IIT-JEE sample test paper for class XI

7/29/2019 IIT-JEE sample test paper for class XI

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Date : 09-02-2013 Duration : 3 hours Max. Marks : 204

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

Do not break the seal of the question paper booklet before instructed to do so by the invigilator.

This Paper contains 60 questions. Please ensure that theQuestion paper you have received contains ALL THEQUESTIONS.

QUESTION PAPER FORMAT

1. The question paper consists of Maths, Physics and Chemistry. Each part has four sections.2. Section I contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

whichonly ONE is correct.Each questions is of3 marks.1 markwill be deducted for each wrong answer.3. Section II contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out ofwhichONE or MORE is/are correct.Each questions is of4 marks.No negative marking will be donefor this Section.

4. Section III contains 2 groups of questions. Each group has 2 questions based on a paragraph. Each questionhas four choices (A), (B), (C) and (D) out of whichonly ONE is correct.Each questions is of3 marks.1markwill be deducted for each wrong answer.

5. Section IV contains 4 questions.Each questions is of4 marks.The answer to each of the questions is aninteger, ranging from 00 to 99. The answer will have to be appropriately bubbled in OMR.No negativemarking will be done for this Section.,

NOTE : GENERAL INSTRUCTION FOR FILLING THE OMR ARE GIVEN BELOW :

1. Use only HB pencil or blue/black pen (avoid gel pen) for darkening the bubble.2. Indicate the correct answer for each question by filling appropriate bubble in your OMR answer sheet.3. The Answer sheet will be checked through computer hence, the answer of the question must be marked by

shading the circles against the question by dark HB pencil or blue/black pen.4. While filling the bubbles please be careful about question paper format.

Name of the student EW Roll Number .

Class - XI J EE Advanced

I have read all the instructions and shallabide by them.

................................................................Signature of the Student

I have verified all the information filled inby the candidate.

................................................................Signature of the invigilator

Corporate Office : Eduwave, 46, Rajiv Gandhi Nagar, Kota (Raj.) Tel. : 92142-11999Branch Office : Eduwave, SP -12A, Om Tower, Indra Vihar, Kota (Raj.) Tel 92142-13666

Website : www.eduwave.in, Email : [email protected]


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MATHEMATICS

SECTION-A[STRAIGHT OBJ ECTIVE TYPE QUESTIONS]

Q.1 to Q.8has four choices (A), (B), (C), (D) out of whichONLY ONE is correct.

Q.1 The distance of the point(1, 2) from the line x +y +5 =0 measured parallel to the line 2x y +3 =0

is equal to

(A) 4 5 (B)2 53

(C)8 5

3(D) 53

Q.2 In a sequence of 9 terms, first 5 terms are in AP with common difference 2 and last 5 terms are in GP

with common ratio 2. If the middle term of AP is equal to the middle term of the GP then the middle

term of the entire sequence is

(A)34

(B)32

(C)328

(D)37

Q.3 If reflection of circle x2+y2 4y +3 =0 in the line y =x intersect the circle x2+y2 6x 8y +k =0

orthogonally then K is equal to

(A) 3 (B) 6 (C) 9 (D) 12

Q.4 If Sn =

n

1r

1r

0t

t

t

r

r

n

n3CC

5

1

then the value of

, where

=

1n n)S1(, is equal to

(A) 2 (B) 3 (C) 4 (D) 5


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Q.5 The number of integral roots of the equation

2xx34x5xlog 22 = 4x5x2log 2 is(are)

(A) 0 (B) 1 (C) 2 (D) infinite

Q.6 Letbe the maximum value of expression sin10x +cos5x. If in aABC sinAcosB +cosAsinBsinC =,(where A


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SECTION-B[MULTIPLE OBJ ECTIVE TYPE QUESTIONS]

Q.9 to Q.12has four choices (A), (B), (C), (D) out of whichONE OR MORE THAN ONE is/are correct.

Q.9 If in aABC a2 + b2 + c2 = bc + 3ca , then

(A) c is longest side (B) ABC is right angled triangle

(C) B, C, A are in AP (D) ABC is scalene triangle

Q.10 If a1, a2, a3...an are the positive numbers in AP such that a22 +a79 =100 then identify the correctstatement

(A)100

ii 1

a 5000

(B) 50aa 7229 (C) 50aa 7229 (D)75 100

i ii 26 i 1

2 a a

Q.11 Iff(x) =ax2

bx +c is many one in (4, 12) & has roots Ar & Ar +1(where Ar =5

Cr) then the valueof r can be(A) 1 (B) 2 (C) 3 (D) 4

Q.12 Two concentric circles, whose centre is origin and radii are 3 & 6 respectively as shown in the figure.

Then the value of log3MN +log3TS +log3(MN +NR) +log3(TS +SR) is a factor of

(A) (4C0 +4C1) +(

4C1 +4C2) +......+(

4C3 +4C4)

(B) The number of different ways in which 8 different books can

be distributed among 3 students, if each students receives at least 2 books.

(C) The number of words formed by arranging the letters of the word 'BULBUL'

(D) The number of six digit numbers which contains exactly four different digits such that exactly one

digit is repeated


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SECTION-C[COMPREHENSION TYPE QUESTIONS]

Q.13 to Q.16are based upon aparagraph. Each question has four choices (A), (B), (C), (D) out of whichONLY ONE is correct.

Paragraph for Question Nos. 13 to 14Consider a fucntion f whose domain is [3, 4] and range is [2, 2] with following graph

Q.13 Domain & Range of g(x) = f(|x|) are [a, b] & [c, d] respectively then b a + c + d is equal to

(A) 11 (B) 10 (C) 8 (D) 7

Q.14 If h(x) =|f(x) 3/2| has range [e, f] & n be number of real solution of h(x) = 1/4 then n + e + 2fis equal to

(A) 8 (B) 9 (C) 10 (D) 11

Paragraph Question Nos. 15 to 16

Let ABCDEF be a regular hexagon, whose equation of sides AB & BC are 7x3y &

5x3y respectively and if point C is (0, 5) then

Q.15 The radius of circle passing through ABC(A) 34 (B) 38 (C) 36 (D) 33

Q.16 The area of triangle ACE is

(A) 318 (B) 236 (C) 336 (D) 216


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SECTION-D[INTEGER TYPE QUESTIONS]

Q.17 to 20are "Integer" type questions. (The answer to each of the questionsare upto 2 digit)

Q.17 Let f be an odd periodic function from R R with period 2 & satisfies

1.....32

16

32

16

32

16

32

1log65.3f 4/9

then find the value of f2(0.85).

Q.18 Consider f(r, ) =n 100

i2 n

r 1i 1

rcos(r /2 ),A 2n log sin f(r, )

2

. If the value of A at

= )r23(r6

is an +b, where a, b I then find the value of a +b .

Q.19 If A =sin50|cos50 sin50| +cos50 {|tan50 cot50| +|cot50 cos50| | tan50 sin50|}B =|sin 100 cos 100|+|sec100 cos100| +|cosec100 sin100| |cosec100 sec100|

+cosec100 then value of expression B2 (A B)2+A2+ 2B

1

Q.20 Let and be roots of x2 3x +5 =0, with >.If S

n=n 1+n 2 +n 32 +.... +n 2+n 1 for n 1,

then find the value of 2012 2010

2011

S 5S

S

.


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PHYSICS

SECTION-A

[STRAIGHT OBJ ECTIVE TYPE QUESTIONS]


Q.21 The brick shown in the drawing is glued to the floor. A 3500-N force is applied to the top surface ofthe brick as shown. If the brick has a shear modulus of 5.4 109N/m2, how far to the right does thetop face move relative to the stationary bottom face?

0.10 m 3500 N

0.250.10 m

(A) 5.8 106 m (B) 2.6 106 m (C) 1.1 106m (D) 6.5 107 m

h

W

Q.22 Figure shows an iron paddle mounted in a tank of water. There is20.0 kg of water in the tank and the iron has a mass of 2.0 kg. Thepaddle is rotated for 5.0 min at a constant rate. A 2.2 kW motor turnsthe paddle, but the paddle rotates at only 30% of its maximum ratebecause of the resistance of the water. If the tank is originally at 20C

and no heat escapes, the final temperature of the water is approximately.

(A) 35C (B) 40C (C) 25C (D) 30C


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Q.23 A speaker generates a continuous tone of 440 Hz. In the drawing, sound travels into a tube that splitsinto two segments, one longer than the other.

The sound waves recombine before being detected by amicrophone. The speed of sound in air is 340 m/s.

What is the minimum difference in the lengths of the two paths for sound travel if the waves arrivein

phase at the microphone?(A) 0.10 m (B) 0.39 m (C) 0.77 m (D) 1.11 m

Q.24 Suppose one mole of an ideal gas undergoes the reversible cycle ABCAshown in the P-V diagram above, where AB is an isotherm. The molarheat capacities are C

Pat constant pressure and C

vat constant volume.

The net heat added to the gas during the cycle is equal to

(A) RThV

2/V

1(B) C

P(T

hT

c)

A

ThTc

B

V

V2V1

P2

P1

P

C

(C) Cv(T

hT

c) (D) RT

hln V

2/V

1 R (T

hT

c)

Q.25 A particle of mass m moves in a one dimension such that its potential energy is given as :U(x) =ax2+bx4 , where a and b are positive constants. The angular frequency of small oscillationsabout the minima of the potential energy is equal to

(A) (a/2b)1/2 (B) (a/m)1/2 (C) (a/m)1/2 (D) 2(a/m)1/2

Q.26 A hoop of mass M and radius R is at rest at the top of an inclined plane a shown figure. The hoop rollsdown the plane without slipping. When the hoop reaches the bottom, its angular momentum around itscenter of mass is

(A) MR gh

(B) 1MR gh2

(C) M 2gh

(D) Mgh


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Q.27 A cylinder with moment of inertia 4kg - m2about a fixed axis intially rotates at 80 radian per secondabout this axis. A constant torque is applied to slow it down to 40 radian per second. If the cylindertakes 10 seconds to reach 40 radian per second, the magnitude of the applied torque is

(A) 80 N-m (B) 40 N-m (C) 32 N-m (D) 16 N-m

Q.28 Small-amplitude standing waves of wavelengthoccur on a string with tension T, mass per unit length

, and length L. One end of the string is fixed and the other end is attached to a ring of mass M thatslides on a frictionless rod, as shown in the figure. When gravity is neglected, which of the followingconditions correctly determines the wavelength ? (You might want to consider the limiting casesM 0 and M )

M

L

(A) 2 2 L/M cot (B) 2 2 L/M tan

(C)2 2 L

/M sin

(D) 2L /n, n 1,2,3...


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SECTION-B[MULTIPLE OBJ ECTIVE TYPE QUESTIONS]


Q.29 For a particle, x A cos t6

then the value(s) of t when it is at rest is :

(A)6

(B)

65

(C)3

(D)

611

Q.30 A particle moves along y-axis according to the equation, y =sin 150 t +4 sin3 50 t +2.y is in cm and t is in seconds .(A) it performs SHM of amplitude 3 cm (B) it performs SHM of frequency 25 Hz(C) it does not perform SHM (D) the mean position is at y = 2cm

Q.31 Which of the following statements is/are true(A) work done by kinetic friction on a rigid body may be positive

(B) a uniform sphere rolls up an inclined plane without sliding. The friction force on it will be up theincline. (only contact force and gravitational force is acting)(C) a uniform sphere rolls down an inclined plane without sliding. The friction force on it will be up theincline. (only contact force and gravitational force is acting)(D) a uniform sphere is left from rest from the top of a rough inclined plane. It moves down the planewith slipping. The friction force on it will be up the incline.

Q.32 Two coherent waves represented by y1=A sin

4t

x2 1and y2=A sin

6t

x2 2

are superposed. The two waves will produce

(A) constructive interference when (x1x2) =2 (B) constructive interference when (x1x2) =223

(C)destructive interference when (x1x2) =1.5(D)destructive interference when (x1x2) =211


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Paragraph for question nos 33 to 34

Because heating a solid increases the vibrational energy of its molecules resulting in an increase in spacerequired by each molecule, a typical solid will expand when heated. For such solids, the fractionalchange in their length per unit temperature is given by a coefficient of linear expansion, which is specificfor each solid. Although the change in length varies slightly with temperature for any solid, The followingequation gives a good approximation.

L L T where L is the original length of the solid,L is the change in length, is the coefficient of linearexpansion for the particular substance, andT is the change in temperature.Of course, any solid that increases in length when heated will also expand in both other directions. The

change in volume Vfor such a solid is given by:V V T

where is the coefficient of volume expansion which is exactly three times the coefficient of linearexpansion. The equation for the change in volume can be applied to most liquids as well as solids.Water, however, has a maximum density at 4C. A list of the coefficients of linear expansion for somecommon substances is provided in Table 1.

6Substance (10 /C)

Ice(at0C) 51

Aluminium 23

Brass 19Steel 11

Glass(ordinary) 9

Table-1


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Q.33 A bimetallic strip consisting of brass and steel is welded together lengthwiseas shown. As the temperature increases:

steel

Brass

(A) the brass will contract and the steel will expand, bending the rod to the left.

(B) the steel will contract and the brass will expand, bending the rod to the right.

(C) the brass will expand faster than the steel, bending the rod to the right.

(D) the steel will expand faster than the brass, bending the rod to the left.

Q.34 Which of the following is true concerning an aluminum buoy that floats in a lake all year round? (Note:The volume coefficient of expansion for water is 2 103/C.)

(A) The buoy floats higher in the winter because the density of water changes more than the density ofaluminum.

(B) The buoy floats higher in the winter because the density of water changes less than the density ofaluminum.

(C) The buoy floats lower in the winter because the density of water changes more than the density of

aluminum.(D) The buoy floats lower in the winter because the density of water changes less than the density ofaluminum.

Paragraph for question nos 35 to 36

Alice places two stereo speakers a distance d apart. She sends a signal which is a sine wave offrequency f, so that the speakers are producing the same pure tone in phase. The sound wave in air hasa wavelength.

She enlists her friend Bob to do an experiment. Alice sits directly in front of the speakers on the linewhich bisects the line segment connecting the speakers (see figure) but relatively far away from thespeakers. Bob starts at the same place, but he slowly moves to the right. For him the sound gets quieteras he moves right, until he can barely hear it. Then it begins to get louder again. The figure shows Bobsposition : where he first can barely hear the sound. This is the set up.


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Inexperiment 1, Alice and Bob keep their positions and Alice changes

the frequency of the signal sent to both speakers, so that both speakers

are still producing a sound in phase at the same frequency (a different

frequency from the set up).

Inexperiment 2, Alice changes the frequency of the second speakerslightly, but the first speaker remains at the original frequency.

dspeakers

d1 d2

Alice bob

The distance d is large compared to the wavelength, and it is small

compared to the distance Alice and Bob sit from the speakers. The distance

from Bob to the left speaker is d1, and his distance to the right speaker is d

2.

Q.35 Inexperiment 1, what is the best prediction for what Alice and Bob will observe ?

(A) Alice will hear very little sound, and bob will hear sound clearly.

(B) Alice will continue to hear sound, and Bob will continue to hear little.

(C) Alice will continue to hear

(D) Nothing can be predicted, in that Alice and Bobs sharing of sound frequency.

Q.36 Inexperiment 2, what is the best prediction for what Alice and Bob will observe ?

(A) Alice will continue to hear sound, and bob bill continue to hear little

(B) Alice will continue to hear sound, and bobs hearing of sound depends on the chosen frequency

(C) Alice and bob will hear a sound which grows and fades and grows(D) Neither Alice nor Bob will hear very much sound.


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SECTION-D

[INTEGER TYPE QUESTIONS]


Q.37 The velocity of blood flow in an artery can be measured using Dopplershifted ultrasound. Supposesound with frequency 1.5 106Hz is reflected straight back by blood flowing at 1 m/s. Assuming thevelocity of sound in tissue is 1500 m/s and that the sound is incident at a very small angle as shown infigure, calculate the frequency shift (in KHz) between the incident and reflected waves.

v=1m/s

Sound sourceand

receiver

Q.38 A massmtravels at speedv0perpendicularly to a stick of massmand lengthl, which is initially at rest.The mass collides completely inelastically with the stick at one of its ends, and sticks to it. What is thelocation of point from end A (in cm) which is at instantaneous rest just after collision. (takel=1.2meter)

A

B


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Q.39 Find the kinetic energy of pulse travelling in a taut string. Given T =10 N & =0.1 kg/m.[Give answer in micro joules] fill the first two digits.

1mm

10cm 5c

Q.40 One stick leans on another as shown in figure. A right angle is formed where they meet, and the rightstick makes an anglewith the horizontal. The left stick extends infinitesimally beyond the end of theright stick. The coefficient of friction between the two sticks is. The sticks have the same massdensity per unit length and are both hinged at the ground. What is the minimum value of tan for whichthe sticks do not fall? (Take =0.04)


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CHEMISTRYSECTION-A

[STRAIGHT OBJ ECTIVE TYPE QUESTIONS]


Q.41 The critical volume occupied by 1 mole of gas is 0.09lmol1. The value of compressibility factor forthis gas under the conditions of high pressure 821 atm and temperature 300K is

[Take R =0.0821 atml1K1mol1]

(A) 1 (B) 2 (C)12

(D) 3

Q.42 Which of the following will not show geometrical isomerism ?

(A) (B)H

Me

(C) (D)

Q.43 In which of the following compound sulphur has maximum electro negativity

(A) SO2

(B) H2SO

3(C) H

2SO

4(D) H

2S


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Q.44 Find the approximate radius in of the orbit in which circumference is 6 times the de Broglie wavelengthin case of H atom if nucleus is non stationary. Consider in H atom (Mn>>>me), where Mnis the massof nucleus and meis mass of electron.

(A) 0.529 62 (B) 0.529 32 (C) 0.529 (D) None of these

Q.45 Which of the following is not the correct order ?

(A) CH2=CH

2< < < (C=C bond length)

(B) > > (Heat of hydrogenation)

(C) CH3

CH =C =CH2

>CH3

CH2

CH =CH2

>CH2

=CH CH =CH2

(Heat of hydrogenation per-bond)

(D) > > (Heat of hydrogenation per-bond)

Q.46 In H6P6O18compound, how many atoms has sp3hybridization

(A) 20 (B) 18 (C) 24 (D) 22

Q.47 Calculate the mole ratio of C2H5OH to CH3OH in aqueous solution if molality of C2H5OH is 40/9 andmole fraction of CH3OH is 0.1 in solution.

(A) 0.33 (B) 0.66 (C) 0.24 (D) 0.45


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Q.48 Choose the correct statement :

(A) N

H

is less basic than CH3 N CH

|CH

3

3

. .

(B) is more stable than

(C)

is more basic than

(D) is nonaromatic


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SECTION-B

[MULTIPLE OBJ ECTIVE TYPE QUESTIONS]


Q.49 Which of the following ions are paramagnetic in nature -

(A) Fe+2 (B) Hg+2 (C) Sc+3 (D) Ti+3

Q.50 Select the correct statement(s)(A) Volume of gas is always equal to volume of container(B) Boyle's temperature is 3.375 times of critical temperature(C) Critical pressure is the maximum pressure at which gas can be liquified at critical point(D) At critical temperature value of compressibility factor for van der Waal gas is always 3/8

Q.51 In which of the following pair, first compound is more basic than second.

(A)

NMe2

Meand

NH2

Me(B)

NH2

NO2and

NH2

(C)

NH2

CH3and

NH2

(D)

NH2

and

NH2

CCl3

Q.52 If photon having wave length 6.2 nm was allowed to strike a metal plate having work function 50eVwhich of the following is/are correct [Given hc =1240 eVnm]

(A) When accelerating potential is 10V is applied the KEmaxcan be 160 eV(B) KE of photo electron may be between 0 to 150 eV if no potential is applied(C) Stopping potential will be 150 volt.(D) If wavelength of photon increases the KE of photo electron will increase


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Paragraph for questions Nos. 53 to 5410 moles of pure PCl5gas is put into a closed container of volume 'V' and temperature 'T' and allowedto come at equilirbium, at an equilibrium pressure 20 atm. The pure PCl5is found to be 50% dissociatedat equilibrium PCl5(g) PCl3(g) +Cl2(g)

Q.53 Kpfor the above reaction is (in atm.)(A) 20/3 (B) 100 (C)10/3 (D) 20/6

Q.54 By Changing the volume if equilirbium is restablished, then the partial pressure of PCl5 is, if newequilibrium pressure is 35 atm(A) 10 atm (B) 15 atm (C) 18 atm (D) 12 atm

Paragraph for questions Nos. 55 to 56

Consider the following compound and answer the questions given below:

HO

NH2

COOH

NH2

HO S3NH2

p

r

b

s

c

q

a

dNHMe

Q.55 Which of the following is correct order of acidic strength(A) q >r >p >s (B) q >r >s >p (C) r >q >p >s (D) r >p >q >s

Q.56 Which of the following is correct order of basic strength(A) d >b >c >a (B) a >b >c >d (C) d >a >b >c (D) d >c >b >a


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SECTION-D

[INTEGER TYPE QUESTIONS]


Q.57 How many compounds has non zero dipole moment-

CCl4, CH

2Cl

2, BF

3, XeF

4,6PCl ,

46XeO , XeO3, BH2

, 5XeF

Q.58 A solution of solute 'y' contains 20% 'y' by weight of solution. 400 g of this solution was cooled when38 g of solute gets precipitated. Now 100 g of solvent is added. Calculate the mass % of solute in newsolution(Fill your answer by multiplying it with 1/2)

Q.59 PCl5dissociates according to the reaction, PCl5(g) PCl3(g) +Cl2(g)

The density of equilirbium mixture at 1 atm and 5C is 6.25 gm/l, then calculate the value of Kpfor the

dissociation at this temperature. [Given R =0.08] Fill your answer by multiplying it with '3'Q.60 Consider the following pair(s) of compound(s) and find the relationship between them:

(A) C O CH3||O

and C OH||O

H C3

(B) and (C) and

Write (1) If the compounds are chain isomer

(2) If the compounds are position isomer (3) If the compounds are functional group isomer

(4) If the compounds are ring chain isomer (5) If the compounds are metamers

Give the answer in 1 digit (sum) for example if answer of (A) is 1, (B) is 2 and (C) is 3, then

fill 6 {1 +2 +3}in the OMR sheet

IIT-JEE sample test paper for class XI

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