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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 32 pages having 22 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 wri te these

anywhere else.

C. Question paper format and Marking Scheme :

10. The question paper consists of 3 parts (Part -1 : Mathematics, Part -2 : Physics, Part-3 : Chemistry).

Each part has four section.

11. SECTION I (TOTAL MARKS : 45)

(i) For each Single Correct Choice Type (Total Marks : 24)question of SECTIONI , you will beawarded 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 Linked Comprehension Type (Total Marks : 9)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 : 8)

For Matrix Match Type(Total Marks : 8)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 : 16)

For each Integer Answer Type (Total Marks : 16)question of SECTIONIII, you will be awarded

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

is darkened. There is No negative marking .

14. SECTION IV (TOTAL MARKS : 12)

For each Integer Answer Type (Total Marks : 12)question of SECTIONIV, you will be awarded

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

is darkened. There is No negative marking .

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

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

INSTRUCTIONS

PAPER 1Time : 3 Hours Maximum Marks : 243

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.allen.ac.in E1/32

MEDIUM : ENGLISH

IIT EE

NURTURE COURSEPHASE : [TP, TJ & TK]

TARGET : IIT-JEE 2013

TM

Path to success KOTA (RAJASTHAN)

TYPE : MAJOR

DATE : 18 - 02 - 2012

TEST#03

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Space for Rough Work

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PART1 : MATHEMATICS

SECTION I (Total Marks : 45)

Single Correct Choice Type (Total Marks : 24)

Single Correct Choice Type contains 8 multiple choice questions. Each question has 4 choices (A),

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

1. Period of (x) = {x} +1 2

x x3 3

+ + +

is equal to (where {.} denotes fractional part function)

(A) 1 (B)2

3(C)

1

2(D)

1

3

2. If 10C3+ 2.10C2+

10C1= xCy, then maximum value of (x + y) is equal to -

(A) 15 (B) 221 (C) 439 (D) 21

3. The minimum value of a6+ a4+ a2+ 128 + a2+ a4+ a6, a > 0 is equal to -

(A) 14 (B) 128 (C) 134 (D) 256

4. The sum of the length of intervals in which

2

2 4

3 6

1 x x

(x) 1 x x 0

1 x x

= < , is (where x [ 5,5] - )

(Length of interval (a, b) is b a)

(A) 1 (B) 2 (C) 3 (D) 7/2


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5. In DABC, if a2cos2A = 2b2+ 2c2 a2, then A belongs to -

(A) 0,6

p

(B) ,6 4

p p

(C) ,4 2

p p

(D) ,2

p p

6. The number of values of x [0, 2p] satisfying the equation 2sin2x + sinx cosx + 1 = 0, is/are

(A) 1 (B) 2 (C) 3 (D) 4

7. If Cr=99C

r, then the value of 35 36 67 68 83 84 91 92 95 96 97 98

36 68 84 92 96 98

C C C C C C C C C C C C

C C C C C C

+ + + + + ++ + + + + is

(A)6

r

r 1

162

9 =(B)

7r

r 1

162

9 =(C)

6r

r 0

252

16 = (D)

5r

r 0

252

16 =

8. The vertices of a triangle are (1,3), (2cosq, 3sinq) and (2sinq, 3cosq), then the locus of centroid of

the triangle is -

(A) (3x + 1)2+ 4(y 1)2= 8 (B) (3x + 1)2+ 4(y + 1)2= 2

(C) (3x 1)2+ 4(y 1)2= 8 (D) (3x + 1)2+ 4(y + 1)2= 8

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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.

9. Consider the function (x) = exand g(x) = sin1x, then which of the following is/are necessarily true.

(A) Domain of go = Domain of (B) Range of go Range of g

(C) Domain of go is (, 0] (D) Range of go is , 02

p -

10. For a positive integer n, if the expansion of

n

7 3xx

-

has a term independent of x, then n can be -

(A) 8 (B) 12 (C) 16 (D) 24

11. If1 1 12 tan ( 3 2 2 ) sin

6 2

- - a = - + - ,

( )1 11

cot 3 2 sec ( 2)8

- -b = - + -

&

1 11 1

tan cos2 3

- -

g = + , then

(A) a = b (B) a + b= 3g (C) 4(b - g) = a (D) b = g


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Linked Comprehension Type (Total Marks : 9)

Linked Comprehension Type contain 1 paragraph. Based upon 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 12 to 14

Let the function :23x 9x 183 , [3 , ); (x) (3sgn x)

2a - + =

and g : R [b, g]; g(x) = cos2(2x) + cos3(2x) be two onto functions.

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

12. The number of solution(s) of the equation1 1

|x|

1

sin ( ) sin ( 1)e 3

tan (tan(1 ))

- -

-

b + g -- =

+ bgis -

(A) 1 (B) 2 (C) 3 (D) 4

13. The value of ( )( )( )1 2sin cos log 4 44- a - is -

(A)3

p(B)

2

p(C) 0 (D) 1

14. The incorrect statement for the function h(x) = (x).g(x) is -

(A) h(x) is many-one (B) h(x) is not periodic

(C) h(x) is neither even nor odd (D) h(x) is invertible in its domain.


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SECTIONII : (Total Marks : 8)

(Matrix-Match Type)

This Section contain 1 question. 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) The number of possible ordered pairs of form (x, y) of the (P) 2

equation 1 + x2 + 2sin(sin1x).sin(cot1y) = 0 is (Q) 1

(B) The value of 1 14 2

k 1

1 2kcos cos tan tan

2 3 k k 2

- -

=

p - + + + + is (R) 0

(C) If 2sin1x=

( )1 2sin 2x 1 x--p - - in 1 2x [k ,k ] , then the value of (S) 1

2 1( 2k k )+ is (T) 3

(D) The number of integers in the range of the function

( )1 24 /3(x) sin log (x x 1)-= + +


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SECTIONIII : (Total Marks : 16)

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. Line L 3x + 4y + c = 0 has two distinct points A and B from which pair of perpendicular tangents

are drawn to the circle x2+ y2+ 2x + 2y = 0, then total number of possible integral values of 'c'

is

2. Let a1, a2, a3, ...... anare in sequence such thatn

rr 1

n(n 1)(n 2)a

3=

+ += and

10

r 1 r

1 p

a q== , where p and

q are co-prime numbers, then value of p + q is


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3. Sachin moves from A(2,0) to B(0,b) to C(10,c) to D(9,5) along a linear path. If minimum distance

travelled by Sachin is 'd', then value of d2 is

4. N is number of ways in which all the letters of the word 'SATAYPAL' are arranged such that all the

words begin with A and no two A's are consecutive, then value ofN

2is


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SECTIONIV : (Total Marks : 12)


This Section contains 3 questions. The answer to each of the question is a single digit integer, ranging


1. The number of solutions of 2 x 2x 110 3

log 7 log 7+ += is

2. If a + b=4

pand a + g=

2

p, where a, b, g 0,

2

p

, then number of integral value(s) in range

oftan tan

tan tan

a + ba + g

is

3. Let a, b are real roots of equation x2 + ax + 4 = 0 and g, d are real roots of equation

x2+ bx + 3 = 0 such thata g

=b d

. Ifa m

b n= (where m and n are coprime numbers), then value

of |m n| is


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PART-2 : PHYSICS




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

1. A particle is oscillating simple harmonically with angular frequency wand amplitude A . It is at a point

(A) at certain instant (shown in figure). At this instant it is moving towards mean position (B). It takes

time t to reach mean position (B). If time period of oscillation is T, the average speed between A and

B is

A B

m.p.

(A)sinA t

t

w(B)

cosA t

t

w(C)

sinA t

T

w(D)

cosA t

T

w

2. A particle is oscillating along x-axis. Its position with time t is given as x = A sinwt. This particle is now

observed by an observer who himself is oscillating along y-axis such that his position is given by

y = A cos wt. To this observer the particle will move along the path

(A) x = y (B) x2+ y2= 4A2 (C) x2+ y2= A2 (D) none of these


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3. A particle is projected at an angle qabove the horizontal with a speed u. After some time the direction

of its velocity makes an angle fabove the horizontal. The speed of the particle at this instant is

(A) cosu q (B)

cos

cos

u q

f (C)

sin

sin

u q

f (D) cosu f

4. A spherical shell rolls up an inclined plane, reaches some height, and then rolls down (without slipping

throughout these motions). The direction of the frictional force acting on the spherical shell are

(A) up the incline while ascending and down the incline descending.

(B) up the incline while ascending as well as descending.

(C) down the incline while ascending and up the incline while descending.

(D) down the incline while ascending as well as descending.

5. In the balance machine shown in the figure, which arm will move downward (assume string and the

pulley to be ideal)

2m

3m

m

4m

l l

\\\\\\\\\\\\\\\\\

(A) left (B) right

(C) remains stationary (D) Depends on ratio m/ l

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6. A small bob of mass m is suspended by a massless string from cart of the same mass m as shown

in the figure. The friction between the cart and horizontal ground is negligible. The bob is given a

small velocity V0in horizontal direction towards right. The maximum height attained by the bob is,

m

l

frictionless

surface

m

(A)0

22V

g(B)

0

2V

g(C)

0

2

4

V

g(D)

0

2

2

V

g

7. A block of mass m is oscillating on smooth surface between two light springs of spring constant k

separated by a distance l colliding elastically with the springs. If the velocity of the block is increased

by an external impulse when it is not touching either of the spring then time period

l

m

(A) Increases. (B) Decreases

(C) remains same. (D) Time period is independent of l


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8. A particle of mass m is released from a point A on a smooth fixed circular track as shown in the figure.

The particle is released from rest at t=0, then variation of normal reaction (N) on the particle with (q)

angular displacement from initial position is

AR

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

(A)

N

q

3mg

(B)

N

q

3mg

(C)

N

q

3mg

(D)

N

q

3mg


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9. A bead is connected at one end of an inextensible massless string whose other end is fixed to a fixed

cylinder. Cylinder does not rotate. The bead can move on a horizontal smooth surface. The bead is given

a velocity v0perpendicular to the string. The bead moves on a curve and consequently collides on the

cylinder after sometime. Then, before it collides :

v0

l

(A) Work done by string on the bead is positive.

(B) The average speed of the bead is v0.

(C) Angular momentum of bead about centre of cylinder remains conserved

(D) The tension in the string increases gradually.


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10. Two blocks A and B, each of mass m, are connected by an ideal spring of stiffness k and placed on a

smooth horizontal surface. A ball of mass m moving with a velocity v0strikes the block A and gets

embedded to it. Then,

v0

m m m

A Bk

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

(A) velocity of block A just after collision is v0/2

(B) velocity of block B just after collision is zero

(C) the maximum compression produced in the spring is 06mv

k

(D) the kinetic energy lost during collision is2

0

1

4mv

11. A block of mass m is placed on a planck of mass M and given velocity v0. Friction between planck

and ground is zero. The coefficient of friction between the block and plank ismand its value is suchthat block becomes stationary with respect to plank before it reaches the other end. Then

(A) the work done by friction on the block is negative

(B) the work done by friction on the plank is positive

(C) the net work done by friction is negative

(D) net work done by the friction is zero


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is correct.

Paragraph for question nos. 12 to 14

Two small balls of masses 12 kg & 6 kg respectively are attached by a spring of spring constant k = p2

N/m and natural length l=1

pm. Initially spring is compressed such that balls are almost touching

each other. Now they are projected at an angle 45 in the vertical plane towards right. At the time of

projection, line joining centres of the balls is horizontal.

12. Choose CORRECTstatement

(A) In flight, initially, the heavier ball will be lower than the lighter ball.

(B) In flight, initially, lighter ball will be lower than the heavier ball.

(C) The ball which was towards right initially will be lower in entire flight

(D) Both balls will remain at same horizontal level during entire flight.

13. The minimum speed of projection, so that the final energy of spring is equal to initial energy of spring

is(A) 102 m/s (B) 202 m/s (C)10 m/s (D)20 m/s

14. In the previous question, if spring breaks at highest position, the range of COM is

(A) 20 m (B) 40 m (C) 30 m (D) 80 m


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(Matrix-Match Type)






1. Column -I describes about bodies kept in an enviroment where temperature of air is T0.In all cases

area, mass & specific heat of each body is same.

Column-I Column-II

(A) Black body is placed in shade away from any radiation (P) Temp. is T0

and temperature at steady state is T1.

(B) Black body is placed in Sun light and temperature at (Q) Temperature

steady state is T2. is maximum

(C) Grey body is placed in shade away from any radiation and (R) Temperature is

temperature at steady state is T3. Greater than T

0.

(D) Grey body is placed in Sun light and temperature at steady (S) reflected energy is

state is T4

maximum

(T) Rate of convection

is maximum


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1. A calorimeter of negligible heat capacity contains 50 ml of water at 40C. The water cools to 35C in

50 minutes. The water is now replaced by another liquid of equal volume at 40C. The time taken (in

minute) for the temperature to become 35C under similar condition is [density of liquid = 0.8 (density

of water), specific heat of liquid = 0.5 (specific heat of water)

2. A thin ring of an alloy of inner diameter 20 cm and cross-sectional area 1 mm2, is heated until it easily

slides on a rigid cylinder of diameter 20.025 cm. [For the alloy : a= 105/C, Y = 400 GPa] when the

ring cools down, what is the tension (in N) in it?


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3. The two ends of a uniform thin rod of length 2R and of mass 2 kg can move without friction along

a vertical circular path of radius R. The rod is released from the vertical position (ab). Find the force

(in N) exerted by an end of the rod on the path when the rod passes the horizontal position(cd).

a

bcd

4. A rod AB (length L ) lying on a smooth horizontal surface is pulled by two horizontal forces 10F and

F as shown ( 2

3

LAP BQ= = ). If stress at P is S

Pand that at Q is S

Q. Find the value of

5Q

P

S

S

.

QPA B

10FF


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1. A thin rod of length 1m is fixed in a vertical position inside a train, which is moving horizontally with

constant acceleration 8 m/s2. A bead can slide on the rod, and friction coefficientms=0.5 and m

k=0.25.

If the bead is released from rest at the top of the rod, it will reach the bottom in t seconds. What is the

value of 12t2?

2. A small ball of mass m is connected by an inextensible massless string of length l = 2 meter with another

ball of mass M = 4m. They are released with zero tension in the string from a height h = 0.2 meter as

shown. After the release, the string becomes taut for the first time at5

nsec, then find the value of n. (All

collisions are elastic, assume only one collision takes place between the mass M and the ground).

M

m

h

l


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3. Two planks A and B of length 24 cm and 16 cm and mass 4 kg and 12 kg respectively are connected

by a frictionless, massless hinge as shown in the figure. Initially the system is at rest on a level,

frictionless surface. The plank A falls clockwise and finally comes to rest on the top of the plank B. What

is the displacement (in cm) of the hinge just after the two planks come into contact?

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

A

B


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PART-3 : CHEMISTRY




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

1. It is a data sufficiency problem in which it is to be decided on the basis of given statements whether

the given question can be answered or not. No matter whether the answer is yes or no.

Is the final pressure of a container, containing an inert gas is greater than initial pressure -

Statement-1 : Volume of a closed container is reduced to half of its initial volume

Statement-2 : Temperature is doubled.

(A) Statement-1- is alone sufficient

(B) Statement-2- is alone sufficient

(C) Both statement together are sufficient but neither statement alone is sufficient

(D) Statement-1- and 2 together are not sufficient

2. Which of the following structure is having same shape of SO32

(A) F2SeO (B) F2SeO2 (C) SO42

(D) SO23. Which of the following is most acidic :

(A)

(B)

(C)

(D)

4. In which reaction H2O

2acts as reducing agent -

(A) Ag2S + H

2O

2 2Ag + H

2S+ O

2(B) 2KI

+ H

2O

22KOH + I

2

(C) PbS + 4H2O

2PbSO

4+ 4H

2O (D) H

2O

2+

SO

2H

2SO

4


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5. Which molecule AX3, AX

4, AX

5, AX

6is most likely to have a trigonal bipyramidal structure if A

has no lone pair

(A) AX3

(B) AX5

(C) Both (A) and (B) (D) AX6

6. Identify most stable anion :

(A)

1

(B)

1

(C)

1

(D)

1

7. A container containing 16 mole of CH4& 12 1023atoms of He gas, after successive effusion steps

mole ratio of gases was found to be 1 : 1. The number of effusion steps are (Use NA

: 6 1023)

(A) 3 (B) 2 (C) 1 (D) 4

8. Which orbital fills completely immediately before the 4f?

(A) 6s (B) 5p (C) 5d (D) 4d

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9. Select correct statement(s) :

(A) orbitals having same principle quantum number do have same no. of total nodes.

(B) for 2s orbital number of maxima in radial probability distribution curve is 2.

(C) An orbital having non-planar angular node and 2 radial node, have priniciple quantum number 4

(D) fraction of molecules in range Umps

0.002 Umps

to Umps

+0.002 Umps

is lesser for O2than CH

4

at same temp.

10. Which of the following statement is/are false

(A) Lanthanum is the first element of lanthanides

(B) Actinium violates the Aufbaus principle

(C) Chromium violates the paulis exclusion principle

(D) Total 10 exchange are possible for d-electrons in Zn.

11. In which case Istcompound (cis isomer) has more dipole moment than 2ndcompound (trans isomer)

:

(A)Br Br

H HC C

(I)

Br

Br H

HCC

(II)

; (B)H3C CH3

H HC C

(I)

CH3

H3C H

HCC

(II)

;

(C)NC CH3

H HC C

(I)

CH3

NC H

HCC

(II)

; (D)Br C2H5

H HC C

(I)

C2H5

Br H

HCC

(II)

;


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is correct.

Paragraph for question nos. 12 to 14

Throughout the ancient history it is always being debated that "do we exist alone in universe",

"do aliens exist or not" ! Suppose in 2015 there will be an alien attack on our planet, and they have

more advanced technology and sophisticated weapon. To save earth and to design our weapons we

should know atomic model existing in aliens planet. ISROfind out that their atomic model follows

Bohr's postulates completely, except that they have Bohr's quantisation rule as mvr =nh

4. In a special

task force you are being choosen to answer these (for aliens planet).

12. Ratio of radius of fourth to third orbit for an atom will-

(A) 4/3 (B) 16/9 (C) 8/3 (D) 16/3

13. Energy difference between fourth & second orbit for H-atom -

(A)2.55

eV2

(B) 10.2 eV (C) 2.55 eV (D) 5.1 eV

14. Which transition in H-atom will result radiation in visible spectrum -

(A) 5 1 (B) 5 2 (C) 4 3 (D) None of these


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(Matrix-Match Type)






1. Match Column-I with Column-II.

Column-I (Compounds) Column-II (pKa)

(A) (P) 7.15

(B) (Q) 10.14

(C) (R) 9.98

(D) (S) 9.38

(T) pKa is more than phenol


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1. Calculate the % labelling of an oleum sample if mass fraction of H2SO

4 in the oleum is 0.6.

2. How many unpaired electron(s) is/are present in tripositive chromium ion.


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3. Total number of possible dichloro biphenyl systems are.

4. Find the number of acid(s) which are having hypo prefix in its name from the following.

H3PO4, H3BO3, H3PO3, H3PO2, HClO3, HClO, (HNO)2, H4P2O6


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1. Consider the reaction

N2(g) + 3H

2(g) 2NH

3(g)

How many of given changes will result in decrease in number of moles of N2gas initially present

at equilibrium in a closed vessel.

(1) increase in temperature.

(2) decrease in volume of container

(3) increase in total pressure

(4) addition of He gas at constant pressure

(5) addition of He gas at constant volume

(6) addition of H2gas in vessel at constnat volume

(7) removing some mole of NH3

(8) addition of N2gas

(9) decrease in total pressure.

2. How may SOS linkage in dithionous acid?

3. Total number of esters and acids possible for the compound having molecular formula C4H8O2.


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Name of the Candidate

I have read all the instructions and shall

abide by them.

Signature of the Candidate

Form Number

I have verified all the information filled

in by the Candidate.

Signature of the Invigilator


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