1sec tan

11 7sec tanx x K

x x


36/168



# 36


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

51. A ship is fitted with three engines E1, E

2and E

3. The engines function independently of each

other with respective probabilities1 1

,2 4

and1

4. For the ship to be operational at least two of

its engines must function. Let X denote the event that the ship is operational and let X1, X2and X

3denote respectively the events that the engines E

1, E

2and E

3are functioning. Which of

the following is (are) true ?

a) 13

|16

cP x X b) P [Exactly two engines of the ship are functioning | X]7

8

c) 25

|16

P X X d) 17

|16

P X X

Ans. B,D

A)

1

1 1 112 4 4

1 8

4

cP X X

P X

1 1 3 1 1 1 1

2 22 4 4 2 4 4 4

P X

B)

1 1 3 1 1 1272 4 4 2 4 4

/1 8

4

P Exactly twoengines of theship are functioning X

C)

2

2

2

1 1 3 1 1 12

52 4 4 2 4 4/

1 8

4

P X XP X X

P X

D)

1

1

1

1 1 3 1 1 12

72 4 4 2 4 4/

1 16

2

P X XP X X

P X


37/168



# 37


52. Tangents are drawn to the hyperbola2 2

19 4

x y , parallel to the straight line 2 1x y . The

points of contact of the tangents on the hyperbola are

a)9 1

,2 2 2

b)9 1

,2 2 2

c) 3 3, 2 2 d) 3 3,2 2

Ans. A, B

2 2

19 4

x y

Tangent to the hyperbola is of the form

2y x

2 9 4 4 36 4 32

4 2

Tangent is : 2 4 2 0x y

Point of contact is

2 2 9 1 9 1, , , ,

2 2 2 2 2 2

a l b m

n n

53. Let S be the area of the region enclosed by2

xy e

, y = 0, x = 0, and x = 1. Then

a)1

Se

b)1

1Se

c)1 1

14

Se

d)

1 1 11

2 2S

e

Ans. A, B, D

21 1

0 0

11

x xI e dx e dxe

11I

e

21 1x

e e

2

1 1 1

1

0 0 0

xe dx e dx dx

21

0

1xe dxe


38/168



# 38


54. If y (x) satisfies the differential equation ' tan 2 secy y x x x and y (0) = 0, then

a)

2

4 8 2y

b)

2

'4 18

y

c)

2

3 9y

d)

24 2'

3 3 3 3y

Ans. A,D

tan 2 sec

dy

y x x xdx

tan

. cosdx

I F e x

General solution is cos 2 sec cosy x x x x dx

2x c

2 sec secy x x c x

0,0

0 0 0c c .

2 secy x x

2

24 16

y

2

8 2

2

23 9

y

2 sec tan 2 secdy

x x x x xdx

.

2

1 2 3 2 23 9 3

y

22 4

33 3


39/168



# 39


55. Let , 0,2 be such that

22cos 1 sin sin tan cot cos 12 2

,

tan 2 0 and3

1 sin2

.

Then cannot satisfy

a) 02

b)

4

2 3

c)

4 3

3 2

d)

32

2

Ans. A, C, D

3

tan 2 0, 1 sin2

3 5 1, 0 cos

2 3 2

______ (1)

22cos 1 sin sin tan / 2 cot / 2 cos 1

1

sin cos2

1

sin 12

(from (1))

13 17

6 6

2 7

3 6

(from (1))

cannot satisfied by A, C, D


40/168



# 40



This section contains 5 questions . The answer to each of the questions is a single digit integer, ranging from 0 to9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened.

56. Let p (x) be a real polynomial of least degree which has a local maximum at x = 1 and a local

minimum at x =3. If p (1) = 6 and p (3) = 2, then ' 0p is

Ans. 9

3 2P x ax bx cx d

1 6 6P a b c d

3 2 27 9 3 2P a b c d

1 1 0 3 2 0P a b c

1 3 0 27 6 0P a b c

1, 6, 9a b c

1 23 2P x ax bx c

1 0 9P c

57. If ,a b

and c

are unit vectors satisfying

2 2 2

9a b b c c a

,then 2 5 5a b c

is\

Ans. 3

sol. 1a b c

2 2 29a b b c c a

3

.2

a b b c c a

3 2 . . 0a b b c c a

22 2

2 . . . 0a b c a b b c c a

2

0a b c


41/168



# 41


0a b c (1)

Taking dot product with (1) by , &a b c

then1 1 1

. , . , .2 2 2

a b b c c a

2 5 5 3a b c

58. The value of 32

1 1 1 16 log 4 4 4 ...

3 2 3 2 3 2 3 2

is

Ans. 4

sol.1

43 2

x x

3 2 4x x

squaring on both sides

218 4x x

218 4 0x x

218 9 8 4 0x x x

9 2 1 4 2 1 0x x x .

2 1 9 4 0x x

1 4,

2 9

x

4

9x 0x

Required answer is

2

3/ 2

36 log

2

= 6 2

= 4

59. Let S be the focus of the parabola 2 8y x and let PQ be the common chord of the circle

2 2 2 4 0x y x y and the given parabola. The area of the triangle PQS is

Ans. 4


42/168



# 42


sol.P

Q

S(0, 0)

(2,4)

(2, 0)2

(0,4)

2 8 2 4 2 0x x x x

0,2 0,0 , 2,4x P Q

area of SPQ

=1

2 42

= 4

60. Let :f IR IR be defined as 2 1f x x x . The total number of points at which f attains

either a local maximum or a local minimum is

Ans. 5

sol. 2 1, 1f x x x x

21 , 1 0x x x

21 , 0 1x x x

2 1, 1x x x

' 2 1, 1f x x x

2 1, 1 0x x

0-1 1x

y

1 2 , 0 1x x

1 2 , 1x x

differentiable at1 1

,2 2

x ,

not differentiable at 1, 0, 1

The number of points = 5


43/168

Sri Chaitanya IIT Academy., A.P.

IIT-JEE 2012Paper - 1 along with Key

& Solutions

Admin Off : Plot No : 304, Kasetty Heights.

Ayyappa Society - Madhapur , Pin : 500081


44/168

INSTRUCTIONS

A. General

1. This booklet is your Question Paper. Do not break the seals of this boolket before being instructed to do so by the

invigilators.

2. The question paper CODE is printed on the right hand top corner of this page and on the back page (Page No. 28)

of this booklet.

3. Blank spaces and blank pages are provided in this booklet for your rough work. No additional sheets will be

provided for rough work.4. Blank papers, clipboards , log tables, slide rules, calculators, cameras, cellular phones, pagers and electronic

gadgets are NOT allowed inside the examination hall.

5. Answer to the questions and personal details are to be filled on a two-part carbon-less paper, which is provided

separately. You should not separate these parts. The invigilator will separate them at the end of examination. The

upper sheet is a machine-gradable Ob jective Response Sheet (ORS) which will be taken back up the invigilator.

You will be allowed to take away the bottom sheet at the end of the examination.

6. Using a black ball point pen, darken the bubbles on the upper original sheet. Apply sufficinet pressure so that the

impression is created on the bottom sheet.

7. DO NOT TAMPER WITH / MUTILATE THE ORS OR THE BOOKLET.

8. On breaking the seals of the booklet check that it contains 28 pages and all the 60 questions and corr es pond-

ing answer choices are legible. Read carefully the instructions printed at the beginining of each section.

B. Filling the Right Part of the ORS

9. The ORS has CODES printed on its left and right parts.

10. Check that the same CODE is printed on the ORS and on this boolet. IF IT NOT THEN ASK FOR A CHANGE OF THE

BOOKLET. Sign at the place provided on the ORS affirming that you have verified that all the codes are same.

11. Write your name , Registration Number and the name of examination centre and sign with pen in the boxes provided

on the right part of the ORS. Do not write any of this information anywhere else. Darken the appropriate bubble

UNDER each digit of your Registration Number in such a way that the impression is created on the bottom sheet. Also

darken the paper CODE given on the right side of ORS (R4)

C Question Paper Format

The questions paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consist of three sections.

12. Section I contains 10 multiple choice questions. Each question has four choices. (A), (B), (C) and (D) out of

which ONLY ONE is correct.

13. Section II contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which

ONE or MORE are correct.

14. Section III contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both

inclusive).

D.Marking Scheme

15. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding to the correct

answer ONLY and zero marks if no bubbles are darkened. In all ohter cases, minus one (1) mark will be awarded

in this section.

16. For each question in Section II, you will be awareded 4 marks if you darken ALL the bubble(s) corresponding to the

correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for

incorrect answers in this section.

17. For each question in Section III, you will be awarded 4 marks if you darken the bubble corresponding to the correct

answer ONLY. In all other cases zero (0) will be awarded. No negative marks will be awarded for incorrect answers

in this section.


45/168



# 3


PHYSICSSECTION I


This section conta ins 10 multi p le choicse questions. Each question has 4 choices (A), (B), (C) and (D) fo r it s


1. A small block is connected to one end of massless spring of unstretched length 4.9 m. The

other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless

surface. The block is stretched by 0.2 m and released from rest at t= 0. It then executes

simple harmonic motion with angular frequency /3

rad s

. Simultaneously at t= 0, a

small pebble is projected with speed v from point P at an angle of 450 as shown in the figure.

Point P is at a horizontal distance to 10 m from O. If the pebble hits the block at t= 1s, the

value ofv is (take g = 10 m/s2)

a) 50 /m s b) 51 /m s c) 52 /m s d) 53 /m s

Ans : A

Equation of SHM cosy A t

At 1t 0.2cos (1) 0.2cos 0.13

y m

Block is at a distance 5m

Range of pebble is R =5m

22sin90 50

10

VR V

50 /V m s


46/168



# 4


2. In the determination of Youngs modulus 24MLg

Yld

by using Searles method, a wire of

length L = 2 m and diameter d= 0.5 mm is used. For a load M= 2.5 kg, an extension

l = 0.25 mm in the length of the wire is observed. Quantities dand l are measured using a

screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The num-

ber of divisions on their circular scale is 100. The contributions to the maximum probable

error of the Ymeasurement.

a) due to the errors in the measurements ofdand l are the same

b) due to the error in the measurement ofdis twice that due to the error in the measurement ofl.

c) due to the error in the measurement ofl is twice that due to the error in the measurement ofd.

d) due to the error in the measurement ofdis four times that due to the error in the measure-

ment ofl.Ans :A

2

2 2 4d d

dd v

40.25

l ll

l

3. A small mass m is attached to a massless string whose other end is fixed at P as shown in the

figure. The mass is undergoing circular motion in thexy plane with centre at O and constant

angular speed . If the angular momentum of the system, calculated about O and P are de-

noted by0L

andPL

respectively, then


47/168



# 5


a)0L

andPL

do not vary with time

b)0L

varies with time whilePL

remains constant

c)0L

remains constant whilePL

varies with time

d) 0L

and PL

both vary with time

Ans :C

Torque about O is zero angular momentum will be constant about O. Torque about P is non

zero. Angular momentum about P varies with time.

0L m r v

PL m OP v

direction ofPL

changes with OP and PL OP

4. Youngs double slit experiment is carried out by using green, red and blue light, one color at

a time. The fringe widths recorded are ,G R and B , respectively. Then

a) G B R b) B G R c) R B G d) R G B

Ans :D

D

d

R G B

R G B


48/168



# 6


5. Consider a thin spherical shell of radiusR with its centre at the origin, carrying uniform

positive surface charge density. The variation of the magnitude of the electric field E r

and the electric potential V(r) with the distance rfrom the centre, is best represented by

which graph ?

a) b)

c) d)

Ans : D

From centre to surface E = 0, then1

Er

From centre to surface V = k, then1

V

r

6. A biconvex lens is formed with two thin planoconvex lenses as shown in the figure. Re-

fractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both the curved

surfaces are of the same radius of curvatureR = 14 cm. For this biconvex lens, for an object

distance of 40 cm, the image distance will be

a) 280. 0 cm b) 40.0 cm c) 21. 5 cm d) 13.3 cm


49/168



# 7


Ans :B

1 2

1 1 1

F f f =

1 21 1

R

=

0.5 0.2 0.7 1

14 14 20

20F cm

40R cm

1 1 1 1 1 1 1 1 1 2 1 1

20 40 20 40 40 40F v u v v

40v cm

7. Two large vertical and parallel metal plates having as separation of 1 cm are connected to a

DC voltage source of potential differenceX. A proton is released at rest midway between the

two plates. It is found to move at 450 to the vertical JUST after release. ThenXis nearly

a) 51 10 V b) 71 10 V c) 91 10 V d) 101 10 V

Ans :C

mg Eq

45

mg

EqpVq

d

910mgd

V V approxq

8. Three very large plates of same area are kept parallel and close to each other. They are con-

sidered as ideal black surfaces and have very high thermal conductivity. The first and third

plates are maintained at temperatures 2Tand 3Trespectively. The temperature of the middle

(i.e. second) plate under steady state condition is

a)

1

465

2T

b)

1

497

4T

c)

1

497

2T

d) 1

497 T

Ans : C

4 4 4 41 2 2 3A T T A T T

1

44 44 4

2 2 2

972 3

2T T T T T T


50/168



# 8


9. A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular

speed , as shown in the figure. At time t= 0, a small insect starts from O and moves with

constant speed v with respect to the rod towards the other end. It reaches the end of the rod at

t= T and stops. The angular speed of the system remains throughout. The magnitude of the

torque of the torque

on the system about O, as a function of time is best represented by

which plot ?

a) b)

c) d)

Ans :B

dL d dI

Idt dt dt

constantrod

I

2

red

dI mr

dt = 0 2

drm r

dt

v

r = vt

22 2mr v m v t

t

when the insect reaches the end it stops v = 0

0


51/168



# 9


10. A mixture of 2 moles of helium gas (atomic mass = 4amu) and 1 mole of argon gas (atomic

mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds

helium

argon

rms

rms

v

v

is

a) 0.32 b) 0.45 c) 2.24 d) 3.16

Ans : D

rms

TV

M

1 2

2 1

4010

4

He

Ar

VV M

V V M




11. A small block of mass of 0.1 kg lies on a fixed inclined plane PQ which makes an angle with the horizontal. A horizontal force of 1 N acts on the block through its center of mass as

shown in the figure. The block remains stationary if (take 210 /g m s )

a) 045

b) 045 and a frictional force acts on the block towards P.

c) 045 and a frictional force acts on the block towards Q.

d) 045 and a frictional force acts on the block towards Q.

Ans : A (or) AC


52/168



# 10


1cos sinmg

45

when 45

friction force is upwards

If friction force sufficient block will be in state of rest

12. Consider the motion of a positive point charge in a region where there are simulataneous

uniform electric and magnetic fields0E E j

and0B B j

. At time t= 0 , this charge has

velcoity v

in thex y plane, making an angle with thex axis. Which of the following

option(s) is(are) correct for time t> 0 ?

a) If 00 , the charge moves in a circular path in thex z plane

b) If 00 , the charge undergoes helical motion with constant pitch along they axis.

c) If 010 , the charge undergoes helical motion with its pitch increasing with time, along they axis

d) If 090 , the charge undergoes linear but accelerated motion along theyaxis

Ans :C,D

when 90

0mF

when 10

path is helical and with increasing pitch.


53/168



# 11


13. For the resistance network shown in the figure, choose the correct option(s).

a) The current through PQ is zero b) 1 3I A

c) The potential at S is less than that at Q. d) 2 2I A

Ans : A,B,C,D

1

123

4I

2

123

18I 2A

P QV V

S QalsoV V

14. A person blows into open end of a long pipe. A s a result, a high pressure pulse of air

travels down the pipe.When this pulse reaches the other end of the pipe,

a) a high pressure pulse starts travelling up the pipe, if the other end of the pipe is open

b) a low pressure pulse starts travelling up the pipe, if the other end of the pipe is open

c) a low pressure pulse starts travelling up the pipe, if the other end of the pipe is closed

d) a high pressure pulse starts travelling up the pipe, if the other end of the pipe is closed

Ans : B, D


54/168



# 12




Open end

At open end pressure should not change pressure wave will get phase change as



Closed end

At enclosed end pressure wave will get reflected without phase change

15. A cubical region of side a has its centre at the origin. It encloses three fixed point charges,

q at 0, / 4,0 , 3a q at (0, 0, 0) and q at 0, / 4,0a . Choose the correctoption(s).

a) The net electric flux crossing the plane / 2x a is equal to the net electric flux crossing

the plane / 2x a

b) The net electric flux crossing the plane / 2y a is more than the net electric flux crossing

the plane / 2y a .

c) The net electric flux crossing the entire region is0

q

.

d) The net electric flux crossing the plane / 2z a is equal to the net electric flux crossing

the plane / 2x a


55/168



# 13


Ans : ACD

Net flux passing the plane2

ax and

2

ax is same

Net flux through cube is0

q

Flux through plane2az and

2ax is same



(both inclusive).

16. A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform

mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina

about axes passing through O and P is0

I andP

I , respectively. Both these axes are perpen-

dicular to the plane of the lamina. The ratio0

PII

to the nearest integer is

Ans :3

2 2 2 2 2 2

0

1 12 2

2 2I R R R R R R

4 4382

R R

4 213 13

2 2R MR

2 2 2 21 14 2 4 2 5

2 2

PI M R M R MR M R

2 2 2118 16

2MR MR MR

2 211 3724

2 2MR MR


56/168



# 14


17. A circular wire loop of radius R is placed in the x - y plane centered at the origin O. A square

loop of side a a R having two turns is placed with its center at 3z R along the axis of

the circular wire loop, as shown in figure. The plane of the square loop makes an angle of

45with respect to the z - axis. If the mutual inductance between the loops is given by2

0

/ 22pa

R

,

then the value of p is

Ans : 7

220

3/22

2

2 1

4 23

iRB a

iR R

(n = 2)

22 20 0

9/21

2 22aM R a

18. A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the

figure. Both the cylinder and the cavity are infinetely long. A uniform current density J flows

along the length. If the magnitude of the magnetic field at the point P is given by 012

NaJ ,

then the value of N is


57/168



# 15


Ans : 5

01

2

jaB

2

20

02

2

3 1222

aj

jaB

a a

1 2 0

1 1

2 12B B ja

0 5

12

ja

19. A proton is fired from very far away towards a nucleus with charge 120Q e , where e is the

electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wave-

length (in units of fm) of the proton at its start is:

(take the proton mass, 275 / 3 10 ;pm kg 15/ 4.2 10 . /H e j S c ;

9

0

19 10 / ;

4m F

151 10fm m )

Ans :7

2 29

15

1209 10

10 10 2 p

e P

m

9 2 27

2

15

59 10 120 2 10

3

10 10

e

P

17

15

3 2 10 3 2

10 10

e eP

154.2 10

6

10

h

p


58/168



# 16


20. An infinitely long solid cylinder of radius R has a uniform volume charge density . It has a

spherical cavity of radiusR/2 with its centre on the axis on the cylinder, as shown in the

figure. The magnitude of the electric field at the point P, which is at the distance 2R from the

axis of the cylinder, is given by the expression0

23

16

R

k

. The value ofkis

Ans: 6

3

2

2

4

2 3 8

2 2p

RK

k RE

R R

4 11

3 32pE k R

0

1 114 24

R

0

23

4 24p

RE

24 46

16K


59/168



# 17


CHEMISRYSECTION I


This section conta ins 1 0 multi p le cho icse questions. Each question has 4 choices (A), (B), (C) and (D) for i ts


21. The number of aldol reaction(s) that occurs in the given transformation is

. .

34

conc aq NaOHCH CHO CHO

OH

OHHO

OH

a) 1 b) 2 c) 3 d) 4

Ans : C

3 2

OHCH CHO CH CHO

2 2 2H C H CH CHO O CH CH CHO

O

H

2 2

OHCH CHO HO CH CH CHO H - C - H

OH

'HCHO Cannizaro s

NaOH reactionCH CH

CHO

OH

OHCHO

HO

OH

OH OH OH

OHHO

Number of aldol reaction = 3


60/168



# 18


22. A compound MPX

Phas cubic close packing (ccp) arrangement of X. Its unit cell structure is

shown below. The empirical formula of the compound is

a) MX b) MX2

c) M2X d) M

5X

14

Ans : B

Corner

Face center 16 32

18 1

8

4

X :

Edge centre

Body center 1 1 1

14 1

4

2

M :

4 2X M

4 2X M 2MX

23. The carbonyl functional group (COOH) is present in

a) picric acid b) barbituric acid c) ascorbic acid d) aspirin

Ans : DAcetyle salicylic acid = Asprin

COOH

OCOCH3


61/168



# 19


24. The colour of light absorbed by an aqueous solution of CuSO4is :

a) organe-red b) blue-green c) yellow d) violet

Ans : A

Orange - red is absorbed

Based up on Munshell wagon wheel

V

B

G

O

R

Y

25. The number of optically active products obtained from the complete ozonolysis of the

given compound is :

CH3 - CH = CH - C - CH = CH - C - CH = CH - CH 3

HCH3

H CH3

a) 0 b) 1 c) 2 d) 4

Ans : A

As the ozonolysis products do not have chiral centres, number of optically active products = 0

26. As per IUPAC nomenclautre, the name of the complex 2 3 34 2Co H O NH Cl is

a) Tetraaqudiaminecobalt (III) chloride b) Tetraaquadiamminecobalt (III) chloride

c) Diammineteraaquacobalt (III) chloride d) Diamminetetraaquacobalt (III) chloride

Ans : D

2 3 34 2Co H O NH Cl

Diammineteraaquacobalt (III) chloride

27. Which ordering of compound is according to the decreasing order of the oxidation state ofnitrogen ?

a) 3 4 2, , ,HNO NO NH Cl N b) 3 2 4, , ,HNO NO N NH Cl

c) 3 4 2, , ,HNO NH Cl NO N d) 3 4 2, , ,NO HNO NH Cl N


62/168



# 20


Ans : B

35HNO

2NO

2 0N

43NH Cl

Decreasing order of

O -S =3 2 4, , ,HNO NO N NH Cl

28. For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs. I/V plot is shown

below. The value of the van der Waals constant a (atm. liter2 mol2) is

a) 1.0 b) 4.5 c) 1.5 d) 3.0

Ans : C

2

2

n aP v nb nRT

v

n = 1, b = 0

2q

p v b RTv

apv RT

v

apv RT

v

2 221.6 20.1

1.5 .3 2

y c mx m a slop atm t mole


63/168



# 21


29. In allene 3 4C H , the type(s) of hybridisation of the carbon atoms is (are)

a) sp and sp3 b) sp and sp2 c) only sp2 d) sp2 and sp3

Ans : B

2 2H C C CH

2 2sp sp sp

30. The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [a0is Bohr

radius]

a)

2

2 2

04

h

mab)

2

2 2

016

h

mac)

2

2 2

032

h

mad)

2

2 2

064

h

ma

Ans : C

mvr=2

nh

v=2

nh

mr

for second Bohrs orbit

2r=4 0a

V=04

h

ma

22

2 2 2

016

hV

m a

K.E

22

2 2

0

1

2 32

hmv

ma


64/168



# 22





31. Which of the following molecules, in prue form, is (are) unstable at room temperature ?

a) b) c)

O

d)

O

Ans : BC

cyclobutadiene and cyclopentadien are anti aromatic.

32. Which of the following hydrogen halides react(s) with 3AgNO aq to give a precipitate that

dissolves in 2 2 3Na S O aq ?

a) HCl b) HF c) HBr d) HI

Ans : ACD

3 3AgNO HX AgX HNO aq aq

2 2 3 3 2 3 22AgX Na S O Na Ag S O NaX aq

aqs

AgF is soluble

33. Choose the correct reason(s) for the stability of the lyophobic colloidal particles >

a) Preferential adsorption of ions on their surface from the solution

b) Preferential adsorption of solvent of their surface the solution

c) Attraction between different particles having opposite charges on their surface

d) Potential difference between the fixed layer and the diffused layer of opposite chargesaround the coolidal particles

Ans : AD


65/168



# 23


34. For an ideal gas, consider only P-V work in going from an

i ni ti al state X to the fi nal state Z. T he can be reached by

either of the two paths shown in the figure. Which of the

following choice(s) is (are) correct ? [Take S as change

in entropy and w as work done]

a) x z x y y zS S S b) x z x y y zW w w

c) x y z x yw w d) x y z x yS S

Ans : AC

Based up on the given graph

x y x y y zS S S

x y z x yW W

35. Identify the binary mixtrue(s) that can be separated into individual compounds, by differen-

tial extraction,a s shown in the given scheme.

a)6 5 6 5

C H OH and C H COOH b)6 5 6 5 2

C H COOH and C H CH OH

c) 6 5 2 6 5C H CH OH and C H OH d) 6 5 2 6 5 2C H CH OH and C H CH COOH

Ans : BD

Benzyl alcohol is insoluble in both NaOH and 3NaHCO ,


66/168



# 24




(both inclusive).

36. When the following aldohexose exists in its B-configuration, the total numberC

CH2

CHOH

CHOH

CHO

CH2OH

OHH

of stereoisomrs in its pyranose form is :

Ans : 8

As the configration at C-5 is fixed, (D-configration), then only 4 stero isomers are possible

solution

37. 29.2% (w/w) HCl stock solution has a densityh of 1.25 g mL1. The molecular weight of HCl

is 36.5 g mol1

. The volume (mL) of stock solution required to prepare a 200 mL solution of

0.4 M HCl is :

Ans : 8

Molarity of stock solution =10 d x

GMW

=10 1.25 29.2

36.5

=10M

1 1 2 2

1

1

10 200 0.4

8 ( )

V M V M

V

V ML approx

38. The periodic table consists of 18 groups. An isotope of copper, on bombardment with pro-

tons, undergoes a nuclear reaction yielding element X as shown below. To which

group,element X belongs int he periodic table ?

Ans : 8

63 1 1 4 1 52

29 1 0 2 1 266 2CU H n He H X

26Fe 8 th group


67/168



# 25


39. An organic compound undergoes first-order decomposition. The time taken for its decom-

position to 1/8 and 1/10 of its initial concentration are t1/8

and t1/10

respectively. What is the

Ans : 9

1

8

1

10

2.303log

8

2.303log

10

at

ak

at

ak

1

8

1

10

log8

log10

t

t

1

8

1

10

3log2t

t

1

8

1

10

10 9

t

t

40. The substituents R1and R

2for nine peptides are listed in the table given below. How many of

these peptides are positively charged at pH = 7.0 ?

Ans : 4

At pH below pI(Isoelectric point) Aminoacid exist as Cation. As BasicAminoacids of pH

around 9-8, these are expected to exists as cation of pH=7IV,VI,VIII,IX.


68/168



# 26


MATHEMATICSSECTION I


This section conta ins 10 multip le choice q uestions. Ea ch question has 4 choices (A), (B), (C) and (D) fo r it sa nswer, out of which ON LY O NE is correct

41. Let z be a complex number such that the imaginary part of z is nonzero and and 2 1a z z

is real. Then a connot take the value

a) 1 b)1

3c)

1

2d)

3

4

Ans. D

Let Z x iy 0y

21a z z becomes

2 1a x iy x iy

2 2 1 2 0x y x i xy y a i

Comparing real & imaginary parts

2 2 1x y x a (1)

2 0xy y (2)

From (2) 12

x as 0y

Put value of x in (1)

2

21 1 12 2

y a

21 1

4 2y a

2 30

4y a

3

4a


69/168



# 27


42. If

2 1lim 4

1x

x xax b

x

, then

a) a = 1, b = 4 b) a = 1, b = 4 c) a = 2, b = 3 d) a = 2, b = 3

Ans. B

2 1

lim 41x

x x

ax bx

2 1 1 14

1x

x a x a b blim

x

For existense of limit coefficient of 2 0x

1 a = 0

a = 1

1 1lim 4

1x

x a b b

x

1 4a b

b = 4

43. Let ijP a be a 3 3 matrix and let ijQ b , where 2i j

ij ijb a for 1 , 3i j . If the deter-

minant of P is 2, then the determinant of the matrix Q is

a) 210

b) 211

c) 212

d) 213

Ans. D

as 2i jij ijb a

11 11 12 12 13 134 , 8 , 16b a b a b a

21 2 22 22 23 238 , 16 , 32b a b a b a

31 31 32 32 33 3316 , 32 , 64b a b a b a

11 12 13

21 22 23

31 32 33

2

a a a

A a a a

a a a


70/168



# 28


11 12 13

21 22 23

31 32 33

4 8 16

8 16 32

16 32 64

a a a

B a a a

a a a

11 12 13

21 22 23

31 32 33

4 8 16 2 2 2

4 4 4

a a a

a a a

a a a

11 12 13

21 22 23

31 32 33

4 8 16 2 4

a a a

a a a

a a a

4 8 16 2 4 2

132B

44. The ellipse2 2

1 : 19 4

x yE is inscribed in a rectangle R whose sides are parallel to the coor-

dinates axes. Another ellipse E2

passing through the point (0, 4) circumscribes the rectangle

R. The eccentricity of the ellipse E2

is

a)2

2b)

3

2c)

1

2d)

3

4

Ans. C

Given Ellipse2 2

19 4

x y

As ellipse is bounded by &x a y b

Sides of rectangle are

3 & 2x y

3,2 , 3,2C D

D(0,2)

(3,0)

(0,-2)

(-3,0)

A B

C

3, 2 , 3, 2A B

As new ellipse

Circumscribe the rectangle & passes through (0 ,4).


71/168



# 29


Let new ellipse is2 2

2 21

x y

a b

Passes through 2216

0,4 1 16bb

Passes through 3,2 29 4

1

16a

212a

So, Vertical ellipse2 2

112 16

x y

2 2 21a b e

212 16 1 e

2 12 1116 4

e

1

2e

45. The function : 0,3 1, 29f , defined by 3 22 15 36 1f x x x x is

a) one-one and onto b) onto but not one-one

c) one-one but not onto d) neither one-one nor onto

Ans. B

: 0,3 1, 29f

3 22 15 36 1f x x x x

' 26 30 36f x x x

6 2 3x x

'' 6 2 5f x x

2x is pt of maxima.


72/168



# 30


3x is pt of minima.

& 2 29 0f

3 0f

so curve is

nf is not one one

2 3Min value 0 1f

Max value 2 29f

so nf is Onto.

46. The locus of the mid-point of the chord of contact of tangents drawn from points lying on

the straight line 4 5 20x y to the circle2 2

9x y is

a) 2 220 36 45 0x y x y b) 2 220 36 45 0x y x y

c) 2 236 20 45 0x y x y d) 2 236 20 45 0x y x y

Ans. A

Let 1 1, & ,P h k Q x y

As P lies of4x-5y=20

4 20,

5

hP h

P

A

B

Q

Equat

iitjee paper 1 solutions

Documents