Aits Ft II (Paper 1) Pcm(Ques) Jee(Advanced)

7/25/2019 Aits Ft II (Paper 1) Pcm(Ques) Jee(Advanced)

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FIITJEE L t d . , F I I T JEE Hou se, 2 9 -A , Ka l u Sa r a i , Sa r va p r i y a V i h a r , New De l h i -1 1 00 16 , Ph 461 06000 , 2 65694 93 , Fa x 265139 42websi t e : w ww . f i i t j e e .c om

FULL TEST II

Paper 1

Time Allotted: 3 Hours Maximum Marks: 243

Please read the instruct ions carefu l ly . You are a l lo t ted 5 minutesspecif ica l ly for th is purpose.

You are not a l lowed to leave the Examinat ion Hal l before the end ofthe test.

INSTRUCTIONS

A. General Instruct ions

1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.2. This question paper contains Three Parts.3. Part-Iis Physics, Part-IIis Chemistry and Part-III is Mathematics.4. Each part is further divided into three sections: Section-A, Section-B & Section-C

5. Rough spaces are provided for rough work inside the question paper. No additional sheets will beprovided for rough work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronicdevices, in any form, are not allowed.

B. Fill ing o f OMR Sheet1. Ensure matching of OMR sheet with the Question paper before you start marking your answers

on OMR sheet.2. On the OMR sheet, darken the appropriate bubble with black pen for each character of your

Enrolment No. and write your Name, Test Centre and other details at the designated places.3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts.1. Section A (01 06) contains 6 multiple choice questions which have only one correct answer.

Each question carries +3 marks for correct answer and 1 mar k for wrong answer.

Section A (07 09) contains 3 multiple choice questions which have one or more than onecorrect answer. Each question carries +4 marks for correct answer. There is no negative

marking.

Section-A (10 14) contains 2 paragraphs. Based upon paragraph, 2 and 3 multiple choice

questions have to be answered. Each question has only one correct answer and carries+3 marks for correct answer and 1 mark for wrong answer.

2. Section B (01 02) contains 2 Matrix Match Type questions containing statements given in 2

columns. Statements in the first column have to be matched with statements in the secondcolumn. Each question carries +8 marks for all correct answer. For each correct row +2 markswill be awarded. There may be one or more than one correct matching. No marks will be given forany wrong matching in any question. There is no negative marking.

3. Section -C (01 05) contains 5 Numerical based questions with answers as numerical value from0 to 9and each question carries +4 marks for correct answer. There is no negative marking.

Name of the Candidate

Enrolment No.

ALL

INDIA

TEST

SERIES

FIITJEE JEE (Advanced)-2016

FIITJEE

StudentsFromC

lassroom/

IntegratedSchoolPrograms

havesecuredto2Zonal,6State&

18CityToppe

rRanks.

33inTop100,

78inTop200and205inTop500AllIndia

RanksbaggedbyFIITJEEStudentsfromA

llProgramshavequalifiedin

JEE(Advanced),2015.


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AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/16

FIITJEE L t d . , F I I T JEE Hou se, 2 9 -A , Ka l u Sa r a i , Sa r va p r i y a V i h a r , New De l h i -1 1 00 16 , Ph 461 06000 , 2 65694 93 , Fa x 265139 42websi t e : w ww . f i i t j e e .c om

2

Useful Data

PHYSICS

Acceleration due to gravity g = 10 m/s2

Planck constant h = 6.6 1034J-s

Charge of electron e = 1.6 1019 C

Mass of electron me= 9.1 1031kg

Permittivity of free space 0= 8.85 1012 C

2/N-m

2

Density of water water= 103kg/m

3

Atmospheric pressure Pa= 105N/m

2

Gas constant R = 8.314 J K1mol

1

CHEMISTRY

Gas Constant R = 8.314 J K1mol

1

= 0.0821 Lit atm K1mol

1

= 1.987 2 Cal K1 mol1Avogadro's Number Na = 6.023 10

23

Plancks constant h = 6.625 1034

Js= 6.625 1027ergs1 Faraday = 96500 coulomb1 calorie = 4.2 joule

1 amu = 1.66 1027 kg1 eV = 1.6 1019J

Atomic No: H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8,N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16,Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25,Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33,Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56,Pb=82, U=92.

Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16,F=19, Na=23, Mg=24, Al = 27, Si=28, P=31, S=32,Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59,Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108,Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238.


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FIITJEE L t d . , F I I T JEE Hou se, 2 9 -A , Ka l u Sa r a i , Sa r va p r i y a V i h a r , New De l h i -1 1 00 16 , Ph 461 06000 , 2 65694 93 , Fa x 265139 42

websi t e : w ww . f i i t j e e .c om

3

PPhhyyssiiccss PART I

SECTION A

Straight Objective Type

This section contains 6 multiple choice questions numbered 1 to 6. Each question has 4 choices (A), (B),(C) and (D), out of which ONLY ONEis correct

1. Which of the following is the most accurate instrument for measuring length?(A) vernier calipers having 20 divisions on the sliding scale which coincide with 19 divisions on

the main millimeter scale(B) a screw gauge having pitch 1 mm and 50 divisions on the circular scale(C) a vernier scale of least count 0.01 mm(D) a screw gauge of least count 0.001 mm

2. A block of mass m is placed on a wedge of mass 2m which rests on a roughhorizontal surface. There is no friction between the block and the wedge. Theminimum coefficient of friction between the wedge and the ground so that the

wedge does not move is 450

2mm

(A) 0.167 (B) 0.20(C) 0.23 (D) 0.33

3. A small ball thrown with an initial velocity u directed at an angle = 37 above the horizontalcollides inelastically (e = 1/4) with a vertical massive wall moving with a uniform horizontalvelocity u/5 towards ball. After collision with the wall, the ball returns to the point from where itwas thrown. Neglect friction between ball and wall. The time tfrom beginning of motion of the balltill the moment of its impact with the wall is (tan37 = 3/4)

(A)3

5

u

g (B)

18

25

u

g

(C) 54125

ug

(D) 5425

ug

Space for Rough work


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4

4. A cube of side l and mass Mis placed on rough horizontal surface and the friction is sufficient sothat it will not move, if a constant force F= Mgis applied horizontally l/4 above the surface. Thenthe torque due to normal force about center of the cube is equal to

(A)2

Mgl (B)

4

Mgl

(C) 8

Mgl

(D) zero

5. A particle of charge qand mass m is projected with a velocity v0towards a circular region having uniform magnetic field Bperpendicular and into the plane of paper from point Pas shownin the figure. R is the radius and O is the centre of the circular

region. If the line OP makes an angle with the direction of v0then the value of v0so that particle passes through Ois

v0q,m

Magnetic field

P

O

(A)sin

qBR

m (B)

2 sin

qBR

m

(C)2

sin

qBR

m

(D)3

2 sin

qBR

m

6. A ray of light from a liquid 3 is incident on a system of tworight angled prism of refractive indices 3 and 2 as shown.The ray suffers zero deviation when emerges into air from CD.The angle of incidence iis

D

CB

A

air2

3

Liquidi

(A) 450 (B) 35

0

(C) 200 (D) 10

0



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5

Multiple Correct Choice Type

This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONEOR MORE is/are correct

7. Two blocksAand Beach of mass1

2

kg is connected

by a massless inextensible string and kept onhorizontal surface. Coefficient of friction between block

and surface is shown in figure. A force F kt (wherek= 1 N/s and tis time in second) applied on A.Then(g = 10 m/s

2)

B AF=kt

k= 0.2 k= 0.2

s= 0.2 s= 0.4

(A) work done by friction force on block Bis zero in time interval t= 0 to t= 3s.(B) work done by friction force on blockAis zero in time interval t= 0 to t= 3s.(C) work done by tension on Bis also zero in time interval t= 0 to t= 3s.(D) speed of blocks at t = 10s is 27.5 m/s.

8. A particle starts SHM at time 0.t Its amplitude isA and angular frequency is . At time 0t its

kinetic energy is 4

E

, where E is total energy. Assuming potential energy to be zero at mean

position, the displacement-time equation of the particle can be written as

(A) cos6

x A t

(B) sin3

x A t

(C) 2

sin3

x A t

(D) cos6

x A t

9. A 4F capacitor is given 20C charge and is connected with an uncharged capacitor of

capacitance 2F as shown in figure. When switch S is closed.

(A) charged flown through the battery is40

C

3

(B) charge flown through the battery is20

C3

(C) work done by the battery is200

J3

(D) work done by the battery is100

J3

10V

2F

20C

C

S

++++++

4F



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6

Comprehension Type

This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and basedon the other paragraphs 3 multiple choice questionshave to be answered. Each of these questions hasfour choices (A), (B), (C) and (D) out of whichONLY ONEis correct

Paragraph for Question Nos. 10 and 11

A massive disc of radius Ris mounted on a light axle with the axle held horizontal, the disc is made to

spin with angular speed 0. It is then lowered gently on to a level table and released as soon as its rimmakes contact with the table top. The disc begins to move along the table, skidding and picking up speedas it goes.

10. If kis the coefficient of kinetic friction between the rim of the disc and table top, disc will continueto skid for a time

(A) 0

3 k

R

g

(B) 0

2 k

R

g

(C) 0

k

R

g

(D) 0

3

k

R

g

11. If initial kinetic energy of the disc is K, then the kinetic energy of the disc after it stars pure rollingwill be

(A)2

3K (B)

1

2K

(C)1

3K (D)

3

4K



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7


A uniform ring of mass mand radius Rcan rotate freely about an axis passingthrough centre C and perpendicular to plane of paper. Half of ring is positivelycharge and other half is negatively charge. Uniform electric field E0is switched onalong ve x-axis (Axis are shown in figure)

[magnitude of charge density ]

y

x

++

++

+

+

+

+++

C

E0

12. The dipole moment of ring is

(A) 2 R2 (B) 4 R2(C) 2 R2 (D) 4 R2

13. The equilibrium of ring is(A) stable (B) unstable(C) neutral (D) cant say

14. If ring is slightly disturb from given position, find the angular speed of ring when it rotate by /2.

(A)

0

2

E

m

(B)

0E

m

(C) 08 E

m

(D) none



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8

SECTION B

(Matrix-Match Type)This section contains 2 questions. Each question contains statements givenin two columns, which have to be matched. The statements in Column I arelabelled A, B, C and D, while the statements in Column IIare labelled p, q, r,s and t. Any given statement in Column I can have correct matching withONE OR MORE statement(s) in Column II. The appropriate bubblescorresponding to the answers to these questions have to be darkened asillustrated in the following example:If the correct matches are A p, s and t; B q and r; C p and q; and D s

and t; then the correct darkening of bubbles will look like the following:

p q r s

p q r s

p q r s

p q r s

p q r s

D

C

B

A t

t

t

t

t

1. Three sound sources of same frequency fare arranged as shown in figure. S2moves towards left

with speed ,v

nS3moves on a circular path of radius Rwith constant speed

2v

n, and S1performs

S.H.M. with frequency 1100

n

vs

and amplitude 1 cm. (n> 12 and vis speed of sound)

S2

S3

S1

Column I Column II

(A) Beat frequency heard by S1 may be (p) f

n

(B) Beat frequency heard by S2 may be (q) 2

1

f

n

(C) Beat frequency heard by S3 may be

(r) zero(D) Change in the wave length of wave emitted by

S3and observed by S2may be(s) 2

1

f

n

(t)



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9

2. Match the following:Column I Column II

(A) The voltage applied to X-ray tube is increased. (p) Average K.E. of the electronsdecreases

(B) In photo electric effect work function of thetarget is increased.

(q) Average K.E. of the electronsincreases

(C) Stopping potential decreased by (r) Cut off wavelength decreases(D) Wavelength of K,X-ray increased by (s) Atomic number of target

material decreases(t)

SECTION C

(One Integer Value Correct Type)

This section contains 5 questions. Each question, when worked out will result in one integerfrom 0 to 9(both inclusive).

1. A particle starts moving with velocity 10 m/s in a straight line under an

acceleration varying linearly with time. Its velocity time graph is as shownin figure. Its velocity is maximum at t = 3 sec. Find the time (in sec) whenthe particle stops (tan 37

0= )

O

v(m/s)

10

t(s)345

37

2. A block of mass 1 kg start moving at t= 0 withspeed 2 m/s on rough horizontal surface withcoefficient of friction 0.2. A horizontal force F isapplied in the direction of velocity which varieswith time shown in figure (B). Find the speed (inm/s) of particle at t= 3 s (g= 10 m/s

2).

=0.2

1 kg 2 m/s

Figure (a)

2N

F

1 2 3t

Figure



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10

3. One end of a massless rope, which passes over a massless andfrictionless pulley P is tied to a hook Cwhile the other end is free.Maximum tension that the rope can bear is 360 N with what value ofminimum safe acceleration (in ms

2) can a monkey of 60 kg move

down on the rope

P

C

4. Two sources of emf 6V and internal resistance 3and 2are connectedto an external resistance R as shown. If potential difference acrossbatteryAis zero, then find the value of R(in ohm)

A B

R

6V,3 6V,2

5. Two radioactive elements Rand Sdisintegrate as

R P ; 34.5 10R years 1

S Q ; 33 10S

years 1Starting with number of atoms of Rand Sin the ratio of 2 : 1, find the ratio after the lapse of three

half lives of R..



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11

CChheemmiissttrryy PART II

SECTION A



1. The formula of the following chain silicate (pyroxene) can berepresented as

(A) 63 9( )Si O (B) 34( )

n

nSiO

(C) 33( ) n

nSiO

(D) 23( ) n

nSiO

2. Which of the following equations must be used for the exact calculation of [H+] of an aqueous HCl

solution at any concentration 14 2. [ 10 ]HCl w

C K M

(A) [H+]

HClC (B)

HCl wH C K

(C) WHCl

KH C

H

(D) wHCl

KH C

H

3. Which of the following salts give different result by the action of heat?(A) Li2CO3and CaCO3 (B) NaHCO3and KHCO3(C) Hydrated MgCl2and hydrated Na2SO4 (D) Li2SO4and MgSO4

4. & 3High P TA B C is a first order reaction. If A is strong mono protic acid and B is strongdiprotic acid and reaction kinetic is studied by using a standard solution of NaOH required toneutralise reaction mixture at different instants of time. When initially we had taken sameconcentration of A in each case.

Now it was observer that volume required after 971 sec was double that required initially, then thehalf life of reaction is:(A) 485 sec (B) 1942 sec(C) 3010 sec (D) 971 sec



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12

5. Consider the following conjugated diketo compounds:O

O

O O

O

OI II III

Which of reduction potential the following is the correct decreasing order of E values:(A) I II III (B) III II I (C) I III II (D) II I III

6. Compound A and B, both were treated with NaOH , producing a single compound C:

OH

O

CH3

+OH

O

CH3

.Compound C :HO

heat

C is

(A) O

(B)

O

O

CH3

(C) O

(D) O



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13



7. For the reaction 3 2 21 3

2 2NH g N g H g . If Kp of the above reaction is 78.1at 400 C

which is not correct:

(A) At pressure P degree of dissociation of 3NH is

1/2

3 31

4p

P

k

(B) 1.413 /c

K mol (C) If we increase pressure it will decrease K(D) If we increase P by bringing piston down , then, degree of dissociation will decrease

8. The correct statement(s) about solvent effect is/are

(A) Decreasing solvent polarity causes a large increase in the rate of the 2NS attack by ammonia

on an alkyl halide 3 3R X NH RNH X

(B) Increasing solvent polarity causes a large decrease in the rate of the 2NS attack by hydroxide

ion on trimethyl sulphonium ion.

3 3 3 3 2( ) ( )Trimethyl sulphonium ion DMS

HO CH S CH OH CH S

(C) Increasing solvent polarity causes a small decrease in the rate of the 2NS attack by trimethyl

amine on trimethyl sulphonium ion

3 3 3 3 3 3 3 3 2( ) ( ) ( ) ( )CH N CH S CH N CH CH S

(D) All are incorrect.



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14

9. 20 mL of KOH solution was titrated with 0.20 mol L-1

H2SO4solution in a conductively cell. Thedata obtained were plotted to give the graph shown below:

Volume of acid added (mL)

00

15 30 45

20

40

60

80

100

Relativeconductivity

The concentration of the KOH solution was:(A) 0.30 mol L

-1 (B) 0.15 mol L

-1

(C) 0.12 mol L-1 (D) 0.075 mol L

-1

Comprehension Type

This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and basedon the other paragraphs 3 multiple choice questionshave to be answered. Each of these questions hasfour choices (A), (B), (C) and (D) out of whichONLY ONEis correct


The Ellingham diagram for the reduction of haematite and that of cuprous oxide given below;

0

900

700

500

300

100

500K 1073K TemperatureinK

G(kJmo

l-1)ofO2(g)

22C O 2CO

2 2 34Fe 3O 2Fe O

2 22CO O 2CO

2 24Cu O 2Cu O

On the basis of the above plot, answer the following two questions:



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15

10. Choose the incorrect statement(A) Above 1073 K carbon can reduce Fe2O3(B)Below 1073 K G of the reaction given below is negative

2 3 2( ) 3 ( ) 2 ( ) 3 ( )Fe O s CO s Fe s CO g (C)Below 1073 K G of formation of CO2 from CO is more negative than G of formation of

Fe2O3.

(D)Above 1073 K G for the formation of CO is less negative than that of Fe2O3.

11. The incorrect statement amongst the following is(A)The G of the formation of CO2(g) will remains almost independent of temperature because

of S of the reaction being almost equal to zero.(B) The reaction: 2C(s) + O2(g) 2CO(g) is most suitable at temperature above 1073 K.(C) It is difficult to reduce Cu2O to the metal by heating with coke as compared to Fe2O3.(D) Reduction with carbon at high temperature is not preferred due to carbide formation.


Dolacaine, a local anesthetic, is a compound with molecular formula, 13 20 2 2C H O N . It is insoluble in water

and dilute NaOH, but soluble in dil. HCl. Upon treatment with 2NaNO and HCl and then with -naphthol,

a highly coloured solid is formed. When Novocaine is boiled with aqueous NaOH , it slowly dissolves.

The alkaline solution is shaken with ether and layers are separated.Acidification of the aqueous layer causes the precipitation of white solid A; continued addition of acidcauses A to redissolve. Upon isolation A is found to have melting point of 185 -186 C and the formula

7 7 2C H O N :

Evaporation of ether layer leaves a liquid B of formula 6 15C H ON. with acetic anhydride gives

8 17 2'C', C H O N which is insoluble in water and dilute bases, but soluble in dilute HCl.

B is found to be identical to the compound formed by the action of diethylamine on ethylene oxide.

12. When compound B is treated with p nitrobenzoyl chloride followed by moderate reduction with

2Ni/H ; the compound formed is:

(A)

C OCH2NH2NH2

O

(B)

C ONH2 CH2CH2N(CH2CH3)2

O

(C)

COCH2NH2OHNH2

O

(D)

CH2OHNO2



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16

13. 2 ,Dolacaine ProductNaNO HCl naphthol (A)

C

O OCH2CH2N(CH2CH3)2

(B)

OH

N N C OCH2CH2N(CH2CH3)2

O

(C) OH

N

N COCH2CH2N(CH2CH3)2

O

(D) OH

N N CH2CH2N(CH2CH3)2



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17

14. Compound B is having:(A) 3 amine (B) ether group(C) acid group (D) nitro group

SECTION B



p q r s

p q r s

p q r s

p q r s

p q r s

D

C

B

A t

t

t

t

t

1. [ 4Use log1.8 0.26, of formicacid 1.8 10 for aceticacidka 51.8 10 , Kaof NH3 51.8 10 1 ,Ka

of H2S =710 and

2

Ka of 14

2

10H S ]Match the entries of column II for which the equality or inequality given in the column I is valid:

Column I Column II

(A) 510 M HCl solution> 20.1M H S solution (p) water (degree of dissociation of

water)(B)

3CH COOH solution at pH equal to

44.74 NH OH solution at pH equal to 9.26

(q) _O H

(C) 0.1M 3CH COOH solution 1.0M HCOOH solution

(r)electrolyte

(degree of dissociation

of weak electrolytes)(D) 0.1M of a weak acid 510cHA K

solution

0.01M of a weak acid 82 10aHA K

solution

(s) pH

(t) Essentially acidic solution



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18

2. Matrix type the following questions:

Column I (Cell)Column II (EMF or Electrode

potential)

(A) Hydrogen electrode, reduction potential, set upin 1.0 M KCl, pH2= 1 atm

(p) 1.24V

(B) 2 1 2Pt H at atm H pH (q) 0.414V

(C) 2 2 20.1 0.01Hg Hg Cl Cl M Cl M Pt Cl

1.1E V

(r) 0.118V

(D) Reduction potential: AgI aq saturated Ag

16/ 0.8 , of 10Ag AgE V Ksp AgI

(s) 0.327V

(t) Metal-metal insoluble saltelectrode

SECTION C



1. Sulphide ion react with Na2[Fe(NO)(CN)5] to form a purple coloured compoundNa4[Fe(CN)5NOS]. In this reaction the change in oxidation state of iron is?

2. Gold number of starch is 25. The amount of 0.3125 a gm of starch is required to preventcoagulation of 100 ml of gold sol adding 10 ml of 10% NaCl solution? Value of a is

3. Dimethyl gloyoxime is added to aqueous solution of nickel chloride, made alkaline, by adding

4NH OH solution, a brilliant red ppt is obtained. The number of Ni N bonds in red pptis..?



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19

4. A coordination compound has empirical formula 3PdF . What is oxidation number of central atom?

Comprehension (Question No. 5)

The cell given below consists of three compartments separated by porous barriers. The first contains acobalt electrode in 5 L of 0.1 M Co(NO3)2; the second contains 5 L of 0.1 M KNO3; the third contains a

silver electrode in 5 L of 0.1 M AgNO3. Assume that the current within in the cell is carried equally by thepositive and negative ions(does not depend on the size) if there is a passage of 0.1 mole of electrons.

Co Ag

I II III

2 / 0.28

Co CoE V

/

0.8Ag Ag

E V

5. The concentrations of Co2+

in the second compartment is1000

xM, then the x will be:



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20

MMaatthheemmaattiiccss PART III

SECTION A



1.1 1

30

sin tanlimx

x x

x

is equal to

(A)1

6 (B)

1

2

(C) 2 (D)1

2

2. Area of the region bounded by the curve1

1,yx

the tangent at3

(2, )2

P and the line 1x is

(A)4

25

n (B)5

34

n

(C)5

28

n (D)5

28

n

3. Solution of the differential equation2 4

2 3 3

3 2

2

dy x y xy

dx x x y

is

(A) 2 32

xx y c

y (B)

23 2 x

x y cy

(C)

22

3

x

xy cy (D)

23 2 x

x y cy



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21

4. Angle between &a b is ;4

| | 2 2a , | | 3b . Length of longer diagonal of the parallelogram

having adjacent sides represented by 5 2a b and 3a b is

(A) 593 (B) 26 (C) 15 (D) none of these

5. A number is selected at random from the set of natural numbers. The probability that the sum ofthe digits of its square is 39 is

(A)1

6 (B) 0

(C)1

10 (D)

1

9

6. ;3

A B

cos cos 1;A B value of | cos cos |A B is

(A)1

3

(B)2

3

(C)3

2 (D)

1

2



7. If k denotes the remainder on dividing200

1

!r

r

by n then (k, n) can be(A) (5, 14) (B) (1, 3)

(C) (3, 10) (D) (3, 15)



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22

8. The square roots of the matrix1 0

0 1

are

(A)1 0

0 1

(B)

1 0

0 1

(C)1 0

0 1

(D)1 1

1 1

9. Range of the function1 | |

( )2 | |

xf x

x

contains

(A) [0,1) (B) [1, 2)

(C) (1, 2) (D) (2, )

Comprehension Type

This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and basedon the other paragraphs 3 multiple choice questionshave to be answered. Each of these questions has

four choices (A), (B), (C) and (D) out of whichONLY ONEis correct


a, b, c, d is an A.P. with integer terms and 2 2 2d a b c .

10. The common difference is(A) 1 (B) 2(C) 3 (D) none

11. The value of 2 3 4a b c d is(A) 0 (B) 10(C) 100 (D) none of these


( ) sin 2 { }: [0,10]f x x x x .

12. Number of points where f achieves local maximum is(A) 10 (B) 11(C) 20 (D) none of these



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13. Number of roots of ( ) 0f x in (0, 10) is(A) 20 (B) 30(C) 31 (D) none of these

14. Number of points where f achieves local minima is(A) 10 (B) 11

(C) 15 (D) none of these

SECTION B



p q r s

p q r s

p q r s

p q r s

p q r s

D

C

B

A t

t

t

t

t

1. Match the following column:Column I Column II

(A) Length of side of equilateral triangle with vertex at

origin and inscribed in the parabola 2 12y x is(p) 18 3

(B) Length of chord through origin of parabola 2 12y x and having slope 1 unit is

(q) 24 3

(C) Length of normal chord of the parabola2 12y x subtending a right angle at focus is

(r) 7 5

(D) Length of normal chord of the parabola 2 12y x

subtending a right angle at the vertex is

(s) 12 2

(t) 15 5



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2. Consider the family of lines 0ax by c where 2 2 24 9 12 0.a b c ab Let p denote distance

of R(6, 8) from the line 0ax by c Match the following columns:

Column I (value of p) Column II (No. of lines)

(A) 41p (p) 1

(B) 2 / 13p (q) 2

(C) 185p (r) 3

(D) 80p (s) 4

(t) 5

SECTION C



1. Number of points of discontinuity of the function 2( ) 1 ; [1, 3]f x x x is

2. A tangent to ellipse 2 24 4x y meets the ellipse 2 22 6x y at P and Q. Tangents at P and Q

are inclined at an angle .k

The value of kis

3. If 2 96 : ,n n is square of an integer then number of possible values of n is

4. If 2 cos sin 1, then maximum value of 7 cos 6 sin is

5. In ,ABC 6A

, .4B

If2 2 2

c ka b then value of2

k is


Aits Ft II (Paper 1) Pcm(Ques) Jee(Advanced)

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