seals · 2015. 12. 21. · 1. the figure shows a potentiometer arrangement. d is the driving cell,...

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

A. General :1. This booklet is your Questions Paper. Do not break the seals of this booklet before being instructed

to do so by the invigilators.2. Blank spaces and blank pages are provided in this booklet for your rough work. No additional

sheets will be provided for rough work.3. Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers,

and electronic gadgets are NOT allowed 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. On breaking the seals of the booklet check that it contains 30 pages and all the 17 questions

in each subject and corresponding answer choices are legible. Read carefully the instructionsprinted at the beginning of each section.

B. Filling the ORS :7. A candidate has to write his / her answers in the ORS sheet by darkening the appropriate bubble

with the help of Black ball point pen as the correct answer(s) of the question attempted.8. Write your Name, FNO and sign with pen in the boxes provied on part of the ORS. Do not write

any of this information anywhere else.

C. Question Paper Format :9. The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of

three sections.10. SECTION – I

(i) In this part of section – I contains 6 multiple choice questions. Each question has four choices(A), (B), (C) and (D) out of which ONE or MORE are correct

(ii) In this part of section – I contains 3 paragraphs each describing theory, experiment, data etc.There are 6 multiple choice questions relating to three paragraphs with 2 questions on eachparagraph. Each question of a particular paragraph has four choices (A), (B), (C) and (D) outof which is ONLY ONE is correct

11. SECTION – II contains 1 question of Matrix Match Type.12. SECTION – IV contains 4 questions. The answer to each question is a single digit integer,

ranging from 0 to 9.

D. Marking scheme :13. For each question in Section – I (i), you will be awarded 4 marks if you darken the bubble

corresponding to the correct answer ONLY. In all other cases, zero(0) marks will be awarded.No negative marks will be awarded for incorrect answers in this section.

14. For each question in Section – I (ii), you will be awarded 3 marks if you darken the bubblecorresponding to the correct answer ONLY and zero marks if no bubbles are darkened. In allother cases, minus one (–1) mark will be awarded in this section.

15. For question in Section – II, you will be awarded 2 marks for each row in which you havedarkened the bubble(s) corresponding to the correct answer. Thus, each question in this sectioncarries a maximum of 8 marks. There is no negative marking for incorrect answer(s) for thissection.

16. For each question in Section – IV, you will be awarded 4 marks if you darken ALL the bubble(s)corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded.No negative marks will be awarded for incorrect answers in this section.

17. Take g = 10 m/s2 unless otherwise stated.

INSTRUCTIONS

PAPER – 2Time : 3 Hours Maximum Marks : 198

MEDIUM : ENGLISH

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

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Note: In case of any correction in the test paper, please mail to [email protected] within 2 days

along with Your Form No. & Complete Test Details.

LEADER & ENTHUSIASTCOURSE

TARGET : JEE 2013 DATE : 13 - 04 - 2013

SCORE : TEST # 01

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USEFUL DATA

Atomic No. H = 1, B = 5, C = 6, N = 7, O = 8, F = 9, Al = 13, P = 15, S = 16, Cl = 17,

Br = 35, Xe = 54, Ce = 58,

Atomic masses : H = 1, Li = 7, B = 11, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24,

Al = 27, P = 31, S = 32, Cl = 35.5, Ca=40, Fe = 56, Br = 80, I = 127,

Xe = 131, Ba=137, Ce = 140,

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PHYSICS

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PART-1 : PHYSICSSECTION–I

(i) Multiple Correct Answer(s) Type

This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and

(D) out of which ONE or MORE are correct.

1. The figure shows a potentiometer arrangement. D is the driving cell, C is the cell whose e.m.f. is to be

determined. AB is the potentiometer wire and G is a galvanometer. J is a sliding contact which can

touch any point on AB. Which of the following are essential conditions for obtaining balance ?

J

GC

A B

D

(A) The e.m.f. of D must be greater than the e.m.f. of C

(B) The positive terminals of D and C both must be joined to A

(C) The resistance of G must be less than the resistance of AB

(D) Resistance of wire AB should be very small

2. Consider an isolated charged capacitor A dielectric slab is introduced so as to completely fill the space

of capacitor. Mark the CORRECT statement.

(A) Energy of capacitor decreases

(B) Energy of capacitor increases

(C) Field due to charges on capacitor plates inside dielectric material remains unchanged

(D) Potential difference between plates decreases

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

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3. Mark the CORRECT statement :-

(A) Virtual image of virtual object can be formed by a single optical element

(B) Virtual image of virtual object formed by a single optical element can be inverted

(C) Virtual image of real object can be formed by a single optical element

(D) Virtual image of real object formed by a single optical element can be inverted

4. A dielectric slab of relative permittivity r and thickness t is inserted into the capacitor. Then

r

t

d

+ –

(A) the capacitance of the system increases by 0

r

A

1t 1

(B) free r

bound r

q

q 1

(C) the fraction change in the energy stored is r – 1

(D) the plates are moved apart by a relative distance r

1t 1

to recover the original energy stored

(or original capacitance)


PHYSICS

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5. An object of length 1 mm is placed on a principle axis of an equi-convex lens of radii 5 cm. Distance

between the lens and object is 20 cm. Space between the lens and object is filled with medium of two

different refractive index 2 and 1, lens being placed in the medium of refractive index 1. Boundary

of both medium is mid-way between the object and lens as shown in figure.

10cm10cm

=2 =11.5

=11mm

(A) The image will be formed at distance of 7.5 cm from the optical centre

(B) The image will be formed at distance of 20/3 cm from the optical centre

(C) The size of the image is 0.5 mm

(D) The size of the image is 0.4 mm

6. A parallel-plate capacitor having plate area A and separation between plates 'd' is connected to a battery

of emf 'V'. The plates are pulled apart to increase the separation to '2d'. Choose the correct option(s) :-

(A) Charge flow through the circuit during the process is 0AV

2d

(B) Charge flow through the circuit during the process is zero

(C) Energy released by the battery in this process is 2

0AV

2d

(D) Energy absorbed by the battery in this process is 2

0AV

2d


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(ii) Paragraph Type

This section contains 6 multiple choice questions relating to three paragraphs with two questions

on each paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE

is correct.

Paragraph for Questions 7 & 8

The Tolman-Stewart experiment. In 1917, the American physicists Tolman and Stewart performed an

experiment that gives direct support to the view that (1) the charge carriers (free electrons) each heaving

mass m and charge q in metals (2) these charge carriers really do act something like the molecules of a

gas. The apparatus is shown below. An insulated metal wire of length L is wound into a coil on a strong

cylinder of radius r that is initially rotating at great angular speed . A brake (not shown) use to bring the

rotating cylinder to a stop very quickly – that is, with great (though not constant) angular acceleration .

Sliding contacts make electrical contact to the ends of the wire. The contacts are connected to the

terminals of a ballistic galvanometer. The result of the acceleration of charge carriers will be an electric

field whose direction is along the wire.

Ballistic

galvanometer

(It is safe to assume that the charge carriers move so quickly that a steady state is reached at every

instant, even though the acceleration changes rapidly on the macroscopic scale.)

7. On account of this internal field, the decelerating cylinder becomes a source of emf what is instantaneous

magnitude is given by

(A) m rL

q

(B)

2m rL

q

(C)

m rL

2q

(D) None of these

8. Let the total resistance of the electric circuit–coiled wire, leads and ballistic galvanometer (a device that

can measure the total charge that flows through it during a short interval of time.) be R total charge Q

that passes through the ballistic galvanometer during the braking is given by

(A)2mrL

qR (B)

mrL

qR (C)

mrL

2qR (D) None of these


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In the circuit shown in figure, switch S is closed at time t = 0. Thereafter the constant current source by

varying its emf, maintains a constant current I out of its upper terminal.

R

Constantcurrentsource

S

C

9. Derive an expression for the charge on the capacitor as a function of time :-

(A)t

RCq iRC e

(B) t

RCq iRC 1 e

(C)

t

RCq it 1 e

(D)t

RCi

q 1 eRC

10. Find the time at which the rate of energy storage on capacitor is equal to the rate of heat dissipation

through resistor :-

(A)RC n 2

t2

(B) t = 2RC n 2 (C) t = RC n 2 (D) Not possible


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The figure below illustrates two ways of using an ammeter and a voltmeter to measure the resistance R

of an unknown resistor. If both meters are ideal that is, if the resistance of the ammeter is zero and the

resistance of the voltmeter is infinite the two circuits give the same result. The resistance is simply the

voltmeter reading divided by the ammeter reading : VR

i . But a real ammeter has nonzero resistance

RA, and a real voltmeter has finite resistance R

V.

11. Suppose that you set up the circuit of figure a and obtain meter readings V1 and i

1. Express the resistance

R in terms of these readings and RV :-

A(R = 0)

RA R

(R = )V

RV

(A)1 V

1 V 1

V R

i R V (B) 1 V

1 V 1

V R

i R V (C)

21 V 1 V

1 V 1

V R i R

i R V

(D)

21 V 1 V

1 V 1

V R i R

i R V

12. Now you set up the circuit of figure b and obtain meter readings V2 and i

2. Express R in terms of these

readings and RA.

A(R = 0)

RA R

RV

V(R = )

(A)2

A

2

VR

i (B)

2A

2

VR

i (C)

2A

2

iR

V (D) None of these


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SECTION–IIMatrix-Match Type

This Section contains 1 question. Question has four statements (A, B, C and D) given in

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

correct matching with ONE or 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 has some conductor across which battery is connected as shown. Variation of resistivity isalso indicated. Which of the quantities in column-II remain constant throughout the volume of conductor.(Assume that the free electron density is uniform in the material).

Column-I Column-II

(A) x

x

(P) Magnitude of electric field

(B)

r

(Q) Magnitude of current density

Hollow cylinder

(C)

r2

(R) Power dissipated per unit volume

Hollow sphere

(D)

=constant

(S) Drift speed of free electron

Hollow sphere (T) Electric current

SECTION – IIIInteger Answer Type

There is no questions in this section.


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SECTION–IV

Integer Answer Type

This section contains 4 questions. The answer to each question is a single digit Integer, ranging from

0 to 9.

1. The potential difference across the 6 ohm resistance in the given circuit is 48 V. The potential differenceacross a to b is 51 × Volt. Then find the value of .

6 ohm 48 V

d

Ia

b8 ohm

30 ohm

15 ohm

10 ohm

12 ohm

2. Initially switch S is open. Charge flows through switch S when it is closed is 6 × Q µC. Then find thevalue of Q ?

S

6.00 µF

3.00 µF

ba

6.00

3.00

V = 18.0 V


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3. Initially the plates of the parallel plate capacitor shown in the figure are A and B containing charge +2µCand –2µC respectively. Negatively charged plate B is connected to a spring of spring constant 5000N/m at one end and the other end of the spring is connected to a rigid support. Now the plate A is fixed and

the system is released from rest. The maximum elongation produced in the spring is 12

0

10

m. The

area of the plates is 2 cm2 , the medium between the plates is air and Electric permittivity of air is 0 (inSI). Then the value of .

A B

K

4. A thin convex lens having focal length 20 cm is cut into two parts 1 mm above the principle axis. Thelower portion is placed with optical centre at origin and upper portion at (90, 0) as shown in the figure.A point object is placed at (–30, 0). Find the y co-ordinates (in mm) of the image. Assuming paraxial rayapproximation to remain valid.

(90,0)(0,0)1 mm

(–30,0)

90 cm30 cm

x

y

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PART-2 : CHEMISTRYSECTION–I




1. Which of the following quantities is the same for all ideal gases at the same temperature :

(A) The kinetic energy of 1 mol (B) The kinetic energy of 1 g

(C) The kinetic energy of 1 molecule (D) The number of molecules in 1 g

2. Decomposition of radioactive elements X proceed by two parallel path

X

Y

Z

-decay

K-capture

; = 1.2 min 1

–1

; = 4.8 min 2

–1

Then, select the correct statements -

(A) t1/2

of X is 6 min

(B) Ratio of Y & Z is 1 : 4 at any time

(C) Product Y & Z are isobar

(D) Sum of the concentration of X, Y, Z increases with time

3. Choose the incorrect statement -

(A) All atoms are sp3 hybridised in diamond

(B) All atoms are sp2 hybridised in benzene

(C) All carbon atoms are sp2 hybridised in benzyne

(D) Formal charge of central N-atom in N3

– remains unchanged in all Lewis structure


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4. Find the molecule having lowest C-C bond distance -

(A) Ph–CC–H (B) CH2=C=C=CH

2(C) CH

2=CH–CN (D) CH

2=CH–CH=CH

2

5. Which of the following carbonyl system show tautomersim :

(A) CH2–C–CH2–C–CH3

OO

(B) CH3–N=O

(C) CH3–CH=O (D)

O

O

6. Which of the followings are anti-aromatic -

(A)

(B) (C) (D)


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(ii) Paragraph Type



is correct.


Initially, flask A contained oxygen gas at 27°C and 950 mm of Hg and flask B contained neon gas at

27°C and 900 mm of Hg. Finally the two flasks were joined by means of a narrow tube of neglizible

volume equipped with a stop cork and gases were allowed to mixup freely. The final pressure in the

combined system was found to be 910 mm of Hg.

AO2

BNe

Consider the above diagram to answer these questions, assuming temperature to be constant throught

out.

7. What is the correct relationship between volumes of the two flasks ?

(A) VB = 3 V

A(B) V

B = 4 V

A(C) V

B = 5 V

A(D) V

B = 4.5 V

A

8. How many moles of gas are present in flask A in the final condition :

(A) 0.455 (B) 0.122 (C) 0.022 (D) 0.222


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"Hydrolysis is defined later as the reaction of water with any susbtance"

9. Choose the correct order of ease of hydrolysis -

(A) PCl5 < SiCl

4(B) TeF

6 > SeF

6(C) AlCl

3 > SiCl

4(D) None

10. Which of the following oxyacid is not formed during the stepwise hydrolysis of P4O

10

(A) trimetaphosphoric acid (B) tetrametaphosphoric acid

(C) tetrapolyphosphoric acid (D) pyrophosphoric acid


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Dehydration of alcohol is an elimination reaction, proceeds via formation of carbocation intermediate.

The energy profiles for such reaction may follow different patterns, some of them are given here.

(A)

Po

ten

tial

energ

y

Progress of reaction

(B)

Pot

enti

al

ener

gy


(C)

Po

ten

tial

energ

y


(D)

Po

ten

tial

energ

yProgress of reaction

(E)

Po

ten

tial

energ

y


11. OHconc.H SO2 4

Product(s)

which of the energy profiles given in the paragraph can represent the above reaction

(A) B (B) C (C) D (D) E

12. Which of the following energy profiles given in the paragraph represent product formation without

rearrangement -

(A) A,C (B) A,D (C) B,D (D) B, D


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SECTION–IIMatrix-Match Type






1. Match the column :

Column-I Column-II

(A)

COOHCH3

(P) React with Na

(B)

OHNO2

O N2

NO2

(Q) React with NaOH

(C)

OH

(R) React with NaHCO3

(D)

O

OHO

HO

(S) React with NaNH2

(T) Weaker acid than water




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SECTION–IV

Integer Answer Type


0 to 9.

1.90

Th232 distintegrate into 82

Pb208 16.8 litre of He(g) were obtained at 273K & 1 atm in time 't' when

1/7 moles of 90

Th232 was taken initially. Find the ratio of 't' to t1/2

of 90

Th232.

2. The acidic hydrolysis of compound (A) in aqueous solution is first order with respect to (A). Upon

varying the pH of solution, the half life varies as follows.

Then order of reaction with respect to H+ is -

pH 3 2 1

Half life(min) 7000 70 0.7



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3. Find the number of 90º angles in XeO3F

2 molecules

4. Find the number of plane containing maximum number of atoms in TeCl6

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PART-3 : MATHEMATICSSECTION–I




1. Let

3x 0 1

3 x 2 sin xL lim

sin x

. If L is finite, then which of the following is/are true-

(A) 1

2 (B)

1L

4 (C)

1L

4 (D) = 0

2. Let ƒ(x) = sin–1

x – x and g(x) = x2 + 3|x| + 2 + cos

–1x. If |ƒ(x)| + |g(x)| = |ƒ(x) + g(x)| holds true, then the

values of x can lie in the interval(s) -

(A) x [–1,1] (B) x [0,1] (C) x [–1,0) (D) 1

x ,12

3. Let ƒ : R R and g : R R be mappings such that ƒ(g(x)) is an injective mapping then which of the

following statement(s) is(are) true ?

(A) ƒ(x) may be many-one mapping

(B) g(x) must be injective mapping

(C) If g(x) is surjective then ƒ(x) must be injective

(D) If g(x) is into mapping then ƒ(x) must be many-one mapping.


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4. Let

n2012 2011 2011

nn 2012 2011

sin x 1 x tan xƒ(x) lim

cos x 1 x

, (n N) then which of the following is(are) true-

(A) ƒ(x) is continuous at x = 0 (B) x 0lim ƒ(x) 0

(C) x 0lim ƒ(x) 0

(D)

x 0lim ƒ(x) 1

5. Let ƒ(x) = tan + tan, where 1sin x , 1cos x (where x I and {.} denotes fractional

part function), then which of the following is/are true-

(A) ƒ(x) is an even function (B) ƒ(x) is an odd function

(C) ƒ(x) is periodic (D)

1

0

ƒ(x)dx

6. Let ƒ be a differentiable function satisfying the integral equation x x

x

0 0

ƒ(t)dt t.ƒ x t dt e 1 then

which of the following is/are true-

(A) 2

1ƒ(2)

e (B) ƒ(0) + ƒ'(0) = 1 (C) ƒ'(0) = 2 (D) ƒ'(0) = 1


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(ii) Paragraph Type



is correct.


Let

x 2

1 20

t dtI

x sin x 2 t

(where is a non-zero constant) and

2x t

2 6

0

e 1 tI dt

x

.

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

7. If 1x 0lim I 1

, then the sum of value(s) of is equal to-

(A) 0 (B) 1

2(C) 1 (D) 2

8. If = –1, then the value of 1 2x 0lim I 6I

is equal to-

(A) 2 (B) 3 (C) –1 (D) 0


MATHEMATICS

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Let ƒ : R R be such that ƒ'(0) = 1 and ƒ(x + y) = ƒ(x) + ƒ(y) + ex+y(x + y)– xex – yey + 2xy

x,yR.


9. If ƒ(x)

dx g(x) cx

, where g(0) = 0, then the value of g(2) is equal to-

(A) e2 + 2 (B) 2e

2(C) e

2 + 1 (D)

2e

2

10. Number of distinct real roots of the equation ƒ(x) – 2x2 = 0 is equal to-

(A) 0 (B) 1 (C) 2 (D) 3


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Let ƒ be a cubic polynomial function such that ƒ(x) + ƒ(–x) = 0 x R and 2

1

x 4

x 0

ƒ(x)lim 1 e

x

.


11. The value of 1

r 1

2rtan

ƒ(r)

equals-

(A) cot–1

1 + cot–1

2 (B) tan–1

1 + tan–1

2 (C) tan–1

2 + tan–1

3 (D) cot–1

2 + cot–1

3

12. If g(ƒ(x)) = x x R and g(4) = m and g(32) = n, then n 32

m 4

ƒ(x)dx g(x)dx is equal to-

(A) 28 (B) 60 (C) 30 (D) 16


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SECTION–II

Matrix-Match Type






1. Column-I Column-II

(A) If x > 1 and 1 2sin cot x 1 dx = ƒ(x) + k, (P) 0

where ƒ(1) = 0, then the value of ƒ(e2) is equal to (Q) 1

(B) If

2

2012

sec xdx g(x) C

tan x tan x

, where n2

g4 2011

, (R) 2

then x

2

lim g(x)

is equal to (S) even number

(C) If the function x

ƒ(x)x

is self inverse, then (T) prime number

() can be

(D) Given x [0,1) and x

20

dtƒ(x)

1 t

, then the value of

22ƒ(x) ƒ 1 x

is equal to




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SECTION–IV

Integer Answer Type


0 to 9.

1. Let 'ƒ' be a differentiable function such that ƒ(xy) = ƒ(x).ƒ(y) x,y R+ and ƒ(1 + x)= 1+x(1+ g(x)),

where x 0lim g(x) 0

. If the value of 2

2

1

ƒ(x) 1 1 a. dx n

ƒ '(x) 1 x 2 b

, where a and b are coprime numbers,

then the value of (a + b) is equal to

2. Let a and b be two distinct positive real numbers, then the value of b x / a b / x

a

e edx

x

is equal to



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3. Let n

1

n r 1r 1r

1L lim tan

12

2

, then the value of (cotL) is equal to

4. Number of values of x satisfying simultaneously

sin–1x = 2tan–1x and 1 1 2tan x x 1 cos ec 1 x x2

, is


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Name of the Candidate

I have read all the instructions and shallabide by them.

Signature of the Candidate

Form Number

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seals · 2015. 12. 21. · 1. the figure shows a potentiometer arrangement. d is the driving cell,...

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