IIT JEE Sample Paper - 1 _12th Grade_ - 12 - 001

8/2/2019 IIT JEE Sample Paper - 1 _12th Grade_ - 12 - 001

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Sample Paper - 1

Class: XII Roll No. ...Subject: PCMCenter:Paper Code: 12 - 001Test Date:

Duration: 3 Hours Maximum Marks: 288

Students Name:

School Name:

Contact Number:

Address:

Email Id:

GeneralInstructions: Paperconsistsof3Sections.Section1Physics,Section2ChemistryandSection3Math.EachSectionhas5parts.

Part16Questionssingleanswercorrect4markseach Part24Questionsmultipleanswercorrect4markseach Part3Comprehensiontypequestions.2Paragraphs.4markseach Part4Columntypequestions.2columntypequestions.4markseach Part5Integertypequestions.6questions.4markseach Studentsarerequestednottowriteanythingonthequestionpaper. Questionpaperconsistsof72questionscomprisingallthesections. Timelimitis3hrs.Noextratimewillbegiventothestudentsfortest.


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SECTION1Mathematics

Par t 1 - Sing le Answ er Cor rec t

This section contains 6 multiple choice questions. Each question has 4 choices (a), (b), (c)

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

1) If b2 < 2ac, then ax3 + bx2 + cx + d =0 has exactly p real root. p= ?

(a) 0

(b) 1

(c) 2

(d). 3

2) If a, b and c are three consecutive odd integers then the variable line ax + by + c = 0always passes through

(a) (-2,3)

(b) (3,-4)

(c) (1, 2)

(d). ( 8, -1)

3) The complex number z =1+i is rotated through an angle 3/2 in anticlockwise directionabout the origin and stretched by additional 2 unit, then the new complex number is

(a) 2 2 i

(b) 2 2 i

(c) 2 2 i

(d) None of these


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4)Consider 23 different coloured beads in a necklace. In how many ways can the beads beplaced in the necklace so that 3 specific beads always remain together?

(a) 20! * 3!

(b) 20!* 3

(c) 21! * 3!

(d) 21! * 3

5) The solution of 2dy y

x xy 1 cosdx x

- = + is :

(a)2

y 1tan c

2x 2x

= -

(b)y 1

tan cx x

= +

(c)

(d) ( )2 2y

x c x tanx

= +

6) Let { }2 20 1 cos a min x 2 x 3, x R and b lim ,then = + + = The value of

n

r n r

r 0a b

= is:

(a)n 1

n

2 1

3.2

+

(b)n 1

n

2 1

3.2

+ +

(c)n 1

n

4 1

3.2

+

(d) None of these


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Par t 2 Mu l t i p le Answer Cor rec t

This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C)

and (D) for its answer, out which ONE OR MORE is/are correct.

7) Let L1 be a straight line passing through the origin and L2 be the straight line X + Y = 1.If the intercepts made by the circle x2 + y2 x + 3y = 0 on L1 and L2 are equal, thenwhich of the following equations can represent L1?

(a) x + y = 0

(b) x y = 0

(c) x + 7y = 0

(d) x 7y = 0

8) If z = 2 + i32 , then z2n + 22n zn + 24n is equal to

(a) 22n

(b) 0

(c) 3. 24n

(d) None of these

9)(Where g(x) = )

(a)

(b)

(c)

(d)

10) The shortest distance between the z-axis and the line, x + y + 2z-3 = 0, 2x + 3y + 4z 4 = 0 is:

(a) 1

(b) 2

(c) 3

(d) None


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Par t 3 Com prehens ion Type Quest ions

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

questions have to be answer. Each question has 4 choices (a), (b), (c) and (d) out of which

ONLY ONE is correct.

Paragraph 1 :

Symmetric Relations:R is called a symmetric relation on A if (x, y) R (y, x) R. That is, y R x whenever x Ry.

Reflexive Relations:R is a reflexive relation if (a, a) R, a A. It should be noted if there is at least one

element

Transitive Relations:R is called a transitive relation if (a, b) R, (b, c) R (a, c) RIn other words if a is related to b, b is related to c, then a is related to c.

Equivalence Relation:A relation R in a set A is called an equivalence relation if(i) R is reflexive i.e., (a, a) R, a A(ii) R is symmetric i.e., (a, b) R (b, a) R(iii) R is transitive i.e., (a, b), (b, c) R (a, c) R

The equivalence relation is usually denoted by the symbol ~.

No w a n sw e r t h e f o l lo w i n g q u e st i o n .

11) N is the set of natural numbers. The relation R is defined on N N as follows:(a, b) R (c, d) a + d = b + c. Then the relation is (choose the single most suitablestatement)

(a) Transitive but not reflexive

(b) Symmetric but not transitive

(c) Symmetric, transitive but not reflexive(d) Equivalence.


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12) A relation R on the set of complex numbers is defined by z1 R z221

21

zz

zz

+

is real, show

that R is an equivalence relation., Then the Relation is ( choose the single mostsuitable statement )

(a) Reflexive but not symmetric

(b) Symmetric, Transitive but not reflexive

(c) Symmetric and Reflexive.

(d) Transitive but not Reflexive ive

13) Let A = {1, 2, 3, 4, 5} and R = {(1, 1), (3, 2), (2, 2), (3, 3), (4, 1), (4, 4), (5, 5)}. Therelation R is

(a) Only symmetric

(b) Only reflexive(c) Only Transitive

(d) Equivalence.

Paragraph 2 :

1b

y

a

x2

2

2

2

= Represents a Hyperbola with the following properties:

(i) The eccentricity e is given by the relation

+= 2

22

a

b1e

(ii) Since the curve is symmetrical about the y - axis, there exists another focus S at (-ae,0) and a corresponding directirx ZM with the equation x= -a/e

(iii) The points A and A are called the vertices of the hyperbola.

(iv) The straight line joining the vertices is called the transverse axis of the hyperbola, itslength AA is 2a.

(v) The straight line BB is called the conjugate axis.

The straight line, to which the tangent to a curve tends as the point of contact tends toapproach infinity, is called an asymptote of the curve. The paired of asymptote differ fromthe equation of corresponding hyperbola by a constant.


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14) The eccentricity of the hyperbola which passes through (3, 0) and (3 2 , 2).

(a) - /3

(b) /3

(c) 2. /3

(d) -2 /3

15) The equation of the hyperbola whose directrix is 2x + y =1, focus (1, 2) and

eccentricity 3 .

(a) 7x2 2y2 + 12xy 2x + 14y 22 = 0

(b) 7x

2

+2y

2

+ 12xy 2x + 14y 22 = 0(c) 7x2 2y2 - 12xy 2x + 14y 22 = 0

(d) 7x2 2y2 + 12xy 2x + 14y+22 = 0

16) The equation of the hyperbola whose asymptotes are x + 2y + 3 = 0 and 3x + 4y+ 5 = 0 and which passes through the point (1, -1).

(a) 3x2 + 10xy + 8y2 +14x + 22y -7 = 0

(b) 3x2 + 10xy + 8y2 +14x - 22y +7 = 0

(c) 3x2 + 10xy + 8y2 -14x + 22y +7 = 0

(d) 3x2 + 10xy + 8y2 +14x + 22y +7 = 0

Par t 4 Co lum n Type Quest ions

This section contains 2 column questions. Each question contains statements given in two

columns, which have to be matched. The statements in Column I are labeled a, b, c and d,

while the statements in Column II are labeled p, q, r, s and t. Any given statement in

Column I can have correct matching with ONE OR MORE statement(s) in column II.


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17)

ColumnI ColumnII(a) If f() = 2 and ( )

0

f ( x ) f ''( x ) sin x dx 5

+ = then f(0) isequalto,(itgiventhatf(x)iscontinuousin[0,])

(p)1

(b) [ ] [ ]( ) 2

2

min x x , x x dx , where [.] is thegreatestintegerfunction=

(q)0

(c) x+y+z=15ifa,x,y,z,bareinA.P.and 35

z

1

y

1

x

1

= ifa,x,y,zbareinH.Pfora0,thenxisequalto

(s)4

18)

ColumnI ColumnII(a) Ifx,y,zarethree integers inA.P, lyingbetween1and9

andx51,y41andz31are threedigitsnumbers, then thevalueof

zyx

31z41y51x

345 is

(p)1

(b)Theareaboundedbythecurvey=x(3x)2 ,thexaxisandtheordinatesofthemaximumandminimumpointsofthecurveis

(q)4


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(c)IfA=

1xtan

xtan1,thenthevalueof|ATA1|forx=pi/4

is(r)2

(d)Theareaenclosedbythecurve|x+1|+|y+1|=2 isA.Then A/2= (s)0

Par t 5 I n t ege r T ype quest i ons

This section contains 6 questions. The answer to each of the questions is a single digit integer, ranging

from 0 to 9.

19) Two systems of rectangular axes have the same origin If a plane cuts them at the

distance a, b, c and a', b', c' respectively from the origin, then

. Find k.

20) If ax2 + bx + c = 0, a, b, c R. then the condition such that this equation would haveat least one root in (0, 1) is aA+bB+cC. Hence, B+C equals to ?

21) The greatest and least values of the function f(x) = ax + b x + c, when a > 0, b > 0,

c > 0 in the interval [0,1] are M and m respectively. Find M+m?

22) If e1 and e2 are the eccentricities of the hyperbola 1b

y

a

x2

2

2

2 = and its conjugatehyperbola, prove that e1

-2 + e2-2 = 1.

23) The indefinite integral of . Find a*b-c?

24) If the coefficients of the second, third and fourth terms in the expansion of (1 + x)n arein A.P. find n?


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SECTION2Physics




25) Mercury thermometer can be used to measure temperature up to

(a) 260C

(b) 100C

(c) 357C

(d) 500C

26) Two racing cars of masses m and 4m are moving in circles of radii rand 2r respectively.

If their speeds are such that each makes a complete circle in the same time, then the

ratio of the angular speeds of the first to the second car is

(a) 8:1

(b) 4:1

(c) 2: 1

(d) 1:1

27) ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the

figure. IAB, IBC and ICA are the moments of inertia of the plate about AB, BC and CA as

axes respectively. Which one of the following relations is correct?


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(a) IAB > IBC

(b) IBC > IAB

(c) IAB + IBC = ICA

(d) ICA is maximum

28) Two cells, having the same e.m.f, are connected in series through an external

resistance R. Cells have internal resistances r1 and r2 (r1 > r2) respectively. When the

circuit is closed, the potential difference across the first cell is zero. The value of R is

(a)

(b)

(c) r1 + r2

(d) r1 - r2

29) A sample of radioactive element has a mass of 10 gm at an instant t = 0. The

approximate mass of this element in the sample after two mean lives is

(a) 6.30 gm

(b) 1.35 gm

(c) 2.50 gm

(d) 3.70 gm


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30) A particle, with restoring force proportional to displacement and resisting force

proportional to velocity is subjected to a force F sin t. If the amplitude of the particle

is maximum for = 1 and the energy of the particle is maximum for = 2, then

(a) 1 = 0 and 2o

(b) 1 = 0 and 2 = 0

(c) 1 0 and 2 = 0

(d) 10 and 20


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

31) Nickel shows ferromagnetic property at room temperature. If the temperature isincreased beyond Curie temperature, then

(a) it will show Diamagnetism

(b) it will show Paramagnetism

(c) Above Curie temperature a diamagnetic substance becomes paramagnetic

(d) Above Curie temperature a ferromagnetic substance becomes paramagnetic

32) Out of the following expressions for couple per unit twist, time period of a compound

pendulum, time period of a simple pendulum and frequency of a stretched wire

respectively, the dimensionally consistent expressions are

(a) C =

(b) T = 2

(c) T = 2


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(d) f =

33) If yellow light emitted by sodium lamp in Young's double slit experiment is' replaced bya monochromatic blue light of the same intensity

(a) Fringe width will decrease

(b) Fringe width will increase

(c) Fringe width will remain unchanged

(d) Fringes will become less intense

34) For a satellite escape velocity is 11 km/s. If the satellite is launched at an angle of 60

with the vertical, then escape velocity will be(a) 11 km/s

(b) 11 km/s

(c) dependent of angle of projection

(d) independent of angle of projection


This section contains two paragraph. Based upon the paragraph, 2 multiple choice questions

have to be answer. Each question has 4 choices (a), (b), (c) and (d) out of which ONLY ONE

is correct.

Paragraph 1 :

A small toy train is moving with a constant speed of 10 m/s in a circle of radius m. The

circle lies in horizontal plane. At time t= 0 train is at point P and moving in anticlockwise

direction. At this instant a stone is projected from the train with velocity m/s

relative to train. Answer following questions based on above situation.


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35) What is velocity vector of stone relative to train when the stone is at highest point of its

trajectory

(a) 4 + 10

(b) 4 10

(c) 4 + 10(d) 4 10

36) What is angular displacement of train during this time interval?

(a) /4

(b) /2

(c)

(d) 2/4

37) What is displacement of the stone till it finally lands on the ground

(a) 9.2 8

(b) 9.2 + 8

(c) 9.6 16

(d) 9.6 + 16


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Paragraph 2 :

A car is moving on a straight road. The velocity of the car varies with time as shown in the

figure. Initially (at t = 0), the car was at x = 0, where, x is the position of the car at any

time t.

38) The displacement time graph will be best represented by


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39) The maximum displacement from the starting position will be

(a) 200 m

(b) 250 m

(c) 160 m

(d) 165 m

40) Average speed from t = 0 to t = 20s will be

(a) 16/7 m/s

(b) 24/7 m/s

(c) 20/7 m/s

(d) Zero


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This section contains 2 column questions. Each question contains statements given in two

columns, which have to be matched. The statements in Column I are labeled a, b, c and d,

while the statements in Column II are labeled p, q, r, s and t. Any given statement in

Column I can have correct matching with ONE OR MORE statement(s) in column II.

41)

ColumnI ColumnII(a)RelativePermittivity (p) Joule/coulomb(b)ElectricPotential (q)ML2T3A1(A=current)(c)Electricfieldintensity (r) Unitless(d)Dielectricconstant (s)MLT3A1

42)

ColumnI ColumnII(a) AquantityisrepresentedbyX=MaLbTc.The%errorinmeasurementofM,LandTare%, %and%respectively.The%errorXwouldbe

(p) 3%

(b) WhatisthefractionalerroringfromT=2 ?GivenfractionerrorsinTandlare+xand +yrespectively.

(q) (y+2x)

(c) Relativedensityofametalmaybefoundwiththehelpofspringbalance.Inairthespringbalancereads(5.00+0.005)Nandinwateritreads(4.00+0.05)N.The%errorinrelativedensitywouldbe

(r) 6%

(d) Errorinthemeasurementofradiusofasphereis1%.Thenerrorinthemeasurementofvolumeis (s) (a+b+c)%


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Pa r t 5 I n te g e r Typ e q u es t i o n s

This section contains 6 questions. The answer to each of the questions is a single digit

integer, ranging from 0 to 9.

43) A coil of inductive reactance 31 has a resistance of 8 . It is placed in series with a

condenser of capacitative reactance 25. The combination is connected to an a.c.

source of 110 volt. The power factor of the circuit is P. Now P*100=Q. The Sum of

Digits of Q = ? ( If Q=21, your answer should be 2+1=3, if Q=99, then your answer

must be 9+9=18=1+8=9 )

44) A light ray falls on a rectangular glass slab as shown. The index of

refraction of the glass, if total internal reflection is to occur at the

vertical face, is a .Then a+b+c=?

45) Two charges q1 and q2 are placed 30 cm apart, as shown in the

figure. A third charge q3 is moved along the arc of a circle of

radius 40 cm from C to D. The change in the potential energy of

the system is where k is?

46) The current gain for a transistor working as common-base amplifier is 0.96. If the

emitter current is 7.2 mA, then the base current is C. Find the remainder when C*100 is

divided by 13?

47) In rising from the bottom of a lake, to the top, the temperature of ail air bubble remains

unchanged, but its diameter gets doubled. If h is the barometric height (expressed in m

of mercury of relative density p) at the surface of the lake, the depth of the lake is A h.The value of A is?

48) Photoelectric work function of a metal is 1eV. Light of wavelength = 3000 falls on it.

The photo electrons come out with velocity 10A m/sec2? The value of A is?


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SECTION3Chemistry




49) C6H5 CH2 Cl X

C6H5 CH2 Cl YIn the above two reactions the products formed X and Y are respectively

(a) C6H5 CH2 NO2 and C6H5 CH2 CH2 NH2

(b) C6H5 CH2 CHO and C6H5 CH2 CH2 CHO

(c) C6H5 CH2 CHO and C6H5 CHO

(d) C6H5 CHO in both cases.

50) C6H5 CHO Product.

The final product formed is

(a) optically inactive acid

(b) optically inactive -hydroxy acid

(c) racemic mixture of two optically active -hydroxy acids.

(d) racemic mixture of two optically active secondary alcohols.


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51) Consider the following rearrangement

The product of the reaction is

C6H5

(a) C = N CH3

C6H11

CH3(b) N C6H5

CH3

(c)

(d)

52) -Amylose and Cellulose both are linear polymers of glucose. The difference between

them is

(a) -Amylose has (1 4) linkage and cellulose has (1 4) linkage

(b) -Amylose has (1 4) linkage and cellulose has (1 4) linkage

(c) -Amylose has (1 4) linkage and cellulose has (1 6) linkage

(d) -Amylose has (1 4) linkage and cellulose has (1 6) linkage


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53) 90Thorium 232 decays in steps ultimately yielding 82Pb 208. The particles emitted

are

(a) 4 and 6

(b) 4 and 4

(c) 6 and 4

(d) 6 and 6

54) Reaction of cyclohexanone with dimethyl amine in the presence of catalytic amount

of an acid forms

(a) a Schiffs base(b) an enamine

(c) an imine

(d) an amine


This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C)

and (D) for its answer, out which ONE OR MORE is/are correct.

55) Consider the following reaction

O

||

(CH3)3C Mg Cl + (CH3)3C C C(CH3)3 [X] + Y

[X] Products.

The products formed are


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(a) (CH3)2C = CH2

(b) (CH3)3C CH C(CH3)3

|

OH

(c) [(CH3)3C]3COH

(d) (CH3)3C C(CH3)3

56) Which of the following react with hydroxylamine?

(a) C2H5 COCl

(b) CH3 CO CH3

(c) CH3 CO NH2(d) CH3 COOC2H5

57) Which of the following statements are correct?

(a) p-Nitro aniline is a stronger base than aniline

(b) ortho-methyl benzoic acid is a weaker acid than benzoic acid

(c) The order of acidic strength is as follows

(d) Pyridine is a stronger base than pyrrole.

58) Which of the following give the same osazone on treatment with phenyl hydrazine?

(a) Glucose

(b) Galactose

(c) Fructose(d) Mannose


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This section contains one paragraph. Based upon the paragraph, 2 multiple choice questions

have to be answer. Each question has 4 choices (a), (b), (c) and (d) out of which ONLY ONE

is correct.

Paragraph 1 :

Organic compounds having phenolic OH, COOH and SO3H groups show acidic

character. The strength of acid is dependent on inductive effect and mesomeric effect. The

acidic strength of ortho substituted benzoic acids are explained by ortho effect.

59) The correct order of strengths of acids is

(a)

(v)

(c)

(d)


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60) Strongest acid among the following is

(a)

(b)

(c)

(d) CH3COOH

61) Consider the following ortho substituted benzoic acids and choose the strongest

acids.

(a)

(b)

(c)

(d)


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Paragraph 2 :

Amino acids are bifunctional having COOH and NH2 groups. Depending upon the

position, they may be -amino acids, , or -amino acids. There are about 20 -amino

acids, commonly found in proteins. They are soluble in water, but insoluble in organic

solvents. It is due to formation of zwitterions. These show the properties of NH2 group as

well as COOH group.

Every amino acid has its own characteristic isoelectric point.

62) The following amino acids has characteristic pKa values

H3N CH2 CH2 CH2 CH2 CH COOH

(3) | (1)

NH3

pKa(1) = 2.18; pKa(2) = 8.95 and pKa(3) = 10.79

(a) 5.56

(b) 9.87

(c) 11.13

(d) 12.97

63) What is the structure of the above amino acid in a solution of pH = 9.87?

(a) H2N CH2 CH2 CH2 CH2 CH COOH

|

NH3

(b) H3N CH2 CH2 CH2 CH2 CH COOH

|

NH3


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(c) H3N CH2 CH2 CH2 CH2 CH COO

|

NH3

(d) H3N CH2 CH2 CH2 CH2 CH COO

|

NH2

64) On heating to 200oC, H2N CH2 CH2 CH2 COOH gives

(a)

(b)

(c)

(d)


This section contains 2 questions. Each question contains statements given in two columns,

which have to be matched. The statements in Column I are labeled a, b, c and d, while the

statements in Column II are labeled p, q, r, s and t. Any given statement in Column I canhave correct matching with ONE OR MORE statement(s) in column II.


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65)

ColumnI ColumnII(a) RCONHCH3 (p) Schmidtreaction

(b)RCOCH3+HCOONH4 (q) Leuckartreaction

(c)RCHCH3 (r) RCH2NHCH3

(d)RCHCH3X

(s) NH2|

RCHCH3(t) Electrophile

66)

ColumnI ColumnII(a) RCH2NH2 (p) KMnO4,H+

(b) R2CHNH2 (q) H2SO5(c) R2NH (r) O3


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(d) R3N (s) H2O2(t) HNO2

Pa r t 5 I n te g e r Typ e q u es t i o n s

This section contains 6 questions. The answer to each of the questions is a single digit

integer, ranging from 0 to 9.

67)

68)

69)

70)

71)

72)

IIT JEE Sample Paper - 1 _12th Grade_ - 12 - 001

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Transcript of IIT JEE Sample Paper - 1 _12th Grade_ - 12 - 001