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DONOTBREAKTHESEALSWITHOUTBEING

INSTRUCTEDTODOSOBYTHEINVIGILATOR

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

A. General :

1. This Question Paper contains 36 pages having 19 questions in each subject.

2. No additional sheets will be provided for rough work.

3. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers, and electronic

gadgets in any form are not allowed to be carried inside the examination hall.

4. The answer sheet, a machine-readable Optical Response Sheet (ORS), is provided separately.

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

6. Do not break the seals of the question-paper booklet before being instructed to do so by the

invigilators.7. On breaking the seals, please check that all the questions are legible.

B. Filling the ORS :

8. A candidate has to write his / her answers in the ORS sheet by darkening the appropriate bubble

with the help of HB Pencilas the correct answer(s) of the question attempted.

9. Write your Form Number, Name & other details in the appropriate boxes. Do not write these

anywhere else.

C. Question paper format and Marking Scheme :

10. The question paper consists of 3 parts (Part1 : Mathematics, Part 2 : Physics, Part 3 : Chemistry).

Each part has three section.

11. SECTION I (TOTAL MARKS : 39)

(i) For each Single Correct Choice Type (Total Marks : 9)question of SECTIONI , you will be

awarded 3 marksif you have darkened only the bubble corresponding to the correct answer

and zero markif no bubble are darkened. In all other cases, minus one (1) markwill be awarded.

(ii) For each Multiple Correct Answer Type (Total Marks : 12) question of SECTIONI , you will

be awarded 4 marksif you have darkened only the bubble corresponding to the correct answer

and zero mark if no bubbles are darkened. There is No negative marking.

(iii) For each Linked Comprehension Type (Total Marks : 18)question of SECTIONI, you will

be awarded 3 marksif you darken only the bubble corresponding to the correct answer and

zero markif no bubble is darkened. In all other cases, minus one (1) markwill be awarded.12. SECTION II (TOTAL MARKS : 24)

For Matrix Match Type(Total Marks : 24)question of SECTIONII, you will be awarded 2 marks

for each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus,

each question in this section carries a maximum of 8 marks. There is no negative marksawarded

for incorrect answer(s) in this section.

13. SECTION III (TOTAL MARKS : 20)

For each Integer Answer Type (Total Marks : 20)question of SECTIONIII, you will be awarded

5 marksif you darken the bubble corresponding to the correct answer, and zero markif no bubble

is darkened. There is No negative marking.

14. Take g = 10 m/s2unless otherwise stated.

Write your Name, Form No. & Sign in the space provided on the back page of this booklet.

MEDIUM : ENGLISH

INSTRUCTIONS

IIT JEE

NURTURE COURSEPHASE : [TP, TJ & TK]

TARGET : IIT-JEE 2013

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Path to success KOTA (RAJASTHAN)

Time : 3 Hours Maximum Marks : 249

Corporate Office : ALLEN CAREER INSTITUTE, SANKALP, CP-6, INDRA VIHAR, KOTA-324005

PHONE : +91 - 744 - 2436001, Fax : +91-744-2435003, E-mail: [email protected] Website: www.a llen.ac.in E1/36

TYPE : SEMI-MAJOR

DATE : 14 - 02 - 2012

TEST#01

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Space for Rough Work

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PART1 : MATHEMATICS

SECTION I (Total Marks : 39)

Single Correct Choice Type (Total Marks : 9)

Single Correct Choice Type contains 3 multiple choice questions. Each question has 4 choices (A),

(B), (C) and (D), out of which ONLY ONE is correct.

1. Number of whole numbers in the range of 2 21

( )2sin 6cos 6sin cos

q =q + q + q q

, is

(A) 0 (B) 1 (C) 2 (D) more than 2

2. Let A(2, 3), B(7,6) & C(0, 0) are vertices of DABC. If P is a point such that area of DPAB, DPBC

& DPCA are equal, then coordinates of P are -

(A) (3, 3) (B) (2, 2) (C) (9, 9) (D) (4, 4)

3. In DABC, if angle A, B and C are in ratio of 1 : 1 : 2, then which of the following must be correct ?

(All symbols have usual meaning in a triangle).

(A) a : b : c = 1 : 1 : 2

(B) Area of triangle ABC2 2 2a b c

8

+ +=

(C) If B is origin and equation of the AC is 3x + 4y = 20, then area of DABC is 4.

(D) Circumradius of DABC = a.


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Multiple Correct Answer Type (Total Marks : 12)

Multiple Correct Answer Type contains 3 multiple choice questions. Each question has 4 choices (A),

(B), (C) and (D), out of which ONE OR MORE is/are correct.

4. Let a,dare roots of equation x2+ k1x 5 = 0 and b, gare roots of equation x2+ k2x + k3= 0. If a, b,

g & dare in A.P., then which of the following is/are correct -

(A) k1= k2 (B) If k3= 3, then |a + b + g + d| = 8

(C) a + b + g + d= 2k1 (D) a + b + g + d= 2k3

5. Let n(q) =3 5 7

2sin sin 2sin sin 2sin sin ...... 2sin sin(2n 1)2 2 2 2 2 2 2 2

q q q q q q q q+ + + + + , n N, then which

of the following is/are correct ?

(A) 91

4 2

p =

(B) n2

0, n Nn

p =

(C)5

20

7

p =

(D) 91

4 2

p = -

6. Consider an infinite G.P. whose first term is minimum value of (x) = 16sec2x + 9cos2x and common

ratio is maximum value of g(x) = x x2

1

2 . Then sum of this infinite G.P. will be greater than

(A) 15 (B) 20 (C) 18 (D) 25

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Linked Comprehension Type (Total Marks : 18)

Linked Comprehension Type contains 2 paragraphs. Based upon each paragraph, 3 multiple choice

questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY

ONE is correct.

Paragraph for Question 7 to 9

Circle C1is x2+ y2= 9. From a point P(4, 0) two distinct tangents PA & PB are drawn to the circle

C1such that A & B lie on circle C1. C2is another circle circumscribing DPAB.

On the basis of above information, answer the following questions :

7. If m1& m2are slopes of PA & PB, then 14

2 2

1 2(m m )+ equals -(A) 21 (B) 28 (C) 36 (D) 42

8. Locus of centre of a variable circle which cuts C1& C2orthogonally is -

(A) x = 9 (B) x = 9/4 (C) x = 4 (D) x = 1

9. A circle C3touches line y = 4 at (0, 4) and passes through centre of circle C2. Then y-intercept of circle

C3is -

(A) 6 (B) 17 (C) 4 (D) 5


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Line x+y = k intersects the circle C1 : x2+ y2 2x 2y = 0 at A & B. Circle C2 has its center

at (2, 1).

On the basis of above information, answer the following questions :

10. Which of the following is correct ?

(A) If chord AB subtends an acute angle at origin, then k > 2.

(B) If chord AB subtends an obtuse angle at origin, then k > 0.

(C) If chord AB subtends an obtuse angle at origin, then k (0, 2)

(D) If chord AB is of maximum length, then k = 1

11. If circle C1& C2cut each other orthogonally, then power of origin with respect to C2is

(A) 12 (B) 6 (C) 5 (D) 8

12. If p = power of origin with respect to C2in Q.11and logp(b2+ 1) = 1, then sum of absolute values of

bis

(A) 2 11 (B) 4 (C) 2 5 (D) 0

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SECTIONII : (Total Marks : 24)

(Matrix-Match Type)

This Section contain 3 questions. Each question has four statements (A, B, C and D) given in

Column Iand five statements (P, Q, R, S and T) in Column II. Any given statement in Column I can

have correct matching with ONEor MORE statement(s) given in Column II. For example, if for a given

question, statement B matches with the statements given in Q and R, then for the particular question,

against statement B, darken the bubbles corresponding to Q and R in the ORS.

1. Column-I Column-II

(A) Value of ab

2

c +

1 1

b ac+ (where a > 0, b > 0, c > 0) can be (P) 0

(B) If2 3

3 4 5S 2 ......

3 3 3= + + + + , then S is greater than (Q) 1

(C) Two mutually perpendicular lines passing through origin (R) 2

form an isosceles triangle with line 2x + y =5

2. (S) 3

Then area of triangle is greater than (T) 4

(D) If1 1 1

K ......1.4 4.7 7.10

= + + + , then 12K is greater than

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(A) If 6tan(a - b) = 5tan(a + b), thensin2

sin2

ab is (P) 10

(B) Number of solution(s) of the equation sin2q 2cosq= 0 (Q) 11

in the interval [0, 12p] is/are (R) 12

(C) If one member L1of the family of lines (S) more than 10

x(1 + 2k) + y(1 + k) = (18k + 12) has equal (T) less than 10

non-zero intercepts, then x intercept of L1 is

(D) If1 sin sin

10 sin 1 sin

sin sin 1

- q qa = q q

q q

, then maximum value

of a is

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(A) If angle between pair of tangents drawn from (k, 0) (P) 3

to circle x2 + y2= 16 lies in the range ,3

p p

(Q) less than 5

then number of possible integral values of |k| is (R) more than 2

(B) Families of lines represented by equation (S) 4

x + cy = 2 + c are concurrent at P(a, b). (T) 5

Then (a + b) is

(C) Distance of line x + 3y = 17 from point P(5,1)

measured parallel to the line 4x + 3y = 0, is

(D) If length of tangent from P(k, 0) to the circle

x2 + y2= 8 is equal to radius of circle, then |k| is


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SECTIONIII : (Total Marks : 20)

Integer Answer Type (000 to 999)

This Section contains 4 questions. The answer to each of the question is a three digit integer, ranging

from 000 to 999. The bubble corresponding to the correct answer is to be darkened in the ORS.

1. If x, y3

0,2

p , then the number of possible ordered pairs (x, y) which satisfies the system of equation

2 2sin x cos y 1-p = and2

2

4 cos x

4 cos y

39

3= , is

2. In an acute angled triangle ABC, with usual notations, if a = 3, b = 4 and area of the triangle is 3 3 ,

Then 3R2equals

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3. The number of solutions of the equation cos22x sin24x =1

cos6x3

- lying in the interval (0,p) is

4. If radius of the circle touching the curve y = cot(cot1(x)) at (0,0) and passing through (3,1) is r, then

(4r2) equals

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PART2 : PHYSICS



Single Correct Choice Type contains 3 multiple choice questions. Each question has 4 choices (A),

(B), (C) and (D), out of which ONLY ONEis correct.

1. The wave function of a triangular wave pulse is defined by the relation below at time t = 0 sec .

02

( )2

0 , where m

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4. The energy of a particle executing simple harmonic motion is given by E = Ax2+ Bv2where x is the

displacement from mean position x =0 and v is the velocity of the particle at x then choose the

CORRECT statement(s).

(A) Amplitude of SHM is2E

A

(B) Maximum velocity of the particle during SHM isE

B

(C) Time period of motion is 2 B

Ap

(D) Displacement of the particle is directly proportional to the velocity of the particle.

5. Consider a travelling simple harmonic wave on a string of mass per unit length mand tension T. Kinetic

energy per unit length is given by m

=

21

2ku

tand potential energy per unit length is given by

21

2pu T

x

= . Mark the CORRECToption(s).

(A) Power transmitted by wave equals (uk+ u

p)

m

T.

(B) ukand u

psimultaneously attain their maximum and minimum values.

(C) Total energy per unit length of a string is constant when a harmonic wave travels on it.

(D) A small part of string has maximum potential energy when it is at its equilibrium position.

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6. A ball of mass m is suspended from a uniform elastic wire of negligible mass, having cross-section

diameter d, length l, Youngs modulus Y and heat capacity C. Now, when the ball is snapped

then

(A) initial elongation of wire is 24mg

Y dpD =

ll

(B) initial elongation of wire is 22mg

YdpD =

ll

m

l

(C) increase in the temperature of wire is qp

D = l2 2

2

m g

CY d

(D) increase in the temperature of wire is

2 2

22m gCY d

qp

D = l


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ONEis correct.


A 700 g teapot and an insulated thermos are in a 30C room. The teapot is filled with 1000 g of the boiling

tea. The brewed tea is allowed to cool to 80C, then 360 g of the tea is poured from the teapot into the

thermos. The teapot is then kept on an insulated warmer that transfers 300 cal/min to the tea. Assume

that the specific heat of brewed tea is the same as that of pure water. The specific heat of teapot is

0.17 J/g K and that of water is 4.18 J/g K. The entire procedure is done under atmospheric pressure.

There are 4.18 J in one calorie.

7. After the tea is added to the thermos, the temperature of the liquid quickly falls from 80C to 75C as

it reaches thermal equilibrium with the thermos flask. What is the heat capacity of the thermos?

(A) 95 J/K (B) 160 J/K (C) 167.2 J/K (D) 170.2 J/K

8. An alternative method for keeping the tea hot would be to place the teapot on a block that has been heated

in an oven to 300C. Which of the following substances would be best able to keep the tea hot?

(A) copper block (specific heat = 0.39 J/g K, mass 10 kg)

(B) granite (specific heat = 0.79 J/g K, mass 5 kg)

(C) iron (specific heat = 0.45 J/g K, mass 20 kg)

(D) pewter (specific heat = 0.17 J/ g K, mass 30 kg)

9. If, after some of the tea has been transferred to the thermos (as described in the passage), the teapot with

its contents (at a temperature of 80C) was placed on the insulated warmer for 10 minutes, what would

be the temperature at the end of this 10 minute period?

(Assume that no significant heat transfer occurs with the surroundings)

(A) 84.5 C (B) 87.5C (C) 83.2C (D) 81.07C


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A wave represented by equation y = 2(mm) sin [4p(sec1)t2p(m1)x] is superimposed with another wave

y = 2 (mm) sin [4p(sec1)t+2p(m1)x + p/3] on a tight string.

10. Phase difference between two particles which are located at x1= 1/7 and x

2= 5/12 is

(A) 0 (B)5

6

p(C) p (D)

5

3

p

11. Which of the following is not a location of antinode?

(A)2

3(B)

11

12(C)

5

12(D)

7

12

1

12. The location having maximum potential energy is

(A) 1/7 (B) 1/6 (C) 5/12 (D) 23/12


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(Matrix-Match Type)


Column Iand five statements (P, Q, R, S and T) in Column II. Any given statement in Column I can

have correct matching with ONEor MORE statement(s) given in Column II. For example, if for a given

question, statement B matches with the statements given in Q and R, then for the particular question,

against statement B, darken the bubbles corresponding to Q and R in the ORS.

1. A co pper rod (ini ti ally at room temperatu re 20C) of non-uniform cross section is placed

between a steam chamber at 100C and ice-water chamber at 0C. A and B are cross sections as shown

in figure. Then match the statements in Column-I with results in Column-II using comparing only

between cross section A and B. (The mathematical expressions in Column-I have usual meaning in

heat transfer).

0

Ice water

chamber

100

Steam

chamber

A B

Column-I Column-II

(A) Initially rate of heat flowdQ

dt

will be (P) maximum at section A

(B) At steady state rate of heat flowdQ

dt

will be (Q) maximum at section B

(C) At steady state temperature gradientdT

dx

will (R) minimum at section A

(D) At steady state rate of change of (S) minimum at section B

temperature at a certain point will be (T) Same for all section


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2. A sample A of liquid water and a sample B of ice of equal mass are kept in 2 nearby containers so that

they can exchange heat with each other but are thermally insulated from the surroundings. The graphs

in column-II show the sketch of temperature T of samples versus time t. Match with appropriate

description in column-I.

Column I Column II

(A) Equilibrium temperature is above melting (P)

T

t

point of ice.

(B) At least some of water freezes. (Q)

T

t

(C) At least some of ice melts. (R)

T

t

(D) Equilibrium temperature is below (S)

T

t

freezing point of water

(T)

T

t

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3. In a string a standing wave is set up whose equation is given as y = 2A sin kx cos wt. The mass per unit

length of the string is m.

Column-I Column-II

(A) at t = 0 (P) Total energy per unit length at x= 0 is 2mA2w2.

(B) atT

t8

= (Q) Total energy per unit length at x= l/4is 2mA2w2.

(C) atT

t4

= (R) Total energy per unit length at x= l is 2mA2w2.

(D) atT

t2

= (S) power transmitted through a point at x= l is 0.

(T) power transmitted through a point at x= l/4 is 0.


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SECTIONIII : (Total Marks : 20)




1. A container (water equivalent of container is negligible) contains 50 gm of water at 0C. If H amount

of heat is extracted per second from water and keeping the spray closed, then whole water freezes in

10 sec. I f spray is also working and sprays the water with 2 gm/sec at 0C, then water f reezes in t1second

keeping the rate of extraction of heat from water same. Then calculate 6t1. (Latent heat capacity of

ice = 80 cal/gm)

2gm/secspray

water(0C, 50gm)

H.cal/sec.

2. A liquid of volumetric thermal expansion coefficient 200 106/C and bulk modulus = 1.2 109Pa

is filled in a spherical tank of negligible heat expansion coefficient. Its radius is 25 cm and wall thickness

is 2 mm. When the temperature of the liquid is raised by 20 C, find the tensile stress developed (in MPa)

in the wall of the tank ?


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3. A cylinder of radius R made of material of thermal conductivity K is surrounded by a cylindrical shell

of inner radius R and outer radius 2R made of material of thermal conductivity 9K [see fig.]. The two

ends of the combined system are maintained at different temperatures. The cylinder is well lagged and

the system is in steady state. The effective thermal conductivity of the composite cylinder of radius 2R

is xK. Find the value of x.

4. 36 kcal are spent in heating a copper block which weighs 1 kg and is at 0C initially. What is the final

volume of the block (in cc)? gcopper

= 5 105/C, rcopper

at 0C = 10 gm/cc,

specific heat of copper = 0.09 cal/gmC.


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PART3 : CHEMISTRY



Single Correct Choice Type contains 3 multiple choice questions. Each question has 4 choices (A), (B),

(C) and (D), out of which ONLY ONEis correct.

1. The percentage by volume of C3H8in a mixture of C3H8, CH4and CO is 36.5. Calculate the volume

of CO2produced when 100 mL of the mixture is burnt in excess of O2.

(A) 173 mL (B) 106.5 mL (C) 206.5 mL (D) 156.5 mL

2. The observed dipole moment of HI is 0.38D. Calculate the percentage ionic character of the HI bond

if bond distance 1.61.

(A) 16.4 % (B) 12 % (C) 5% (D) 20%

3. Which compound is most basic in nature

(A)

NH2

(B)

NH

(C)

NH2

(D)

NH


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4. Which statement is/are correct for postulates of kinetics theory of gases -

(A) Gases are composed of molecules whose size is negligible compared with the average distance

between them

(B) Molecules moves randomly in straight lines in all directions and at various speeds.

(C) When molecules collide with one another the collisions are elastic. In an elastic collision the loss

of kinetic energy takes place

(D) The average kinetic energy of a molecule is proportional to the absolute temperature.

5. Which of the following molecule(s) is/are having see-saw geometry -

(A) TeBr4 (B) BrF5 (C) XeO2F2 (D) SeCl4

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6. What is the correct order of stability of following carbocation ?

(A)C+

> H2C+ > CH2 CH3

+> CH3

+

(B) CH2 CH2 CH2 CF3+

> CH2 CF3> CF3+ +

(C)OO

>

O

> > >

+ + + + +

(D)

CH2

CH3

+

>

CH2

CD3

+

>

CH2

CT3

+


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ONEis correct.


Hydrogen bond is an important aspect of chemical bonding. It is formed in the molecule where

hydrogen is attached with highly electronegative atom. There are a number of consequences of

hydrogen bonding.

7. The stickiness of honey which mainly consists of water and sugar is due to -

(A) Presence of sugar (B) Strong bonding in sugar

(C) Hydrogen bonding (D) Presence of some organic compound

8. In which of following compound does not have H-bonding -

(A) K2HPO4 (B) K2HPO3

(C) Chloralhydrate (Cl3CCH(OH)2) (D) H2O

9. The strength of H-bonding order is -

(A) H2O > H2O2 > HF (B) H2O2> H2O> HF

(C) HF > H2O> H2O2 (D) HF = H2O = H2O2


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CH2= CH CH2 H undergoes hyperconjugation process.

CH = CHCH H H CCH = CH H2 2 2 2+

2 more hyperconjugative structure

1

More is the no. of ahydrogen, more is the no. of hyperconjugative structures, more is the stability

of ethene.

C+also undergo hyperconjugation.

H H2C CH2H

+CH2= CH22 more H.S.

10. Which of the following alkene have 9 a-hydrogens.

(A) H2C = CCH3

CH3(B) H3CCH = C

CH3

CH3

(C) (D)

11. Which carbocation is most stable ?

(A) C+ (B) C

+

H

(C) H2C+

(D) CH3+

12.

CH3

Toluene when undergoes hyperconjugation the hyperconjugative structure is -

(A)

C H+H H

(B)

C H+H H

(C)

C HH H

(D)

C HH H


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(Matrix-Match Type)


Column Iand five statements (P, Q, R, S and T) in Column II. Any given statement in Column I can have

correct matching with ONEor MORE statement(s) given in Column II. For example, if for a given

question, statement B matches with the statements given in Q and R, then for the particular question, against

statement B, darken the bubbles corresponding to Q and R in the ORS.


Molar ratio of oxidising agent to Redox reaction

reducing agents in which they reacts

(A) 3 : 1 (P) MnO4+ C2O4

2 MnO2+ CO2

(B) 2 : 3 (Q) ClO2+ H2O2

Cl+ O2

(C) 1 : 1 (R) N2H4+ Cu(OH)2 N2O + Cu

(D) 2 : 1 (S) CrO42+ H2S+ Cr3++ SO2

(T) H2O2+ H2C2O4 H2O + CO2


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2. Match the column -

Column-I Column-II

(A) sp3

d

hybridised central atom (P) BF3

(B) sp3d2 hybridised central atom (Q) H3PO2

(C) sp2 hybridised central atom (R) S3O

9

(D) sp3 hybridised central atom (S) ClF3

(T) XeO64


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3. Match the column :

Column-I Column-II

(A)

CO2H

(P) Soluble in NaOH

(B)

OHNO2

NO2

(Q) Reacts with Na

(C)

OH

(R) Soluble in NaHCO3

(D)

O3H

(S) Aromatic

(T) Any group attached with benzene ring

show I and R simultaneously.


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SECTION III (Total Marks : 20)




1. A sample of H2SO4(density 1.8g/mL) is 98% by weight. What is the volume (in mL) of acid that has

to be used to make 1 Litre of 0.216M H2SO

4solution -

2. Find the number ofClAlCl angle in [AlCl4].

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3. An aq. solution of 0.5M KMnO4is divided into two parts. One part of it requires 125 ml of 1.5M aq.

solution of oxalate ions in acidic medium, while another part requires 270 ml of 0.5M aq. solution of

iodide ions in neutral medium which are converted into I2

only. Calcualte total volume (mL) of the initial

KMnO4solution.

4. Calculate the value of xin the following arrangement.

x cm

16 cm

30

Vacuum

Hg

Hg


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