jee (main + advanced) : leader & enthusiast course · pdf filejee (main + advanced) :...

READ THE INSTRUCTIONS CAREFULLY

GENERAL :

1. This sealed booklet is your Question Paper. Do not break the seal till you are instructedto do so.

2. Use the Optical Response sheet (ORS) provided separately for answering the questions.

3. Blank spaces are provided within this booklet for rough work.

4. Write your name and form number in the space provided on the back cover of thisbooklet.

5. After breaking the seal of the booklet, verify that the booklet contains 32 pages and allthe 20 questions in each subject and along with the options are legible.

QUESTION PAPER FORMAT AND MARKING SCHEME :

6. The question paper has three parts : Physics, Chemistry and Mathematics. Each parthas three sections.

7. Carefully read the instructions given at the beginning of each section.

8. Section-I contains 10 multiple choice questions with one or more than one correctoption.

Marking scheme : +4 for correct answer, 0 if not attempted and –2 in all other cases.

9. Section-II contains 2 ‘match the following’ type questions and you will have to matchentries in Column-I with the entries in Column-II.

Marking scheme : for each entry in column-I. +2 for correct answer, 0 if not attemptedand –1 in all other cases.

10. There is no questions in SECTION-III

11. Section-IV contains 8 questions. The answer to each question is a single digit integerranging from 0 to 9 (both inclusive)

Marking scheme : +4 for correct answer and 0 in all other cases.

OPTICAL RESPONSE SHEET :

12. The ORS is machine-gradable and will be collected by the invigilator at the end of theexamination.

13. Do not tamper with or mutilate the ORS.

14. Write your name, form number and sign with pen in the space provided for this purposeon the original. Do not write any of these details anywhere else. Darken theappropriate bubble under each digit of your form number.

DO

NO

T B

REA

K T

HE

SEA

LS W

ITH

OU

T B

EIN

G IN

ST

RU

CT

ED T

O D

O S

O B

Y T

HE

INV

IGIL

ATO

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PAPER – 1

Test Type : ALL INDIA OPEN TEST Test Pattern : JEE-Advanced

TEST DATE : 15 - 05 - 2016

TARGET : JEE (ADVANCED) 2016

JEE (Main + Advanced) : LEADER & ENTHUSIAST COURSE

Paper Code : 0000CT103115008

CLASSROOM CONTACT PROGRAMME(Academic Session : 2015 - 2016)

Time : 3 Hours Maximum Marks : 264

EN

GL

ISH

Please see the last page of this booklet for rest of the instructions

E-2/32

ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1

0000CT103115008

SOME USEFUL CONSTANTSAtomic 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,

Space for Rough Work

Boltzmann constant k = 1.38 × 10–23 JK–1

Coulomb's law constant

9

0

1= 9×10

4

Universal gravitational constant G = 6.67259 × 10–11 N–m2 kg–2

Speed of light in vacuum c = 3 × 108 ms–1

Stefan–Boltzmann constant = 5.67 × 10–8 Wm–2–K–4

Wien's displacement law constant b = 2.89 × 10–3 m–K

Permeability of vacuum µ0 = 4 × 10–7 NA–2

Permittivity of vacuum 0 = 2

0

1

c

Planck constant h = 6.63 × 10–34 J–s


PHYSICS

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PART-1 : PHYSICS

SECTION–I : (Maximum Marks : 40)

This section contains TEN questions.

Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these

four option(s) is (are) correct.

For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS

Marking scheme :

+4 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened

0 If none of the bubbles is darkened

–2 In all other cases

1. Two identical blocks are resting on supports as shown. Two identical bullets travelling with the

same speed hit the blocks & get embedded in them in very short time. The blocks leave thecontact immediately after bullet strikes them. In case (i) bullet's velocity is toward centre of

mass and in case (ii) bullet's velocity is off centre. The kinetic energies after collision are K1 & K2

and maximum height reached by the centre of mass are h1 & h2 respectively. Then :

Case (i) Case (ii)

(A) K1 < K2 (B) K1 = K2 (C) h1 > h2 (D) h1 = h2

2. A barometer is made of glass. It contains mercury (density 13.6 × 103 kg/m3, surface tension0.085 N/m, angle of contact 143°). The barometer scale has a least count of 1mm. If the radius of

barometer tube is 0.5 mm, and height of mercury column recorded is 762 mm, what can be trueatmospheric pressure (in mm of mercury column) :-

(A) 760 mm (B) 761 mm (C) 763 mm (D) 765 mm

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS


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PHYSICS


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3. For a certain transverse standing wave on a long string, an antinode is formed at x = 0 and nextto it, a node is formed at x = 0.10 m. The displacement y(t) of the string particle at x = 0 is shownin figure.

y(cm)0.05 0.1 0.15 0.2

t(s)

4

–4

(A) Transverse displacement of the particle at x = 0.05m and t = 0.05 s is – 2 2 cm.

(B) Transverse displacement of the particle at x = 0.04 m and t = 0.025 s is – 2 2 cm.

(C) Speed of the travelling waves that interfere to produce this standing wave is 2 m/s.

(D) The transverse velocity of the string particle at x =1

15 m and t = 0.1 s is 20 cm/s

4. In the figure shown is the surface charge density on the upper metallic plate.

d/3

2d/3

Area of plate = A

A

B

I Dielectricst

II nd

Dielectric

K = 31

K = 52

(A) The ratio of energy density in st dielectric to second dielectric is 5

3

(B) The ratio of energy density in st dielectric to second dielectric is 3

5

(C) Total induced surface charge density on the interface of the two dielectric is – 3

15

(D) Total induced surface charge density on the interface of the two dielectric is – 2

15


PHYSICS

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5. A parallel beam of light is incident on a lens of focal length 10 cm. A parallel slab of refractiveindex 1.5 and thickness 3 cm is placed on the other side of the lens. The Nature of the finalimage from the lens slab combination is: (Assume rays to be paraxial) :-

x

(A) At Distance of 11 cm and Image is virtual if x = 12 cm.

(B) At Distance of 11 cm and Image is real if x = 14 cm.

(C) At the Distance of 11 cm and Image is Virtual if x = 16 cm

(D) At Distance of 11 cm and Image is real if x = 5 cm.

6. A bead is connected at one end of an inextensible massless string whose other end is fixed to afixed vertical cylinder. Cylinder does not rotate. The bead can move on a horizontal smoothsurface. The bead is given a velocity v

0 perpendicular to the string. The bead moves on a curve

and consequently collides on the cylinder after sometime. Then, before it collides:

R

V0

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

(B) The speed of the bead remains v0.

(C) The tension in the string remains constant.

(D) Kinetic energy of bead increases gradually.

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7. In the figure shown the block of mass 6 kg is slowly released till the rod is in equillibrium of thefollowing figures, which figure can be equillibrium position of the rod :-

10kg

4m

smooth

6kg8m

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

8. A small bead of mass m is threaded on a smooth circular ring of radius a in xy plane as shown.

The bead experiences a force whose potential energy is given by 2 2

2 2

x yV C

a b

{b > a} . The

bead is at x = a at rest as shown. Neglect gravity. Choose the CORRECT statement(s):-

x

y

(A) At initial position, normal force = 2c

a(B) At initial position, there is no acceleration.

(C) If the bead was at y = a at rest , it's normal force is 2

2ca

b(D) If the bead was at y = a at rest, there is no acceleration.



PHYSICS

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9. A particle is subjected to two simultaneous SHM

x = A sin t

y = A sin (t + )

Choose the correct path(s) followed by particle.

(A) 2

x

y

(B) = x

y

(C) 3

x

y

(D) 3

x

y

10. In a toy gun, we have a horizontal hollow smooth pipe. Two blocks of different masses are fitted

in it. The spring can be compressed by a certain distance and then released. It was seen that

(case-1) when m1 is fixed & m

2was released, it comes out with a speed of 4 m/s. (case-2) when m

2

was fixed & m1 was released, it comes out with a speed of 2m/s. In all cases, initial compression

of spring was same & finally it remains at natural length (spring is not connected to either

blocks).

m1 m2

(A) If both blocks are released simultaneously, v1 =

2

5 m/s and 2

8v

5 m/s.

(B) If both blocks are released simultaneously, 1

20v

4 m/s and

2v 20 m/s.

(C) m2 took lesser time to come out in case-1 than m

1 in case-2.

(D) m2 took more time to come out in case-1 than m

1 in case-2.


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SECTION–II : (Maximum Marks : 16) This section contains TWO questions. Each question contains two columns, Column-I and Column-II. Column-I has four entries (A), (B), (C) and (D) Column-II has five entries (P), (Q), (R), (S) and (T) Match the entries in Column-I with the entries in column-II. One or more entries in Column-I may match with one or more entries in Column-II. The ORS contains a 4 × 5 matrix whose layout will be similar to the one shown below :

(A) (P) (Q) (R) (S) (T)

(B) (P) (Q) (R) (S) (T)

(C) (P) (Q) (R) (S) (T)

(D) (P) (Q) (R) (S) (T)

For each entry in column-I, darken the bubbles of all the matching entries. For example,if entry (A) in Column-I matches with entries (Q), (R) and (T), then darken these three bubblesin the ORS. Similarly, for entries (B), (C) and (D).

Marking scheme :For each entry in Column-I+2 If only the bubble(s) corresponding to all the correct match(es) is (are) darkened0 If none of the bubbles is darkened–1 In all other cases



PHYSICS

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1. A double slit interference pattern is produced on a screen as shown in the figure, usingmonochromatic light of wavelength 500nm. Point P is the location of the central bright fringe,that is produced when light waves arrive in phase without any path difference. A choice of threestrips A, B and C of transparent materials with different thicknesses and refractive indices isavailable, as shown in the table, these are placed over one or both of the slits, singularly or inconjunction, causing the interference pattern to be shifted across the screen from the originalpattern. In the column-I, how the strips have been placed, is mentioned whereas in thecolumn-II, order of the fringe at point P on the screen that will be produced due to the placementof the strip (s), is shown. Correctly match both the column.

Slit I

Slit II

P

Screen

Film A B C

Thickness5 1.5 0.25

in m

Re fractive index 1.5 2.5 2

Column-I Column-II

(A) Only strip B is placed over slit-I (P) First Bright

(B) Strip A is placed over slit-I and strip C is (Q) Fourth Dark

placed over slit-II

(C) Strip A is placed over the slit-I and strip (R) Fifth Dark

B and strip C are placed over the slit-II

in conjunction.

(D) Strip A and strip C are placed over slit-I (S) Central Bright

(in conjuction) and strip B is placed over slit-II. (T) First dark


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0000CT103115008

2. A square loop of conducting wire is placed near a long straight current carrying wire as shown.

Match the statements in column-I with the corresponding results in column-II.

Column-I Column-II

(A) If the magnitude of current I is increased (P) Induced current in the loop will be

clockwise

(B) If the magnitude of current I is decreased (Q) Induced current in the loop will

be anticlockwise

(C) If the loop is moved away from the wire (R) wire will attract the loop

(D) If the loop is moved towards the wire (S) wire will repel the loop

(T) Torque about centre of mass of

loop is zero due to magnetie force

SECTION–III : Integer Value Correct Type

No question will be asked in section III



PHYSICS

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SECTION–IV : (Maximum Marks : 32)

This section contains EIGHT questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive For each question, darken the bubble corresponding to the correct integer in the ORS Marking scheme :

+4 If the bubble corresponding to the answer is darkened

0 In all other cases

1. An electron moving with velocity 1v 1i

m/s at a point in a magnetic field experiences a

force 1F ejN

, where e is the charge of electron. If the electron is moving with a velocity

2ˆ ˆv i j

m/s at the same point, it experiences a force 2

ˆ ˆF e i j N

. Find the magnitude of

force (in N) the electron would experience if it were moving with a velocity 3 1 2ˆv v v

at the

same point.

2. Find current in the branch CD of the circuit (in ampere).

2 22

B

A

C

D

10V


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PHYSICS


0000CT103115008

3. Figure shows a conducting disc rotating about its axis in a perpendicular uniform and constant

magnetic field B. A resistor of resistance R is connected between the centre and the rim. The

radius of the disc is 5.0 cm, angular speed = 40 rad/s, B = 0.1 T and R = 1 . The current

through the resistor in milliampere is.

× ×

R

×

×

×

×××××

×

×

×

×

4. A continuous flow geyser has water flowing in it at a continuous rate. It comes in at a rate of

0.08 litres/sec and leaves at a rate of 0.081 litres/sec. The temperature coefficient of thermal

expansion of water is 2 × 10–3/°C. The specific heat capacity of water is 4000 J/kg°C. If the inlet

temperature is 7°C at which the density of water is 103 kg/m3, what is the power consumed by

geyser (in kW)?



PHYSICS

E-13/320000CT103115008

5. Two positive and two negative point charges (|Q| = 0.01 µC) are placed at the corners of a

square insulator frame of side 15 m and the side of the frame are hinged together. The frame is

deformed into a rhombus as shown. The new potential at the centre is given by volt. Fill in

OMR sheet.

+Q –Q

–Q +Q

+Q –Q

–Q +Q74º

6. While expanding a mixture of gas did work P1V

1 – P

2V

2 on the piston. Here P

1 and V

1 are initial

pressures and volumes and P2 and V

2 are final pressures and volumes. Find molar heat capacity

of the gas in this process. Take for mixture as 1.5. Express your answer in terms of xR where R is

universal gas constant. Fill x in OMR sheet.


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PHYSICS


0000CT103115008

7. The body of mass m = 0.5 kg is held on a vertical wall by a force F of 15 N as shown in the figureis applied on the body at an angle = 53º to the vertical (Figure). The coefficient of friction

between the body and the wall is µ = 0.5. Determine acceleration of the body in m/s2.

F

8. An electron of mass m when accelerated through a potential difference V, has de Broglie

wavelength . The de-Broglie wavelength associated with a particle of mass m/4 and charge e

accelerated through the same potential difference is n. Then find the value of n.



CHEM

ISTRY

E-15/320000CT103115008

PART-2 : CHEMISTRY

SECTION–I : (Maximum Marks : 40)





Marking scheme :




1. Select the correct statement(s) for an ideal gas -

(A) All the molecules move with same speed

(B) Kinetic energy of a molecule remains unchanged due to collision with other molecule

(C) Kinetic energy of molecules depends only on temperature

(D) Speed of molecules depend on both molecular mass & temperature

2. If heat of formation of PCl3(g) and PH

3(g) are 140 and 8 kJ /mole respectively and heat of

atomisation of phosphorous[P4(s)], chlorine and hydrogen are 320, 120 and 216 kJ/mole

respectively then.

(A) Bond energy of P–Cl is 63 kJ/mole

(B) Bond energy of P–H is 210 kJ/mole

(C) Heat of formation of isolated gaseous hydrogen atom is 108 kJ/mole

(D) Heat of formation of isolated gaseous chlorine atom is 60 kJ/mole

3. 100 L aqueous solution of KBr is electrolysed by using current of 9.65 ampere for 10 sec. using

Pt electrodes. Which of the following species will be produced due to electrolysis ?

(A) H2 (B) O2 (C) Br2 (D) KOH

4. Which of the following molecule(s) is/are non planar -

(A) BF3

(B) SF6

(C) IF5

(D) PCl5

5. Which of the following option is/are CORRECT for solution of liquid NH3 with alkali metal -

(A) It is paramagnetic (B) It is blue in colour

(C) It is good conductor of electricity (D) It is nonconductor of electricity


E-16/32

CHEM

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0000CT103115008


6. Which of the following anion(s) give 'x' gas with dil. HCl, which turns lime water milky :-

(A) SO32– (B) CO

32– (C) S2– (D) CH

3COO–

7. Which of the following complex/ion is/are paramagnetic.

(A) Ni(CO)4

(B) [MnCl4]2– (C) K

4[Fe(CN)

6] (D) [CoCl

4]2–

8. Which statement(s) is/are correct for the compounds X and Y :

H–C C–CH –C–CH –CH2 2 3

O(X)

CH –C C–CH –CH –C–H3 2 2

(Y)

;

O

(A) X and Y are chain isomers

(B) X and Y are functional isomers

(C) X and Y can be differentiated by Tollen's reagent

(D) X and Y both have same degree of unsaturation

9. C = CH C3

H H

CH3 OsO / NaHSO4 3 (A)

(B)

(i) CF C3–

(ii) Aq. KOH

OO

H

O

Select correct statement(s) for above reaction sequence :

(A) A is pair of enantiomer and A and B are distereomers

(B) B is pair of enantiomer and A and B are distereomers

(C) A represents meso compound

(D) B represents meso compound

10. Which of the following compound(s) will form stable (isolable) hydrate on addition of H2O ?

(A) CCl –C–H3

O

(B)

O

(C)

O

O O(D)

O


CHEM

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SECTION–II : (Maximum Marks : 16)

This section contains TWO questions.

Each question contains two columns, Column-I and Column-II.

Column-I has four entries (A), (B), (C) and (D)

Column-II has five entries (P), (Q), (R), (S) and (T)

Match the entries in Column-I with the entries in column-II.

One or more entries in Column-I may match with one or more entries in Column-II.

The ORS contains a 4 × 5 matrix whose layout will be similar to the one shown below :

(A) (P) (Q) (R) (S) (T)

(B) (P) (Q) (R) (S) (T)

(C) (P) (Q) (R) (S) (T)

(D) (P) (Q) (R) (S) (T)

For each entry in column-I, darken the bubbles of all the matching entries. For example,

if entry (A) in Column-I matches with entries (Q), (R) and (T), then darken these three bubbles

in the ORS. Similarly, for entries (B), (C) and (D).

Marking scheme :

For each entry in Column-I

+2 If only the bubble(s) corresponding to all the correct match(es) is (are) darkened



1. Column-I Column-II

(A) pH of mixture of 0.1N HCN (Ka = 10–10) and 0.1M NaCN (P) 10

(B) pH of mixture of 0.1N BOH (pKb = 6) and 0.05M B

2SO

4(Q) 7

(C) pH of mixture of 0.1M salt of weak acid (pKa = 5) and weak (R) 6

base (pKb = 7)

(D) pH of mixture of 500 litre of 0.02 M HNO3 and 500 litre of (S) 8

0.01M Sr(OH)2

(T) Solution is acidic

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CHEM

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0000CT103115008

2. Column-I (Species) Column-II (Characteristic properties)

(A) XeO2F

2(P) Non-planar

(B) XeOF4

(Q) Utilisation of d-orbital(s) in bonding

(C) PH4+ (R) Planar

(D) ICl4

–(S) Polar molecule

(T) Tetrahedral geometry





CHEM

ISTRY

E-19/320000CT103115008



This section contains EIGHT questions.

The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive

For each question, darken the bubble corresponding to the correct integer in the ORS

Marking scheme :



1. If equivalent weight of Ba(SCN)2 when it reacts with oxidising agent and forms product,

SO42–, CO3

2– & NO3– is

Molecular weight

X.Then calculate value of

X

4.

2. If for the reaction at 27ºC , 2A(g) + B(g) 2C(g), Ur = 25.6 kcal and entropy of

A, B, C are 200, 100 , 500 cal/mole resepectively , then calculate magnitude of G (in Kcal)

of reaction.

[R = 2cal/mole-K]

Fill your answer as sum of digits (excluding decimal places) till you get the single digit

answer.

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CHEM

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0000CT103115008


3. Among the following find out total number of reagent(s), which give white precipitate with aqueous

solution of Zn+2.

NH4OH, NaOH, (NH

4)2S, K

4[Fe(CN)

6]

4. Find the total number of species that do not exist.

H2, HeH–, He

2+, Li

2, O

22–, FeI

3


CHEM

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E-21/320000CT103115008

5.

HOOC COOH

(A)

For the above compound how many statement(s) are true ?

(i) Total number of stereoisomers possible for (A) are 3

(ii) Total number of meso compounds possible for (A) is 1

(iii) Number of plane of symmetry in cis form of A are 2

(iv) cis form of above compound (A) is meso

(v) Number of enantiomeric pair possible for (A) is 1

6. Total number of compound(s) having higher bond order of (C–O) than CH –C3

O

O– :

(i)

O

(ii)

O

(iii)

OH

(iv) CH3–OH (v) CH

3–CH

2–OH

(vi) CH –CH –C3 2

O

H(vii)

O


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CHEM

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0000CT103115008

7. Total number of compounds which react faster than

NO2

F

on reaction with NaOH :

(i)

NO2

Cl

(ii)

NO2

FNO2

(iii)

F

NO2

(iv)

NO2

FNO2O N2

(v) Br NO2 (vi) I NO2

8. Total number of compounds which can show both aldol condensation and iodoform test :

(i) CH –C–CH3 3

O

(ii) CH –C–H3

O

(iii)

O

(iv)

O OH

(v)

O

O

(vi) CH3–CH

2–OH



MATHEM

ATICS

E-23/320000CT103115008

PART-3 : MATHEMATICSSECTION–I : (Maximum Marks : 40)





Marking scheme :




1. Consider the plane P 2x – 2y + z = 9 and a point A(13,–11,15) not on the plane. Now which of

the following holds good ?

(A) foot of perpendicular from A on plane P is (1,1,9)

(B) image of point A in plane P is (–11,13,3)

(C) perpendicular distance of A from plane P is 18.

(D) The volume of tetrahedron formed by xy,yz,zx planes with plane P is 35/23.

2. If z4 + 1 = z2, then-

(A) Least positive argument of z is 6

(B) Greatest positive argument of z in [0,2] is 11

6

(C) The four possible values of z forms square on argand plane

(D) The four possible values of z forms rectangle on argand plane.

3. If ƒ : R R be a continuous function satisfying the equation 2xƒ(x) + (1 + x2)ƒ'(x) = 1 and

ƒ(0) = 0, then-

(A) ƒ(x) is an odd function (B) Number of integers in the range of ƒ(x) is 1.

(C) Number of solutions of 1

ƒ x4

are 2 (D) Number of solutions of 1ƒ ƒ x

2 are 2.


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MATHEM

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0000CT103115008


4. Let A be invertible square matrix whose inverse is given as 1

1 2 3

A 1 3 6

2 5 7

. Now which of the

following holds good (|A| represents determinant of A)-

(A) A is idempotent matrix (B) Trace (adjA) 11

2

(C) Trace (A adjA)3

2 (D) |A–1| = –2

5. Figure shows a parabola with vertex at origin and axis of symmetry along y

0

B(t )2

A(t )1

30º

S (1,0)x

x-axis. S(1,0) is the focus of parabola & A(t1) and B(t2) are the

extremeties of a focal chord making an angle of 30º with positive

x-axis. Which of the following holds good ?

(A) Latus rectum of parabola is 4 (B) 21 1t 2 3t 1

(C) Length AB is 1 (D) 22 2t 2 3t 1

6. Let a,b R and ab 1. If 6a2 + 20a + 15 = 0 and 15b2 + 20b + 6 = 0 and

3

32

b p

qab 9 ab 1

(where p,q are coprime naturals then)-

(A) The digit at units place of 'p' is 6 (B) Digit at unit's place of q is 6

(C) The digit at units place of p is 5 (D) Digit at unit's place of q is 5.


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7. Let ƒ : R+ R be a function satisfying the functional rule ƒ(a.b) = ƒ(a) + ƒ(b) a,bR+. Then

which of the following always holds good for 1

x

0

I ƒ(3 )dx is -

(A) ƒ(3)

I2

(B) log 3

I2

(C) ƒ( 3) (D) 3

ƒ ƒ( 2)2

8. If m

mk 0

1 kƒ x lim x

m m

; then-

(A) 1

ƒ 02

(B) 1

ƒ 12

(C) 3

ƒ 12

(D) 3

ƒ 22

9. For which of the following values of k the equation 4 2

6 3

x xk

x 2x 1

has no solution in [1,] ?

(A) 1

6(B)

1

5(C)

1

4(D)

1

3

10. Let ƒ be a continuous non-algebraic twice derivable increasing function in (0,1) & ƒ"(x) > 0.

If ƒ(0) = 0, ƒ(1) = 1 and g(x) is inverse of ƒ(x), then which of the following holds good ?

(A)

ƒ x

ƒ ' x x 0,1x

(B)

ƒ x

ƒ ' x x 0,1x

(C)

ƒ x xx 0,1

x g x (D)

ƒ x x

x 0,1x g x

E-26/32

MATHEM

ATICS


0000CT103115008

SECTION–II : (Maximum Marks : 16)

This section contains TWO questions. Each question contains two columns, Column-I and Column-II. Column-I has four entries (A), (B), (C) and (D) Column-II has five entries (P), (Q), (R), (S) and (T) Match the entries in Column-I with the entries in column-II. One or more entries in Column-I may match with one or more entries in Column-II. The ORS contains a 4 × 5 matrix whose layout will be similar to the one shown below :

(A) (P) (Q) (R) (S) (T)

(B) (P) (Q) (R) (S) (T)

(C) (P) (Q) (R) (S) (T)

(D) (P) (Q) (R) (S) (T)

For each entry in column-I, darken the bubbles of all the matching entries. For example,if entry (A) in Column-I matches with entries (Q), (R) and (T), then darken these three bubblesin the ORS. Similarly, for entries (B), (C) and (D).

Marking scheme :For each entry in Column-I+2 If only the bubble(s) corresponding to all the correct match(es) is (are) darkened0 If none of the bubbles is darkened–1 In all other cases

1. Consider an experiment of tossing a fair of coin six times. Let A and B be two events defined

as follows

A : Number of heads greater than number of tails.

B : The third toss results in head. Now match the columns.

Column-I Column-II

(A) If a

P Ab

where a and b are relatively prime then 'a' is (P) an even number

(B) If p

P Bq

, where p and q are relatively prime then 'q' is (Q) an odd number

(C) If A u

PB v

where u and v are relatively prime then 'u' is (R) a prime number

(D) If B m

PA n

where m and n are relatively prime then (S) a composite number

3(m + n) is (T) neither prime nor

composite number



MATHEM

ATICS

E-27/320000CT103115008

2. Column-I Column-II

(A) The number

4991000

2k 1k 0

2k 1 C

100

is divisible by (P) 2

(B) 4

3 1

is divisible by (Q) 4

(where [.] denotes greatest integer function)

(C) A non-constant geometric series has sum of its terms (R) 8added to infinity are 12 & if every term is squared this sum

becomes 144

7. If common ratio is

p

q where p & q are

relatively prime then 2q + p is divisible by (S) 9

(D) Let xi {1,2,3,4} where i = 1,2,3,4 and x

i x

j if

i j. If |xi – i| > 0, then number of 4 digit numbers of the (T) 11

form 'x1x2x3x4' is




E-28/32

MATHEM

ATICS


0000CT103115008


This section contains EIGHT questions.

The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive

For each question, darken the bubble corresponding to the correct integer in the ORS

Marking scheme :



1. Let ƒ(x) = (2x – )3 + 2x – cosx. If 1dƒ x

dx

at x = is 1

,a Na

, then the value of 'a' is

2. The least positive integral value of k for which the equation 2

2

x x 1k

x x 1

has no real

solution is

3. A point P lies on the graph

2 2y 1 x 2

164 49

. If distance of P from one focus is 8 and its

distance from other focus is 'd', then sum of digits of number 'd' is



MATHEM

ATICS

E-29/320000CT103115008

4. If log2y + (21+x + 21–x) (log y) + 22x+1 + 21–2x = 0; where x,y R, then the value

of |log(x + y)| is

5. Let a, b, c

be non-zero non-collinear vectors such that c a c b

. The value of

21 a c b a a b a

is

6. If x

1 x 1 alim tan

x 1 2x 2 b

(a,b N); then the value of a + b is


E-30/32

MATHEM

ATICS


0000CT103115008

7. Derivative of n2(nx) with respect to n(nx) at x = ee (which e is Napier's constant)

8. The maximum integral value of 'k' for which 23 x , x 1

ƒ xx k , x 1

has local minima

at x = 1 is



E-31/320000CT103115008



Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005

+91-744-5156100 [email protected] www.allen.ac.in

Your Target is to secure Good Rank in JEE 2016 0000CT103115008E-32/32

DARKENING THE BUBBLES ON THE ORS :

15. Use a BLACK BALL POINT PEN to darken the bubbles in the upper sheet.

16. Darken the bubble COMPLETELY.

17. Darken the bubbles ONLY if you are sure of the answer.

18. The correct way of darkening a bubble is as shown here :

19. There is NO way to erase or "un-darken" a darkened bubble.

20. The marking scheme given at the beginning of each section gives details of how darkened

and not darkened bubbles are evaluated.

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

I HAVE READ ALL THE INSTRUCTIONS

AND SHALL ABIDE BY THEM

____________________________

Signature of the Candidate

I have verified the identity, name and rollnumber of the candidate, and that questionpaper and ORS codes are the same.

____________________________

Signature of the invigilator

NAME OF THE CANDIDATE ................................................................................................

FORM NO. .............................................


1.

2. (ORS)

3.

4.

5. 32 20

6.

7.

8. -I 10

: +4 0–2

9. -II 2 ‘’ -I -II

: -I +2 0 –1

10. –III

11. -IV 8 0 9 ()

: +4 0

12.

13.

14.

PAPER – 1

Test Type : ALL INDIA OPEN TEST Test Pattern : JEE-Advanced

TEST DATE : 15 - 05 - 2016

Time : 3 Hours Maximum Marks : 264

Paper Code : 0000CT103115008

CLASSROOM CONTACT PROGRAMME(Academic Session : 2015 - 2016)H

IND

I

TARGET : JEE (ADVANCED) 2016

JEE (Main + Advanced) : LEADER & ENTHUSIAST COURSE

H-2/32


0000CT103115008

SOME USEFUL CONSTANTSAtomic 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,

Boltzmann constant k = 1.38 × 10–23 JK–1

Coulomb's law constant

9

0

1= 9×10

4

Universal gravitational constant G = 6.67259 × 10–11 N–m2 kg–2

Speed of light in vacuum c = 3 × 108 ms–1

Stefan–Boltzmann constant = 5.67 × 10–8 Wm–2–K–4

Wien's displacement law constant b = 2.89 × 10–3 m–K

Permeability of vacuum µ0 = 4 × 10–7 NA–2

Permittivity of vacuum 0 = 2

0

1

c

Planck constant h = 6.63 × 10–34 J–s


PHYSICS

H-3/320000CT103115008

-1 : –I : ( : 40)

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

:

+4

0

–2

1. (i) (ii) K

1 K

2h

1 h

2

Case (i) Case (ii)

(A) K1 < K

2(B) K

1 = K

2(C) h

1 > h

2(D) h

1 = h

2

2. 13.6 × 103 kg/m3, 0.085 N/m 143° 1mm 0.5 mm 762 mm mm (A) 760 mm (B) 761 mm (C) 763 mm (D) 765 mm

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

H-4/32

PHYSICS


0000CT103115008

3. x = 0 x = 0.10 m

x = 0 y(t)

y(cm)0.05 0.1 0.15 0.2

t(s)

4

–4

(A) x = 0.05m t = 0.05 s – 2 2 cm

(B) x = 0.04 m t = 0.025 s – 2 2 cm

(C) 2 m/s

(D) x =1

15 m t = 0.1 s 20 cm/s

4.

d/3

2d/3

Area of plate = A

A

B

I Dielectricst

II nd

Dielectric

K = 31

K = 52

(A) 5

3

(B) 3

5

(C) –3

15

(D) –2

15


PHYSICS

H-5/320000CT103115008

5. 10 cm 1.5 3 cm

x

(A) 11 cm x = 12 cm

(B) 11 cm x = 14 cm

(C) 11 cm x = 16 cm

(D) 11 cm x = 5 cm

6. v

0

R

V0

(A) (B) v0

(C) (D)

H-6/32

PHYSICS


0000CT103115008

7. 6 kg

10kg

4m

smooth

6kg8m

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

8. m xy a

2 2

2 2

x yV C

a b

{b > a} x = a

x

y

(A) 2c

a

(B)

(C) y = a 2

2ca

b

(D) y = a


PHYSICS

H-7/320000CT103115008

9. x = A sin ty = A sin (t + )

(A) 2

x

y

(B) = x

y

(C) 3

x

y

(D) 3

x

y

10. -1 m

1

m2 4 m/s -2 m

2

m1 2m/s

m1 m2

(A) v1 =

2

5 m/s 2

8v

5 m/s

(B) 1

20v

4 m/s

2v 20 m/s

(C) -1 m2-2 m

1

(D) -1 m2-2 m

1

H-8/32

PHYSICS


0000CT103115008

–II : ( : 16)

-I -II

-I (A), (B), (C) (D) -II (P), (Q), (R), (S) (T) -I -II -I -II 4 × 5 :

(A) (P) (Q) (R) (S) (T)

(B) (P) (Q) (R) (S) (T)

(C) (P) (Q) (R) (S) (T)

(D) (P) (Q) (R) (S) (T)

-I -I (A) (Q), (R) (T) (B), (C) (D)

:

-I +2 0 –1


PHYSICS

H-9/320000CT103115008

1. 500nm P A, B C -I -II P

Slit I

Slit II

P

Screen

Film A B C

Thickness5 1.5 0.25

in m

Re fractive index 1.5 2.5 2

-I -II

(A) B -I (P)

(B) A -I C (Q)

-II

(C) A -I B C (R)

-II

(D) A C -I (S)

B -II (T)

H-10/32

PHYSICS


0000CT103115008

2.

-I -II

(A) I (P)

(B) I (Q)

(C) (R)

(D) (S)

(T)

–III : III


PHYSICS

H-11/320000CT103115008

–IV : ( : 32)

0 9

:

+4

0

1. 1v 1i m/s

1F ejN

e

2

ˆ ˆv i j m/s 2

ˆ ˆF e i j N

3 1 2ˆv v v

(N )

2. CD

2 22

B

A

C

D

10V

H-12/32

PHYSICS


0000CT103115008

3. B R 5.0 cm= 40 rad/s, B = 0.1 T R = 1

× ×

R

×

×

×

×××××

×

×

×

×

4. 0.08 0.081 2 × 10–3/°C 4000 J/kg°C 7°C 103 kg/m3 kW


PHYSICS

H-13/320000CT103115008

5. 15m (|Q| = 0.01 µC)

esa cny fn; k t kr k gSA v c d sUæ i j u; s foHko d k eku

+Q –Q

–Q +Q

+Q –Q

–Q +Q74º

6. P1V

1 – P

2V

2 P

1 V

1

P2 V

2 = 1.5

xR x R

H-14/32

PHYSICS


0000CT103115008

7. m = 0.5 kg 15 N F = 53º µ = 0.5

(m/s2 )

F

8. m V

m/4 e n n


CHEM

ISTRY

H-15/320000CT103115008

-2 :

–I : ( : 40)

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

:

+4

0

–2

1. -

(A)

(B)

(C)

(D)

2. PCl3(g) PH

3(g) 140 8 kJ /[P

4(s)]

320, 120 216 kJ/

(A) P–Cl 63 kJ/

(B) P–H 210 kJ/

(C) 108 kJ/

(D) 60 kJ/

3. KBr 100 L Pt 10 sec. 9.65

(A) H2 (B) O2 (C) Br2 (D) KOH

4. -

(A) BF3

(B) SF6

(C) IF5

(D) PCl5

H-16/32

CHEM

ISTRY


0000CT103115008

5. NH3

(A) (B)

(C) (D)

6. HCl 'x'

(A) SO32– (B) CO

32– (C) S2– (D) CH

3COO–

7.

(A) Ni(CO)4

(B) [MnCl4]2– (C) K

4[Fe(CN)

6] (D) [CoCl

4]2–

8. X Y

H–C C–CH –C–CH –CH2 2 3

O(X)

CH –C C–CH –CH –C–H3 2 2

(Y)

;

O

(A) X Y

(B) X Y

(C) X Y

(D) X Y


CHEM

ISTRY

H-17/320000CT103115008

9. C = CH C3

H H

CH3 OsO / NaHSO4 3 (A)

(B)

(i) CF C3–

(ii) Aq. KOH

OO

H

O

(A) A A B

(B) B A B

(C) A

(D) B

10. H2O

(A) CCl –C–H3

O

(B)

O

(C)

O

O O(D)

O

H-18/32

CHEM

ISTRY


0000CT103115008

–II : ( : 16)

-I -II

-I (A), (B), (C) (D)

-II (P), (Q), (R), (S) (T)

-I -II

-I -II

4 × 5 :

(A) (P) (Q) (R) (S) (T)

(B) (P) (Q) (R) (S) (T)

(C) (P) (Q) (R) (S) (T)

(D) (P) (Q) (R) (S) (T)

-I

-I (A) (Q), (R) (T)

(B), (C) (D)

:

-I

+2

0

–1

1. -I -II

(A) 0.1N HCN (Ka = 10–10) 0.1M NaCN pH (P) 10

(B) 0.1N BOH (pKb = 6) 0.05M B

2SO

4 pH (Q) 7

(C) 0.1M (pKa = 5) (R) 6

(pKb = 7) pH

(D) 500 0.02 M HNO3 500 0.01M Sr(OH)

2(S) 8

pH (T)


CHEM

ISTRY

H-19/320000CT103115008

2. -I () -II ()

(A) XeO2F

2(P)

(B) XeOF4

(Q) d-

(C) PH4

+ (R)

(D) ICl4

–(S)

(T)

–III : III

H-20/32

CHEM

ISTRY


0000CT103115008

–IV : ( : 32)

0 9

:

+4

0

1. Ba(SCN)2 SO42–, CO3

2– NO3–

X

X

4

2. 27ºC 2A(g) + B(g) 2C(g), Ur = 25.6 kcal A, B, C

200, 100 , 500 cal/mole G (Kcal )

[R = 2cal/mole-K]

( )

3. Zn+2

NH4OH, NaOH, (NH

4)

2S, K

4[Fe(CN)

6]


CHEM

ISTRY

H-21/320000CT103115008

4.

H2, HeH–, He

2+, Li

2, O

22–, FeI

3

5.

HOOC COOH

(A)

(i) (A) 3

(ii) (A) 1

(iii) A 2

(iv) (A)

(v) (A) 1

6. CH –C3

O

O– (C–O)

(i)

O

(ii)

O

(iii)

OH

(iv) CH3–OH (v) CH

3–CH

2–OH

(vi) CH –CH –C3 2

O

H(vii)

O

H-22/32

CHEM

ISTRY


0000CT103115008

7. NaOH

NO2

F

(i)

NO2

Cl

(ii)

NO2

FNO2

(iii)

F

NO2

(iv)

NO2

FNO2O N2

(v) Br NO2 (vi) I NO2

8.

(i) CH –C–CH3 3

O

(ii) CH –C–H3

O

(iii)

O

(iv)

O OH

(v)

O

O

(vi) CH3–CH

2–OH


MATHEM

ATICS

H-23/320000CT103115008

-3 : –I : ( : 40)

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

:

+4

0

–2

1. P 2x – 2y + z = 9 A(13,–11,15) (A) P A (1,1,9)

(B) P A (–11,13,3)

(C) P A 18

(D) P xy,yz,zx 35/23

2. z4 + 1 = z2 -

(A) z 6

(B) [0,2] z 11

6

(C) z (D) z

3. ƒ : R R 2xƒ(x) + (1 + x2)ƒ'(x) = 1 ƒ(0) = 0 -

(A) ƒ(x) (B) ƒ(x) 1

(C) 1

ƒ x4

2 (D) 1ƒ ƒ x

2 2

H-24/32

MATHEM

ATICS


0000CT103115008

4. A 1

1 2 3

A 1 3 6

2 5 7

(|A|, A )-

(A) A (B) (adjA) 11

2

(C) (A adjA)3

2 (D) |A–1| = –2

5. x- y

0

B(t )2

A(t )1

30º

S (1,0)x

S(1,0) A(t1) B(t

2)

x-30º

(A) 4 (B) 21 1t 2 3t 1

(C) AB 1 (D) 22 2t 2 3t 1

6. a,b R ab 1 6a2 + 20a + 15 = 0 15b2 + 20b + 6 = 0

3

32

b p

qab 9 ab 1

p,q -

(A) p 6 (B) q 6 (C) p 5 (D) q 5


MATHEM

ATICS

H-25/320000CT103115008

7. ƒ : R+ R ƒ(a.b) = ƒ(a) + ƒ(b) a,bR+

1

x

0

I ƒ(3 )dx

(A) ƒ(3)

I2

(B) log 3

I2

(C) ƒ( 3) (D) 3

ƒ ƒ( 2)2

8. m

mk 0

1 kƒ x lim x

m m

-

(A) 1

ƒ 02

(B) 1

ƒ 12

(C) 3

ƒ 12

(D) 3

ƒ 22

9. k [1,]4 2

6 3

x xk

x 2x 1

(A) 1

6(B)

1

5(C)

1

4(D)

1

3

10. (0, 1) ƒ ƒ"(x) > 0 ƒ(0) = 0,

ƒ(1) = 1 g(x), ƒ(x)

(A)

ƒ x

ƒ ' x x 0,1x

(B)

ƒ x

ƒ ' x x 0,1x

(C)

ƒ x xx 0,1

x g x (D)

ƒ x x

x 0,1x g x

H-26/32

MATHEM

ATICS


0000CT103115008

–II : ( : 16)

-I -II

-I (A), (B), (C) (D) -II (P), (Q), (R), (S) (T) -I -II -I -II 4 × 5 :

(A) (P) (Q) (R) (S) (T)

(B) (P) (Q) (R) (S) (T)

(C) (P) (Q) (R) (S) (T)

(D) (P) (Q) (R) (S) (T)

-I -I (A) (Q), (R) (T) (B), (C) (D)

:

-I +2 0 –1

1. A B

A :

B :

-I -II

(A) a

P Ab

a b a (P)

(B) p

P Bq

p q q (Q)

(C) A u

PB v

u v u (R)

(D) B m

PA n

m n (S)

3(m + n) (T)


MATHEM

ATICS

H-27/320000CT103115008

2. -I -II

(A)

4991000

2k 1k 0

2k 1 C

100

, ........ (P) 2

(B) 4

3 1

, ........ (Q) 4

( [.] )

(C) (R) 8

12

144

7

p

q p q

(2q + p), ....., (S) 9

(D) xi {1,2,3,4} i = 1,2,3,4 x

i x

j,

i j |xi – i| > 0 x

1x

2x

3x

4 (T) 11

–III : III

H-28/32

MATHEM

ATICS


0000CT103115008

–IV : ( : 32)

0 9

:

+4

0

1. ƒ(x) = (2x – )3 + 2x – cosx 1dƒ x

dx

, x = 1,a N

a a

2. k 2

2

x x 1k

x x 1

3.

2 2y 1 x 2

164 49

P P 8

d d


MATHEM

ATICS

H-29/320000CT103115008

4. log2y + (21+x + 21–x) (log y) + 22x+1 + 21–2x = 0, x,y R |log(x + y)|

5. a, b, c

c a c b

21 a c b a a b a

6. x

1 x 1 alim tan

x 1 2x 2 b

(a,b N) a + b

H-30/32

MATHEM

ATICS


0000CT103115008

7. x = ee n(nx)n2(nx) (e )

8. k 23 x , x 1

ƒ xx k , x 1

x = 1


H-31/320000CT103115008


Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005

+91-744-5156100 [email protected] www.allen.ac.in

Your Target is to secure Good Rank in JEE 2016 0000CT103115008H-32/32

:

15.

16.

17.

18. :

19.

20.

21. g = 10 m/s2

____________________________

____________________________

................................................................................................

.............................................

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