JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

56
READ THE INSTRUCTIONS CAREFULLY GENERAL : 1. This sealed booklet is your Question Paper. Do not break the seal till you are told to 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, form number and sign in the space provided on the back cover of this booklet. 5. After breaking the seal of the booklet, verify that the booklet contains 28 pages and that all the 20 questions in each subject and along with the options are legible. If not, contact the invigilator for replacement of the booklet. 6. You are allowed to take away the Question Paper at the end of the examination. OPTICAL RESPONSE SHEET : 7. The ORS will be collected by the invigilator at the end of the examination. 8. Do not tamper with or mutilate the ORS. Do not use the ORS for rough work. 9. Write your name, form number and sign with pen in the space provided for this purpose on the ORS. Do not write any of these details anywhere else on the ORS. Darken the appropriate bubble under each digit of your form number. DARKENING THE BUBBLES ON THE ORS : 10. Use a BLACK BALL POINT PEN to darken the bubbles on the ORS. 11. Darken the bubble COMPLETELY. 12. The correct way of darkening a bubble is as : 13. The ORS is machine-gradable. Ensure that the bubbles are darkened in the correct way. 14. Darken the bubbles ONLY IF you are sure of the answer. There is NO WAY to erase or "un-darken" a darkened bubble. 15. Take g = 10 m/s 2 unless otherwise stated. PAPER – 1 Test Type : MINOR Test Pattern : JEE-Advanced TEST DATE : 08 - 01 - 2017 PHASE : I JEE (Main + Advanced) : NURTURE COURSE Paper Code : 1001CT100116019 CLASSROOM CONTACT PROGRAMME (Academic Session : 2016 - 2017) Please see the last page of this booklet for rest of the instructions Time : 3 Hours Maximum Marks : 222 ENGLISH DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR

Transcript of JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

Page 1: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

READ THE INSTRUCTIONS CAREFULLY

GENERAL :

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

to 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, form number and sign in the space provided on the back cover of this

booklet.

5. After breaking the seal of the booklet, verify that the booklet contains 28 pages and that

all the 20 questions in each subject and along with the options are legible. If not, contact

the invigilator for replacement of the booklet.

6. You are allowed to take away the Question Paper at the end of the examination.

OPTICAL RESPONSE SHEET :

7. The ORS will be collected by the invigilator at the end of the examination.

8. Do not tamper with or mutilate the ORS. Do not use the ORS for rough work.

9. Write your name, form number and sign with pen in the space provided for this purpose on

the ORS. Do not write any of these details anywhere else on the ORS. Darken the

appropriate bubble under each digit of your form number.

DARKENING THE BUBBLES ON THE ORS :

10. Use a BLACK BALL POINT PEN to darken the bubbles on the ORS.

11. Darken the bubble COMPLETELY.

12. The correct way of darkening a bubble is as :

13. The ORS is machine-gradable. Ensure that the bubbles are darkened in the correct way.

14. Darken the bubbles ONLY IF you are sure of the answer. There is NO WAY to erase or

"un-darken" a darkened bubble.

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

PAPER – 1

Test Type : MINOR Test Pattern : JEE-Advanced

TEST DATE : 08 - 01 - 2017

PHASE : I

JEE (Main + Advanced) : NURTURE COURSE

Paper Code : 1001CT100116019

CLASSROOM CONTACT PROGRAMME(Academic Session : 2016 - 2017)

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

Time : 3 Hours Maximum Marks : 222

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SOME USEFUL CONSTANTS

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,

1001CT100116019

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BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

PART-1 : PHYSICS

SECTION–I(i) : (Maximum Marks : 18)

This section contains SIX questions.

Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options

is correct.

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

For each question, marks will be awarded in one of the following categories :

Full Marks : +3 If only the bubble corresponding to the correct option is darkened.

Zero Marks : 0 If none of the bubbles is darkened.

Negative Marks : –1 In all other cases

1. A person hears a single-frequency sound from a speaker that emits sound uniformly in all

directions. The person records the decibel level reading. Which of the following processes would

increase the decibel reading the most?

(A) The power output of the speaker is doubled.

(B) The distance of the person to the speaker is halved.

(C) The frequency of the sound is doubled.

(D) The temperature of the air is doubled on the Kelvin scale.

2. An open-organ tube of air supports standing waves at frequencies of 300 Hz and 400 Hz and at

no frequencies between these two. The second harmonic of this tube has freqency :-

(A) 100 Hz (B) 200 Hz (C) 400 Hz (D) 600 Hz

3. An open pipe of sufficient length is dipping in water with a constant speed V vertically. If at anyinstant 't', l is length of tube above water then the rate at which fundamental frequency of pipechanges at this instant is (C is the speed of sound in air, v = particle velocity of medium at thatinstant) :-

Vl

(A) 2

CV

2(B) 2

CV

4(C) 2 2

CV

2v t(D) 2 2

CV

4v t

Space for Rough Work

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4. A small source S of mass m starts moving with velocity 40 m/s towards a detector D of samemass m on a frictionless surface AB as shown in the figure. The frequency received by thedetector as a function of time in the time interval 0 t 16 s is: [Assume all collisions to beelastic]. Take v

s = 340 m/s.

S D

A B160m 160m

t = 0

(A)

4 8 12 16

f

t

(B)

4 8 12 16

f

t

(C)

4 8 12 16

f

t

(D)

4 8 12 16

f

t

5. A steel wire of length L, cross-sectional area A and density is fixed between two rigid supports,

with the wire just taut. Y = young's modulus and = coefficient of thermal expansion of steel. If

the wire temperature is now lowered by T, then the frequency of the fundamental note produced

by plucking the wire in the middle is :-

(A)

1/21 YL T

L

(B)

1/21 Y T

2L

(C)

1/21 Y T

2L L

(D)

1/21 Y T

L

6. An enclosed one mole of an monoatomic gas is taken through a process A to B as shown in

figure. The molar heat capacity of the gas for this process is

p

2p0

p0

B

A

V0 2V0V

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

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SECTION–I(ii) : (Maximum Marks : 24)

This section contains SIX 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

For each question, marks will be awarded in one of the following categories :

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

darkened.

Zero Marks : 0 If none of the bubbles is darkened.

Negative Marks : –1 In all other cases.

7. The arrow OA in the PV diagram shown in figure represents a reversible adiabatic expansion

of an ideal gas. The same sample of gas, starting from the same state O, now undergoes a

process to the same final volume. Select the appropriate combination of process and final

state.

CAB

P

V

O

(A) Process : isothermal ; final state : B (B) Process : free expansion ; final state : B

(C) Process : isothermal ; final state : C (D) Process : free expansion ; final state : C

8. For two different gases X and Y, having degrees of freedom f1 and f

2 and molar heat capacities

at constant volume 1VC and

2VC respectively, the ln P versus ln V graph is plotted for adiabatic

process, as shown

(A) f1 > f

2(B) f

2 > f

1(C)

2VC > 1VC (D)

1VC > 2VC

Space for Rough Work

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9. A puck is connected to a string kept on a smooth table. The puck revolves about another end of

the string in a horizontal circle with uniform angular velocity.

(A) instantaneous power imparted by string to puck is zero.

(B) the force exerted by the string remains constant in magnitude.

(C) the angular momentum of the puck about the centre keeps on changing direction, but the

magnitude remains constant.

(D) at any given instant, force, velocity and angular velocity vectors are mutually

perpendicular.

10. A disc of mass M radius R is placed on a rough incline of angle as shown in figure. A force is

to be applied parallel to incline at the top most point of disc to keep it at rest.

F

(A) applied force is Mg sin

2

(B) Friction force is Mg sin

2

(C) Minimum friction coefficient required to keep the body at rest in this situation is tan

2

(D) Minimum friction coefficient required to keep the body at rest in this situation is tan

Space for Rough Work

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11. From given graph of SHM we can not conclude about which of the following properties

0 1 2 sec time

cm

Displacementfrom mean

0.2cm

(A) Energy of SHM (B) Maximum velocity

(C) angular frequency of SHM (D) force constant

12. An observer rides with a sound source of frequency n and moving with velocity v towards a

large vertical wall. (C is the velocity of sound in air)

(A) The number of waves striking the surface of the wall per second is C

nC v

(B) The wavelength of the reflected wave is C v

n

(C) The frequency of the reflected wave is nC

C v

(D) beat frequency heard by the observer is n2v

C v

Space for Rough Work

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SECTION–I(iii) : (Maximum Marks : 16)

This section contains TWO paragraphs.

Based on each paragraph, there will be TWO 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.

For each question, marks will be awarded in one of the following categories :

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

darkened.

Zero Marks : 0 If none of the bubbles is darkened.

Negative Marks : –1 In all other cases.

Paragraph for Question no. 13 and 14

1 mole of a gas at temperature of 127°C having a volume of 10–3 m3 confined under a piston issuddenly expanded. Its temperature is seen fall to 27°C. The work done by the gas during the

process is known to be 2500 J. The mass of the gas enclosed under the piston is 40gm. Take

R = 25

3J/mol K.

13. Mark the CORRECT statement(s):

(A) Ratio of p

v

C

C for the gas is

4

3(B) The gas undergoes adiabatic expansion

(C) Gas is monoatomic (D) Translational degree of freedom of gas is 3

14. Choose the CORRECT statement(s) :(A) Speed of sound in the gas at 127°C is 333.33 m/s

(B) Speed of sound in the gas at 127°C is 318.66 m/s

(C) Volume of gas after expansion is 3 364

10 m27

(D) Volume of gas after expansion is 4

3375 m3

Space for Rough Work

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Paragraph for question nos. 15 and 16

A gas is taken from state A to state B to C and then back to A, as shown in the P-V diagram here.

AB

C40

20

p (in Pa)

1 4 V(in m )3

The heat given to the gas, work done by the gas and change in its internal energy are tabulatedin table below.

Q W U

A B a b c

B C d e f

C A g h i

15. The entry that is positive (> 0) is :-

(A) c (B) e (C) f (D) g

16. Mark the CORRECT statement(s) :

(A) If entry ' i ' is –210 J, gas is monoatomic

(B) If entry ' i ' is –210 J, gas is diatomic

(C) Heat given to the gas for the entire cycle is –30 J

(D) Heat given to the gas for the entire cycle is 30 J

SECTION –II : Matrix-Match Type & SECTION –III : Integer Value Correct Type

No question will be asked in section II and III

Space for Rough Work

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SECTION–IV : (Maximum Marks : 16)

This section contains FOUR 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.

For each question, marks will be awarded in one of the following categories :

Full Marks : +4 If only the bubble corresponding to the correct answer is darkened.

Zero Marks : 0 In all other cases.

1. The equation of a longitudinal standing wave due to superposition of the progressive waves

produced by two sources of sound is s = – 20 sin 10 x sin 100 t where s is the displacement

from mean position measured in mm ; x is in metres and t in seconds. The specific gravity of

the medium is 10–3. Find minimum distance between pressure antinode and the displacement

antinode. If your answer is x (in cm) fill x.

2. Many species cool themselves by sweating, because as the sweat evaporates, heat is given up

to the surroundings. A human exercising strenuously has an evaporative heat loss rate of

about 290 W. If a person exercises strenuously for 14 min, how much water (in gm) must he

drink to replenish his fluid loss? The heat of vaporization of water is 580 cal/g at normal skin

temperature. If your answer is N fill value N/25. (Take 1 cal = 4.2 J)

Space for Rough Work

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3. Two tuning forks A and B each of natural frequency 85 Hz move with velocity 10 m/s relative to

stationary observer 'O'. Fork A moves away from the observer while the fork B moves towards

him as shown in the figure. A wind with a speed 10 m/s is blowing in the direction of motion of

fork A. Find the beat frequency measured by the observer in Hz. [Take speed of sound in air as

340 m/s]

4. Two identical wires, one made of iron and the other of aluminum are stretched along - side

on a sonometer board by equal stretching forces.

[Density of iron = 7.5 gm/cc, density aluminum = 2.7 g/cc]

If the frequency of lowest harmonic for which both wires vibrate in unison is 10 Hz fill the

value of . (Given that the length of the wires is 1 m, their diameters 1 mm and tension 75

Newton)

Space for Rough Work

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PART-2 : CHEMISTRY

SECTION–I(i) : (Maximum Marks : 18)

This section contains SIX questions.

Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options

is correct.

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

For each question, marks will be awarded in one of the following categories :

Full Marks : +3 If only the bubble corresponding to the correct option is darkened.

Zero Marks : 0 If none of the bubbles is darkened.

Negative Marks : –1 In all other cases

1. For the given isotherm (P in atm & V in lt) for one mole of an ideal gas, which follows Boyle’s law,

what will be the approximate value of temperature (R = 0.0821 L atm/mol / K) -.

2.0 1.5

1.0 0.5 0

log10P

log 10 V

0.5 1.0 1.5 2.0 2.5

(A) 8.2 × 10–4 K (B) 1220 K (C) 947 K (D) 48 K

2. Wavelength of photon emited when an electron in H-atom jumps from an orbital having 2 angular nodes

with one spherical node to an orbital having total 1 node is -

Given hc = 1240 eV.nm

(A) 1240

nm10.2

(B) 1240

nm1.89

(C) 1240

2.55 nm (D)

1240nm

0.66

Space for Rough Work

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3. Which of the following set of quantum numbers is not possible for an electron in

Mn+2(Z = 25) ion :-

(A) n = 4 , l = 0 , m = 0 , s = +1/2

(B) n = 3 , l = 2 , m = –1 , s = +1/2

(C) n = 3 , l = 2 , m = 0 , s = –1/2

(D) n = 3 , l = 1 , m = +1 , s = –1/2

4. The magnitude of He.g

(electron gain enthalpy) will be maximum for :-

(A) O(g) (B) O+(g) (C) O

+2(g) (D) N(g)

5. Compound in which one of the Tautomeric form can show Geometrical isomerism is :

(A) CH –C–CH3 3

O

(B) CH3–CH

2–NO

2(C)

O

(D)

O

6. Total number of structural isomers are possible with molecular formula C4H

10O are :

(A) 5 (B) 6 (C) 7 (D) 8

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SECTION–I(ii) : (Maximum Marks : 24)

This section contains SIX 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

For each question, marks will be awarded in one of the following categories :

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

darkened.

Zero Marks : 0 If none of the bubbles is darkened.

Negative Marks : –1 In all other cases.

7. Among the following transitions of an electron of H-atom

T1 : 4d 3p

T2 : 4d 3s

T3 : 3d 2p

T4 : 3d 2s

Choose the correct option of order of wavelength of emitted photon during these transitions.

(A) T1 > T

2(B) T

2 > T

3(C) T

3 > T

4(D) T

4 > T

1

8. In an empty cylinder piston arrangement , NO2(g) at 2 atm and N

2O

4(g) at 4 atm is taken and the

constant pressure of 6 atm and temperature, 27°C, is maintained.

2 4 2 pN O g 2NO g ;K 20 atm at 300K

Which of the following property (ies) of system will change correctly (as given) with time ?

(N2O

4 colourless , NO

2 Brown colour)

(A) Density of sample will decrease.

(B) Average molar mass of sample will increase.

(C) The colour of solution becomes more & more deeper

(D) Reaction will not move in any direction

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9. Which of the following set(s) contain isostructural species :-

(A) HCC– , CO

2 , I

3

–(B) XeF

2 , BeF

2 , NO

2

+

(C) SO3 , BF

3 , PCl

3(D) SiCl

4 , CH

4 , NH

4

+

10. Which of the following statement(s) is INCORRECT regarding ICl4

– :-

(A) Hybridisation of central atom is not sp3d.

(B) 'd' orbital is not involved in bonding

(C) The ion has total 2 lone pair of electron

(D) Maximum number of atoms in one plane are equal to four

11. How many of following compounds contain odd number of 'D' atom in its enol form after prolong

treatment with OD / D2O :

(A)

O

(B)

O

(C)

O

(D)

O

12. Identify the correct order :

(A) < (Heat of combustion)

(B) < (Heat of hydrogenation)

(C) C—NH2

+

H C3

H C3

< CH3

H C3

H C3

+ (Stability of carbocation)

(D)

CH2

NO2

–:

>

CH2

OCH3

–:

(Stability of carbanion)

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SECTION–I(iii) : (Maximum Marks : 16)

This section contains TWO paragraphs.

Based on each paragraph, there will be TWO 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.

For each question, marks will be awarded in one of the following categories :

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

darkened.

Zero Marks : 0 If none of the bubbles is darkened.

Negative Marks : –1 In all other cases.

Paragraph for Questions 13 and 14

The orbital wave function for an electron in an atom is a mathematical function and as such

does not convey any physical sense. However, 2 makes a physical sense. Its value at a particular

point in an atom gives the probability density of the electron at that point. The region in which

the probability density function, i.e., 2 reduces to zero is called nodal surface. There are two

types of nodal surface (i) Radial node (ii) Angular node. The shape of an orbital can be obtained

with the help of probability density. The shape of an orbital is defined as a surface of constant

probability density that encloses some large fraction (say 90%) of the probability of finding the

electron.

13. Which of the following statements regarding 2s orbital is/are correct ?

(A) It is spherically symmetrical

(B) It possess one nodal surfaces

(C) it lies along X-axis

(D) In it, the density is maximum at the nucleus which falls off to zero at a certain distance,

further increases to a maximum and then falls off with the increases in distance from the

nucleus.

14. Which of the following radial distribution curves is not correctly plotted ?

(A)

(r)

r

1s

(B)

(r)

r

2s

(C)

2(r)

r

1s

(D)

(r)

r

2s

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Paragraph for Questions 15 and 16

H A— H + A+ :–

Conjugatebase

Acid

Acidic strength of H—A depend on stability of conjugate base ( A

:– ), i.e, more stable

conjugate base A

:–, more acidic strength of H—A

a

1pK

acidic strength

15. In which of the following pair of compounds, order of pKa is correct :

(A)

COHO

OHHO

<

COHO

OH

(B)

COHO

<

OH

(C)

OH

<

OH

NO2

NO2

(D)

COHO

<

COHO

CH3

16. Identify compounds which are more basic than

NH2

?

(A)

N

(B)

NH2

(C)

N

H

(D)

NMeMe

Me Me

SECTION –II : Matrix-Match Type & SECTION –III : Integer Value Correct Type

No question will be asked in section II and III

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Space for Rough Work

SECTION–IV : (Maximum Marks : 16)

This section contains FOUR 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.

For each question, marks will be awarded in one of the following categories :

Full Marks : +4 If only the bubble corresponding to the correct answer is darkened.

Zero Marks : 0 In all other cases.

1. For the reaction 3 A (g) + B (g) 2 C (g) at a given temperature, Kc = 9.0. What must be the volume

(in litre) of the flask, if a mixture of 2.0 mol each of A, B and C exist in equilibrium?

2. Find the number of H-atoms which are linked with each O atom in ice ?

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3. From the following list find the number of molecules/Ions for which net dipole moment (net

) is

NOT ZERO.

PCl4

+ , PCl3F

2 , PCl

2F

3 , NH

3 , NH

4

+ , I3

– , XeF5

– ,

ClCl

4. How many compounds show geometrical isomerism ?

(a) (b) C=C=CCl

Cl

H

H(c)

Br

I

Cl

H(d)

Me

Et

Me

Et

(e)Cl

H H

Cl

(f) (g) (h)

(i)Cl

H H

Cl

Space for Rough Work

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MATHEM

ATICS

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

1001CT100116019

PART-3 : MATHEMATICSSECTION–I(i) : (Maximum Marks : 18)

This section contains SIX questions.

Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options iscorrect.

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

For each question, marks will be awarded in one of the following categories :Full Marks : +3 If only the bubble corresponding to the correct option is darkened.Zero Marks : 0 If none of the bubbles is darkened.Negative Marks : –1 In all other cases

1. The number of values of x (0°,90°) satisfying the equation tanx = tan(x + 10º)tan(x + 20º) tan(x + 30º) is -

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

2. In ABC, if

2

B C3

and R = 8r where R and r are circumradius and inradius of the triangle,

then value of sinA is equal to -

(A) 15

8(B)

1

4(C)

15

16(D)

15

4

3. If the sum of the binomial coefficients in the expansion of

n2

3

2x

x is 243, then the term

independent of x is-

(A) 11 (B) 1

2(C) 15 (D) 40

4. Coefficient of x12 in the expansion of (1 + x2)4.(1 + x3)7.(1 + x4)12 is-

(A) 1671 (B) 1720 (C) 1535 (D) 1755

5. The number of irrational terms in the expansion of

30011

525 7 is -

(A) 31 (B) 270 (C) 30 (D) 271

6. A code is a sequence of 0's and 1's that does not have three consecutive 0's. The possible number

of codes that have exactly 11 digits is -

(A) 927 (B) 9 × 28 (C) 504 (D) 210 – 9

Space for Rough Work

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E-21/281001CT100116019

Space for Rough Work

SECTION–I(ii) : (Maximum Marks : 24)

This section contains SIX 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

For each question, marks will be awarded in one of the following categories :

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

darkened.

Zero Marks : 0 If none of the bubbles is darkened.

Negative Marks : –1 In all other cases.

7. One commercially available Tenbutton lock can be opened by pressing the correct button(s) in

any order. Number of possible ways that these locks are designed so that sets of as many as nine

and as few as one button could serve as combination. (Assume that in every combination a

button can not be pressed more than once)

{The sample shown has 1,2,3,6,9 as its combination}

1

2

3

4

5

6

7

8

9

10

(A) 210 – 2 (B) 210 – 1 (C) 10

10r

r 0

( C ) 1

(D) 10! – 2

8. Let ƒ(x) = [4x – 2x + 1], where [.] denotes greatest integer function. Which of the following

is/are true-

(A) for x (–,2), range of ƒ contains 13 elements

(B) for x (–,2), range of ƒ contains 14 elements

(C) domain of ƒ is (–,2)

(D) domain of ƒ is R (where R is set of all real numbers)

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MATHEM

ATICS

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

1001CT100116019

9. Let P(x) 21 11 x x

3 6, define Q(x) = P(x).P(x3).P(x5)P(x7)P(x9)

50

ii

i 0

a x and

50 50

i ii 0 i 0

m pa , a

n q where m,n are relative prime and p,q are also relative prime, then-

(A) m + n = 275 (B) m – n = 211 (C) p – q = –4651 (D) p + q = 10901

10. Let (|x| 1)

1ƒ x

log [x]

and [x]

1g x

log |x 3|

. Then which of the following holds good.

(where [.] represent greatest integer function)

(A) Number of positive integers which are not present in domain of ƒ(x) is 2.

(B) Number of positive integers which are not present in domain of g(x) is 4.

(C) Domain of ƒ(x) is subset of domain of g(x).

(D) Domain of g(x) is subset of domain of ƒ(x).

11. Which of the following pair of functions is/are identical (where [.] represents greatest integer

function, {.} represents fractional part and sgn(.) denotes signum funtion)

(A) ƒ(x) = [{x}] and g(x) = {[x]}

(B) ƒ(x) = x|x| and g(x) = x2sgn(x)

(C) xneƒ x e and g(x) = ex

(D) ƒ(x) = tan2x.sin2x and g(x) = tan2x – sin2x

12. In ABC with usual notation, which of the following statement(s) is/are true.

(A) The maximum value of sin2A + sin2B + sin2C is same as the maximum value of

sinA + sinB + sinC

(B) R > 2r

(C)

2 abcR

a b c

(D) If r + 2R = s, then ABC is right angled

Space for Rough Work

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Nurture Course/Phase-I/08-01-2017/Paper-1

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ATICS

E-23/281001CT100116019

SECTION–I(iii) : (Maximum Marks : 16)

This section contains TWO paragraphs.

Based on each paragraph, there will be TWO 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.

For each question, marks will be awarded in one of the following categories :

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

darkened.

Zero Marks : 0 If none of the bubbles is darkened.

Negative Marks : –1 In all other cases.

Paragraph for Questions 13 and 14

Let the sum of first 10 terms of an arithmetic progression is equal to 155 and the sum of first

two terms of geometric progression is 9. Also the first term of the arithmetic progression is

equal to the common ratio of the geometric progression and the first term of the geometric

progression is equal to the common difference of arithmetic progression.

13. The common difference of arithmetic progression can be -

(A) 3 (B) 2

3(C)

1

3(D) 2

14. The common ratio of geometric progression can be -

(A) 2 (B) 25

2(C)

1

2(D)

2

25

Space for Rough Work

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MATHEM

ATICS

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

1001CT100116019

Paragraph for Questions 15 and 16

The line x + 2y = a intersects the circle x2 + y2 = 4 at two distinct points A and B. Another line

12x – 6y – 41 = 0 intersects the circle x2 + y2 – 4x – 2y + 1 = 0 at two another distinct points

C and D.

15. The value of 'a' for which the points A,B,C and D are concyclic -

(A) 2 (B) 0 (C) –4 (D) –2

16. Equation of circle circumscribing quadrilateral ABCD is -

(A) 5x2 + 5y2 + 8x – 16y – 36 = 0 (B) 5x2 + 5y2 – 8x – 16y – 36 = 0

(C) 5x2 + 5y2 – 8x + 16y – 36 = 0 (D) 5x2 + 5y2 + 8x – 16y + 36 = 0

SECTION –II : Matrix-Match Type & SECTION –III : Integer Value Correct Type

No question will be asked in section II and III

Space for Rough Work

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Nurture Course/Phase-I/08-01-2017/Paper-1

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ATICS

E-25/281001CT100116019

SECTION–IV : (Maximum Marks : 16)

This section contains FOUR 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.

For each question, marks will be awarded in one of the following categories :

Full Marks : +4 If only the bubble corresponding to the correct answer is darkened.

Zero Marks : 0 In all other cases.

1. Let

2

2

x 4ƒ x

5 36 x, if complete interval of positive values of x in the domain of ƒ(x) is

[2,a) (a,b], then value of a2 – b is

2. The number of integers in the range of the function ƒ(x) = (sinx + 1) (cosx + 1) is

Space for Rough Work

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MATHEM

ATICS

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1001CT100116019

Space for Rough Work

3. The number of ways to select two distinct numbers 'a' and 'b' from the set {51, 52,53.....525} so

that logab is an integer is denoted by k, then sum of the digits of 'k' is

4. The number of integral values of for which the variable line 3x + 4y – = 0 lies between the

circles x2 + y2 – 2x – 2y + 1 = 0 and x2 + y2 – 18x – 2y + 78 = 0 without having any common points

with any circle is equal to 2k, then value of k is

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Space for Rough Work

Page 28: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

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

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

Your Hard Work Leads to Strong Foundation 1001CT100116019E-28/28

QUESTION PAPER FORMAT AND MARKING SCHEME :

16. The question paper has three parts : Physics, Chemistry and Mathematics.

17. Each part has two sections as detailed in the following table.

I have read all the instructions

and shall abide by them.

____________________________

Signature of the Candidate

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

____________________________

Signature of the invigilator

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

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

Que. No. Category-wise Marks for Each Question Maximum

Section Type of Full Partial Zero Negative Marks of theQue. Marks Marks Marks Marks section

+3 0 –1 I(i) Single If only the bubble If none In all

correct option 6 corresponding to — of the other 18 the correct option bubbles is cases

is darkened darkened+4 0 –1

One or more If only the bubble(s) If none In all I(ii) correct

6 corresponding

—of the other

24option(s) to all the correct bubbles is casesoption(s) is(are) darkened

darkenedParagraph +4 0 –1

Based If only the bubble(s) If none In all I(iii) (One or more 4 corresponding to all — of the other 16

correct the correct option(s) bubbles is casesoption(s)) is(are) darkened darkened

+4 0Single digit If only the bubble In all

IV Integer 4 corresponding — other — 16(0-9) to correct answer cases

is darkened

Page 29: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

1.

2. (ORS)

3.

4.

5. 28 20

6.

7.

8.

9.

:

10.

11.

12. :

13.

14.

15. g = 10 m/s2

PAPER – 1

Test Type : MINOR Test Pattern : JEE-Advanced

TEST DATE : 08 - 01 - 2017

PHASE : I

JEE (Main + Advanced) : NURTURE COURSE

Paper Code : 1001CT100116019

CLASSROOM CONTACT PROGRAMME(Academic Session : 2016 - 2017)

Time : 3 Hours Maximum Marks : 222

HIN

DI

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Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

1001CT100116019

SOME USEFUL CONSTANTS

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

Page 31: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

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PHYSICS

H-3/281001CT100116019

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

-1 : –I(i) : ( : 18)

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

: +3

: 0

: –1

1.

(A) (B)

(C)

(D)

2. 300 Hz 400 Hz

(A) 100 Hz (B) 200 Hz (C) 400 Hz (D) 600 Hz

3. V 't'l (C v) :-

Vl

(A) 2

CV

2(B) 2

CV

4(C) 2 2

CV

2v t(D) 2 2

CV

4v t

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PHYSICS

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

H-4/28 1001CT100116019

4. m S 40 m/s m D AB 0 t 16 s : [v

s = 340 m/s]

S D

A B160m 160m

t = 0

(A)

4 8 12 16

f

t

(B)

4 8 12 16

f

t

(C)

4 8 12 16

f

t

(D)

4 8 12 16

f

t

5. L, A

Y = = T

(A)

1/21 YL T

L

(B)

1/21 Y T

2L

(C)

1/21 Y T

2L L

(D)

1/21 Y T

L

6. A B

p

2p0

p0

B

A

V0 2V0V

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

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PHYSICS

H-5/281001CT100116019

–I(ii) : ( : 24)

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

: +4

: 0

: –1

7. PV OA O

CAB

P

V

O

(A) : ; : B (B) : ; : B

(C) : ; : C (D) : ; : C

8. X Y f1 f

2

1VC 2VC ln P ln V

(A) f1 > f

2(B) f

2 > f

1(C)

2VC > 1VC (D)

1VC > 2VC

Page 34: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

PHYSICS

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

H-6/28 1001CT100116019

9.

(A)

(B)

(C)

(D)

10. M R

F

(A) Mg sin

2

(B) Mg sin

2

(C) tan

2

(D) tan

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Nurture Course/Phase-I/08-01-2017/Paper-1

PHYSICS

H-7/281001CT100116019

11.

0 1 2 sec time

cm

Displacementfrom mean

0.2cm

(A) (B)

(C) (D)

12. n v

(C )

(A) C

nC v

(B) C v

n

(C) nC

C v

(D) n2v

C v

Page 36: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

PHYSICS

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

H-8/28 1001CT100116019

–I(iii) : ( : 16)

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

: +4

: 0

: –1

13 14

127°C 1 10–3 m3

27°C 2500 J R = 25

3J/mol K

40 gm

13. :

(A) p

v

C

C

4

3 (B)

(C) (D) 3

14. (A) 127°C 333.33 m/s (B) 127°C 318.66 m/s

(C) 3 36410 m

27

(D) 4

3375 m3

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PHYSICS

H-9/281001CT100116019

15 16

P-V A B C A

AB

C40

20

p (in Pa)

1 4 V(in m )3

Q W U

A B a b c

B C d e f

C A g h i

15. (> 0)(A) c (B) e (C) f (D) g

16. (A) ' i ' –210 J (B) ' i ' –210 J (C) –30 J (D) 30 J

–II : & –III :

II III

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PHYSICS

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

H-10/28 1001CT100116019

–IV : ( : 16)

0 9

: +4

: 0

1.

s = – 20 sin 10 x sin 100t s (mm )x t

10–3 (cm )

2.

290 W 14

(gm )

580 cal/g N N/25 (1 cal = 4.2 J)

Page 39: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

Nurture Course/Phase-I/08-01-2017/Paper-1

PHYSICS

H-11/281001CT100116019

3. 85 HzA B 'O' 10 m/s

A B A

10 m/s [

340m/s ]

4.

[= 7.5 gm/cc, = 2.7 g/cc]

10 Hz

1 m, 1 mm 75

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CHEM

ISTRY

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

H-12/28 1001CT100116019

-2 : –I(i) : ( : 18)

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

: +3

: 0

: –1

1. atm V

(R = 0.0821 L atm/mol / K) -.

2.0 1.5 1.0

0.5 0

log10P

log 10 V

0.5 1.0 1.5 2.0 2.5

(A) 8.2 × 10–4 K (B) 1220 K (C) 947 K (D) 48 K

2. H-

-

hc = 1240 eV.nm

(A) 1240

nm10.2

(B) 1240

nm1.89

(C) 1240

2.55 nm (D)

1240nm

0.66

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Nurture Course/Phase-I/08-01-2017/Paper-1

CHEM

ISTRY

H-13/281001CT100116019

3. Mn+2

(Z = 25) :-

(A) n = 4 , l = 0 , m = 0 , s = +1/2

(B) n = 3 , l = 2 , m = –1 , s = +1/2

(C) n = 3 , l = 2 , m = 0 , s = –1/2

(D) n = 3 , l = 1 , m = +1 , s = –1/2

4. He.g

( ) :-

(A) O(g) (B) O+(g) (C) O

+2(g) (D) N(g)

5.

(A) CH –C–CH3 3

O

(B) CH3–CH

2–NO

2(C)

O

(D)

O

6. C4H

10O

(A) 5 (B) 6 (C) 7 (D) 8

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CHEM

ISTRY

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

H-14/28 1001CT100116019

–I(ii) : ( : 24)

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

: +4

: 0 : –1

7. H- T

1 : 4d 3p

T2 : 4d 3s

T3 : 3d 2p

T4 : 3d 2s

(A) T

1 > T

2(B) T

2 > T

3(C) T

3 > T

4(D) T

4 > T

1

8. 2 atm NO2(g) 4 atm N

2O

4(g) 6 atm

27°C

2 4 2 pN O g 2NO g ;K = 300K 20 atm

?

(N2O

4 , NO

2 )

(A)

(B)

(C)

(D)

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CHEM

ISTRY

H-15/281001CT100116019

9. :-

(A) HCC– , CO2 , I

3

– (B) XeF2 , BeF

2 , NO

2

+

(C) SO3 , BF

3 , PCl

3(D) SiCl

4 , CH

4 , NH

4

+

10. ICl4

– :-

(A) sp3d

(B) 'd'

(C) 2

(D)

11. OD / D2O 'D'

(A)

O

(B)

O

(C)

O

(D)

O

12.

(A) <

(B) <

(C) C—NH2

+

H C3

H C3

< CH3

H C3

H C3

+

(D)

CH2

NO2

–:

>

CH2

OCH3

–:

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CHEM

ISTRY

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

H-16/28 1001CT100116019

–I(iii) : ( : 16)

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

: +4 : 0

: –1

13 14

2

2

(i) (ii)

(90%)

13. 2s ?

(A)

(B)

(C) X-

(D)

14. ?

(A)

(r)

r

1s

(B)

(r)

r

2s

(C)

2(r)

r

1s

(D)

(r)

r

2s

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CHEM

ISTRY

H-17/281001CT100116019

15 16

H A— H + A+ :–

H—A ( A

:– ) A

:–

H—A

a

1pK

15. pKa

(A)

COHO

OHHO

<

COHO

OH

(B)

COHO

<

OH

(C)

OH

<

OH

NO2

NO2

(D)

COHO

<

COHO

CH3

16.

NH2

(A)

N

(B)

NH2

(C)

N

H

(D)

NMeMe

Me Me

–II : & –III : II III

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ISTRY

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

H-18/28 1001CT100116019

–IV : ( : 16)

0 9

: +4

: 0

1. 3 A (g) + B (g) 2 C (g) Kc = 9.0. A, B

C 2.0

2. H-O ?

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CHEM

ISTRY

H-19/281001CT100116019

3. (net

)

PCl4

+ , PCl

3F

2 , PCl

2F

3 , NH

3 , NH

4

+ , I

3

– , XeF

5

– ,

ClCl

4.

(a) (b) C=C=CCl

Cl

H

H(c)

Br

I

Cl

H(d)

Me

Et

Me

Et

(e)Cl

H H

Cl

(f) (g) (h)

(i)Cl

H H

Cl

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ATICS

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

H-20/28 1001CT100116019

-3 : –I(i) : ( : 18)

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

: +3

: 0

: –1

1. tanx = tan(x + 10º)tan(x + 20º) tan(x + 30º) x (0°,90°)-(A) 1 (B) 2 (C) 3 (D) 4

2. ABC

2B C

3 R = 8r R r sinA

-

(A) 15

8(B)

1

4(C)

15

16(D)

15

4

3.

n2

3

2x

x 243 x -

(A) 11 (B) 1

2(C) 15 (D) 40

4. (1 + x2)4.(1 + x3)7.(1 + x4)12x12 -

(A) 1671 (B) 1720 (C) 1535 (D) 1755

5.

30011

525 7 -

(A) 31 (B) 270 (C) 30 (D) 271

6. 0 1 0 11 -

(A) 927 (B) 9 × 28 (C) 504 (D) 210 – 9

Page 49: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

Nurture Course/Phase-I/08-01-2017/Paper-1

MATHEM

ATICS

H-21/281001CT100116019

–I(ii) : ( : 24)

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

: +4

: 0

: –1

7.

()

{1,2,3,6,9 }

1

2

3

4

5

6

7

8

9

10

(A) 210 – 2 (B) 210 – 1 (C) 10

10r

r 0

( C ) 1

(D) 10! – 2

8. ƒ(x) = [4x – 2x + 1], [.] -

(A) x (–,2) , ƒ 13

(B) x (–,2) , ƒ 14

(C) ƒ (–,2)

(D) ƒ R (R )

Page 50: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

MATHEM

ATICS

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

H-22/28 1001CT100116019

9. P(x) 21 11 x x

3 6, Q(x) = P(x).P(x3).P(x5)P(x7)P(x9)

50

ii

i 0

a x

50 50

i ii 0 i 0

m pa , a

n q m,n p,q -

(A) m + n = 275 (B) m – n = 211 (C) p – q = –4651 (D) p + q = 10901

10. (|x| 1)

1ƒ x

log [x]

[x]

1g x

log |x 3|

([.] )

(A) ƒ(x) 2

(B) g(x) 4

(C) ƒ(x) g(x)

(D) g(x) ƒ(x)

11. ([.] {.}

sgn(.) )

(A) ƒ(x) = [{x}] g(x) = {[x]}

(B) ƒ(x) = x|x| g(x) = x2sgn(x)

(C) xneƒ x e g(x) = ex

(D) ƒ(x) = tan2x.sin2x g(x) = tan2x – sin2x

12. ABC

(A) sin2A + sin2B + sin2C sinA + sinB + sinC (B) R > 2r

(C)

2 abcR

a b c

(D) r + 2R = s ABC

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Nurture Course/Phase-I/08-01-2017/Paper-1

MATHEM

ATICS

H-23/281001CT100116019

–I(iii) : ( : 16)

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

: +4

: 0

: –1

13 14

155 9

13. -

(A) 3 (B) 2

3(C)

1

3(D) 2

14. -

(A) 2 (B) 25

2(C)

1

2(D)

2

25

Page 52: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

MATHEM

ATICS

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

H-24/28 1001CT100116019

15 16

x + 2y = a, x2 + y2 = 4 A B

12x – 6y – 41 = 0, x2 + y2 – 4x – 2y + 1 = 0 C D

15. 'a' A,B,C D -(A) 2 (B) 0 (C) –4 (D) –2

16. ABCD -

(A) 5x2 + 5y2 + 8x – 16y – 36 = 0 (B) 5x2 + 5y2 – 8x – 16y – 36 = 0

(C) 5x2 + 5y2 – 8x + 16y – 36 = 0 (D) 5x2 + 5y2 + 8x – 16y + 36 = 0

–II : & –III :

II III

Page 53: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

Nurture Course/Phase-I/08-01-2017/Paper-1

MATHEM

ATICS

H-25/281001CT100116019

–IV : ( : 16)

0 9

: +4

: 0

1.

2

2

x 4ƒ x

5 36 x ƒ(x) x [2,a) (a,b]

a2 – b

2. ƒ(x) = (sinx + 1) (cosx + 1)

Page 54: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

MATHEM

ATICS

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

H-26/28 1001CT100116019

3. {51, 52,53.....525} a b logab

k 'k'

4. 3x + 4y – = 0, x2 + y2 – 2x – 2y + 1 = 0

x2 + y2 – 18x – 2y + 78 = 0 2k k

Page 55: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

Nurture Course/Phase-I/08-01-2017/Paper-1

H-27/281001CT100116019

Page 56: JEE (Main + Advanced) : NURTURE COURSE - Amazon Web Services

Target : JEE (Main + Advanced) 2018/08-01-2017/Paper-1

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

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

Your Hard Work Leads to Strong Foundation 1001CT100116019H-28/28

16. 17.

____________________________

____________________________

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

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

I(i) +3 0 –1

6

18

+4 0 –1

I(ii) 6 — 24

+4 0 –1 I(iii)

4 — 16 +4 0

IV (0-9)

4 — — 16