JEE (Main + Advanced) : LEADER & ENTHUSIAST COURSE · 2019-11-13 · E-6/32 MATHEMATICS Target :...

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 32 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

SCORE(ADVANCED)JEE (Main + Advanced) : LEADER & ENTHUSIAST COURSE

Paper Code : *1001CT102116075* (1001CT102116075)

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 : 180

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Test Type : FULL SYLLABUS Test Pattern : JEE-Advanced

TEST DATE : 26 - 04 - 2017

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Target : JEE (Main + Advanced) 2017/26-04-2017/Paper-1

*1001CT102116075* (1001CT102116075)

Space for Rough Work

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,

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

Leader & Enthusiast Course/Score(Advanced)/26-04-2017/Paper-1

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BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

PART-1 : MATHEMATICS

SECTION–I : (Maximum Marks : 30)

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

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

Full Marks : +3 If only the bubble(s) corresponding to all the correct option(s) is (are)

darkened.

Zero Marks : 0 In all other cases.

1. If the lengths of each of the segments of a focal chord of the parabola y2 = 8x, which are

divided by the focus of the parabola, are integers then the length of the focal chord may

be

(A) 8 (B) 9 (C) 12 (D) 15

2. Each of the circles z 1 i 1 and z 1 i 1 touches internally a circle of radius 2 units.

The equation of the circle touching all the above three circles can be

(A) 3zz z z 1 0 (B) 3zz 7z 7z 15 0

(C) zz z z 3 0 (D) 3zz z z 1 0

3. Let ' S ' represents the complete set of values of the angle which satisfy the inequality:

cos3 + sin3 + (2sin2 – 3) (sin – cos) > 0, then a subset of ' S ' is

(A) 3

2n ,2n4 6

, n I (B) 2n ,2n

3 4

, n I

(C) 3

2n ,2n4 4

, n I (D)

3 52n ,2n

4 4

, n I


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4. Let 1 x

1 xg(x) t f '(t) dt

where f(x) does not behave like a constant function in any interval

(a, b) and the graph of y = f '(x) is symmetrical about the line x = 1 then

(A) g(x) is increasing x R (B) g(x) is increasing only for x > 1

(C) g'(x) is an even function (D) g'(x) is symmetrical about the line x = 2

5. Consider the function

2

x 1, x [0,1]

2xf (x) , x (1,2)

x

x 3x 3, x [2,3]

. Now choose the correct statement(s) :

({·} denotes fractional part function)

(A) The range of f(x) is [0, 3]

(B) Number of points where f(x) is not differentiable is 3

(C) f(x) is not differentiable at x = 2

(D) The range of f '(x) is [1, 4)

6. A cube root of i 1 , may be

(A) i (B) 3 i

2

(C)

3 i

2

(D)

i 3

2

7. Let ƒ be a real valued function and satisfies1 1

ƒ(x) ƒ(y) x, y R {0}x y

.

If

3 5

4

2

3(ƒ(x)) ƒ(x) 1 2dx log

1 (ƒ(x)) 2 3

, then

(A) (B) < 17

(C) 1 1tan sec5

(D) () is not a prime number


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8. Three students A, B and C appear for IITJEE ADVANCED examination and their respective

probabilities of clearing the examination being 3 1

,10 2

and 2

5. Each student clearing or not

clearing the examination is independent of the other. If the probability of A passing the

examination be m

n (m, n N) given that only one of the student has cleared the examination,

then the least value of (m + n) is greater than

(A) 10 (B) 20 (C) 40 (D) 80

9. Let n

nk

k 0

2kf (n) C cos

n

and

n 1n 1

kk 0

2kg(n) C cos ,

n

then

(A) f(6) is a rational number (B) g(8) is an irrational number

(C) f(n) = 2g(n + 2) (D) f(n) = 2g(n)

10. A fair coin is tossed 10 times and the outcomes are listed. Let Hi be the event that the ith

outcome is a head and Am be the event that the list contains exactly m heads, then which

of the following pair(s) of events are independent :

(A) H4 and H

8(B) A

1 and A

9(C) H

3 and A

4(D) H

2 and A

5

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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SECTION–IV : (Maximum Marks : 30)


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.


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


1. The value of 2 2

nlimsin 4(n!) 4(n!) 1

2

, (n N), is

2. Let M be the mid-point of the side AB of the equilateral triangle ABC having side length

2 units. P is a point on BC such that 'AP + PM ' is minimum. If the value of ' AP + PM ' is

b then the value of ' b ' is

3. Let 1 n

n 2012

0

xI dx

x 1

and 1 n

n 2013

0

xJ dx

x 1

, where n N. If matrix A = [aij]

3×3, where

2012 i i

ij

I I , i ja

0 , i j

and matrix B = [b

ij]

3×3, where

2016 j j 3

ij

J J , i jb

0 , i j

, then

1 11det(B ) 2trace(A )

10 is equal to



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4. The radius of the inscribed circle of a triangle whose side-lengths are three consecutive

natural numbers, is 4 units. If the circumradius of the triangle is R, then the value of

8R

13

is

5. The value of 2 4

0

32 dx,

(1 x )

is


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6. Let the function g : R R be a differentiable function and satisfies x.g(0) + g(x) =

ex–1g'(1) +

2x

2 for all x R. The global minimum value of g(x) is equal to

[Note : e denotes Napier's constant]

7. The least possible integral value of ' a ' for which f(x) = 5sin2x – 2cos2x + 3ax – 4 is

increasing for all x R, is

8. Let ' n ' represents the number of Lattice points (x, y, z all being integers) inside the

tetrahedron (not on the surface) having vertices (0, 0, 0), (8, 0, 0), (0, 8, 0) and (0, 0, 8) then

the value of n

7

is


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9. If the equation in x, 2 22 2

1 1 2 1x x xcos sin (x 6x 8) sin (2k 1)

2 2 12 2 4

possesses solution, then number of integral values of k is equal to

10. A curve satisfying the differential equation (x2y2 – 1) dy + 2xy3dx = 0, is passing through

the points (1, 1) and (k, 2) then the value of (8k2) is


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*1001CT102116075* (1001CT102116075)

PART-2 : PHYSICS



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



darkened.


1. A semicircular wire of radius r is supported in its own vertical plane by a hinge at O and smooth

peg P as shown. If peg starts from O and moves with constant speed v along horizontal axisthrough O. The angular speed of wire is

O P

v

(A) 2 2 2

v

4r v t(B)

v

2r(C)

2 2

v

2r v t(D) None of these



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2. A small hole of area a is at the bottom of a container of area A. The liquid is filled up to height

h from base. As liquid comes out then A

a .3

h

(A) level of liquid in container falls at rate of gh

m/s4

(B) magnitude of acceleration of top surface of liquid is2g

m/s8

(C) acceleration of top surface of liquid is g

3 m/s

2

(D) None of these

3. A small solid ball of density is held inside at point A of a cubical container of side L, filled with

an ideal liquid of density 4 as shown. The container is closed at the top. Now, if the container

starts moving with constant acceleration a horizontally and the ball is released from point A,

simultaneously, then :-

P Q

A a

L

L2

L2

(A) For the ball to hit top of container at end Q, a = 3g

(B) For the ball to hit top of container at end Q, a = 2g

(C) Ball hits the top of container at end Q after a time L

t3g

(D) Ball hits the top of container at end Q after a time L

t2g

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4. One end of a heavy uniform rod AB can slide along a rough horizontal rod CD to which it is

attached by a ring, B and C are joined by a string. If ABC is right angle and be the angle

between AB and vertical. What will be the coefficient of friction between ring and horizontal

rod ?

(system just in equilibrium)

DC

B

A

(A) tan (B) tan

2

(C) 2

tan

2 tan

(D) 2

tan 2

tan

5. In the circtuit shown , which of the following statement is/are CORRECT :

X =50C X =100L V=100 2 sin (377t)

R=100 X =100L

(A) Power factor of the circuit is 1

2

(B) Reactance of the circuit is equal to resistance of the circuit.

(C) Circuit is in a state of resonance

(D) Average power dissipated in the circuit is 100 W.


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6. A source of sound and an observer are located in space. The apparent frequency of sound received

by observer varies with time as shown in graph. Which of the following statements may be

TRUE :

vapp

t

(A) Only source is moving with constant velocity

(B) Only observer is moving with constant velocity

(C) Either source or observer or both are moving with constant velocity and their velocities are

always along the line joining source and observer

(D) When source and observer are moving with constant velocity and their velocities are not

directed along the line joining source and observer.7. A semi-circular disc rests in a vertical plane with its curved edge on rough horizontal and equally

rough vertical surface. The coefficient of friction is for both surfaces, then

B

A

(A) friction acts upwards at A and towards left at B

(B) for greatest value of (for no slipping) normal contact force at A is 2

w,

1

where w = weight

of disc

(C) greatest value of will be 2

1

2

3sin

4 1

(D) None of the above


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8. Nucleus A decays to B with decay constant 1 and B decays to C with a decay constant

2.

Initially at t = 0 number of nuclei of A and B are 2 N0 and N

0 respectively. At t = t

0, number of

nuclie of B stops changing. If at this instant number of nuclei of B are 03N

2, then :-

(A) 1

0

1 2

1 4t n

3

(B)

10

2 2

1 4t n

3

(C) 0 2

A

1

3NN

2

at t = t0

(D) 0 2

A

1

2NN

3

at t = t0

9. A conducting ring is placed in a uniform external magnetic field present in the space within the

ring and perpendicular to plane of ring. The magnetic field changes at a constant rate due to

which a current of magnitude 4 amp flows in the ring. The resistance of parts PQR and PSR are

4 and 8 respectively. Then :-

× ××× ×

× ××

××

×

××

×

××

××

××

×

R

S Q

P

(A) The emf induced in the ring 48 V

(B) Potential difference between P & R is 24 V

(C) Potential difference between P & R is 8V

(D) Potential difference between P & R is zero as conservative electric field in the ring wire is

zero



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10. ABCD is plane glass cube. A nearly horizontal beam of light enters the face AB at grazing

incidence. Then,

B

CD

A

(A) sin cot , where is critical angle

(B) Critical angle 45º , for TIR at second surface

(C) Refracting index 2 for TIR at second surface

(D) None of these




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





1. The moment of inertia about x-axis of the solid spherical segment of mass M (see figure) is

253MR.

40XThe value of x is

Ox

R/2R/2



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2. Figure shows a Meter bridge wire AC has uniform cross-section. The length of wire AC is

100 cm. X is a standard resistor of 4 and Y is a coil. When Y is immersed in melting ice the

null point is at 40 cm from point A. When the coil Y is heated to 100ºC, a 12 resistor has to

be connected in parallel with Y in order to keep the bridge balanced at the same point. The

temperature coefficient of resistance of the coil is 2x 10 SI units . Find the value of x.

lA C

G

D

x =4 Y

3. A steel bar of length L is held between rigid supports and heated non-uniformly in such a manner

that the temperature increase T at distance x from one end is given by T = T0x2/L

2 as shown

in the figure The average stress in the bar, (assume that modulus of elasticity for steel is E

and thermal expansion coefficient is ) is given as 0E T

.n

Find the value of n.

L

x

x

Temperature

T


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4. A ring of radius 9m is rolling on a horizontal rough surface with a velocity v0 = 2 m/s. A point ismarked X on the body of ring. Initially X is at the position shown. How soon (in second) speed ofX will become equal to v0. :-

C

X

v = 2 m/s0

5. A photoelectric plate is initially exposed to a spectrum of hydrogen gas excited to second energy

level. Later when the same photoelectric plate is exposed to a spectrum of some unknown hydrogen

like gas, excited to second energy level, it is found that the de-Broglie wavelength of the

photoelectrons now ejected has decreased 6.1 times. For this new gas difference of energies

of first Lyman line and series limit of Balmer series is found to be two times the ionization potential

of the hydrogen atom. find value of Z.



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6. Two thin lens are arranged as shown in figure. The separation between them is 2f, where f is

focal length for each lens, x-coordinate of final image for 30º is Nf

.3

Find value of N.

=30° x

y

2f

90°


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7. A small ball of mass 1kg carrying charge 1C is dropped in a space having uniform horizontal

magnetic field B = 2T and uniform gravity g = 10 m/s2 in vertically downward direction. Maximum

displacement of ball in vertical direction is :-

8. The velocity of block m at an instant = 60° and v is equal to 18 m/s is (in m/s) :

v

m



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9. A circular disc of a diameter d is slowly rotated in a liquid of large viscosity at a small distance

h from a fixed surface. An expression for torque necessary to maintain an angular

velocity4d

is .8hX

Find the value of X.

Liquid

Fixed surface

10. When the voltage applied to an X-ray tube is increased from 10 kV to 20 kV, the wavelength

interval between the K line and the short wave cut off of the continuous X-rays spectrum

increased by a factor 3. Find the atomic number of element of which the tube anode is made.

Fill second digit (tens) of your answer.


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*1001CT102116075* (1001CT102116075)

PART-3 : CHEMISTRY



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



darkened.


1. Select the correct statements

(A) [Fe(C2O

4)3]3– is optically active even though it has simple axis of rotation other than one

fold.

(B) In the complex ion, [Fe(CN)6]4–, the total number of valence electrons around Fe and

formal charge on Fe are respectively 18 & –4

(C) Fac and Mer geometrical isomerism is not possibe in [Co(en)3]3+ , where en is H

2N-CH

2CH

2-

NH2

(D) All of these

2. Select the correct statements :

(A) The density of copper matte is less than molten FeSiO3

(B) CO2(g) + C(s) 2CO(g) is an endothermic reaction

(C) In preparation of wrought iron from cast iron, main slag is FePO4, if limestone is added as

flux

(D) Impurites of S, P, C, Si bring brittleness and lowers the melting point of Fe

3. Al2O

3 can be obtained from which of the following reaction :-

(A) Al(OH)3

ignited (B) AlCl

36H

2O

heated strongly

in absence of dry HCl vapour

(C) Ammonium alum

(D) Bauxite dissolved in

NaOH



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4. Consider following reaction sequence

2CH COOH3

Ca(OH)2 X

organic compound(Y).

Which of the following statement(s) is/are correct about compound Y ?

(A) Compound Y can also be produced by ozonolysis of 2, 3-Dimethylbut-2-ene.

(B) Compound Y can undergo aldol condensation.

(C) Mesitylene is produced when compound Y reacts with conc.H2SO4.

(D) Compound Y forms only one type of oxime when reacts with NH2OH(at pH = 4.5).

5. Consider following reaction

OO

O

HO3+

X + Y (aromatic)Organic compounds

Which of the following statement(s) is/are correct?

(A) Both compounds X and Y are alcohol.

(B) Compound Y on oxidation can produce p-Benzoquinone.

(C) One of the formed product in above reaction can be used for the protection of carbonyl

group.

(D) Compound Y is having non zero dipole moment.

6. How many of the following compound(s) have more than four configurational isomers ?

(A) CH – CH = CH – CH – CHD – CH = CH – CH3 2 3

(B)

CH = CH – CH = CH2

Et

(C)

Et

CH CH2 3

Cl

(D) H – C C– CHD – CH = CCH – CH2 3

CHClBr

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7. In which of following reaction(s), compound

O

is produced?

(A)

OH

KMnO /H4

+

(B)

OH

MnO2 (C)

CH2

O3

Zn/H O2

(D) HIO4

OHOH

8. Which of the following statement are correct -

(A) If a body centred cubic lattice is made up of hollow sphere of B in which sphere of solid A

having radius half of B are present then ratio of total volume of spheres of B unoccupied

by A in a unit cell and volume of unit cell is 7 3 /64

(B) If distance between next to next nearest neighbour in FCC unit cell is 4.8 Å then distance

between corner to it's nearest tetrahedral void will be 1.7 Å. [ 1.5 1.2 , 3 1.7 ]

(C) If distance between two nearest parallel planes in graphite is 3.4Å then density of graphite

will be 1.37 gm/cc [ 3 1.7 ]

(D) In the configuration shown, the size of the smallest circle is 2

13

times the size of the

highest circles.


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9. The standard electrode potentials of some of the alkali metals are :-

Li+/Li = –3.05V Na+/Na = –2.71V K+/K = –2.93V

Alkali metals react with water according to the following reaction. (M = alkali metal)

2M +H2O 2MOH + H

2

It is found that Li reacts gently with water whereas potassium reacts violently with water.

Which of the following statement(s) is/are correct regarding the above two experimental

facts ?

(A) G values have nothing to do with the kinetics of a reaction

(B) The metal having large standard oxidation potential will have lesser reactivity

(C) K has a low melting point, and the heat of reaction is sufficient to make it melt or even

vaporize. This leads to exponential increase in its surface area

(D) The ionization potential of K is smaller than that of Li.

10. The following graph shown the variation in vapour pressure of a solution of two liquids X

and Y as a function of molar composition

X = 100%Y = 0%

X = 0%Y = 100%

Molarcomposition

Vapour pressure (mm of Hg)

It can be deduced that

(A) Hmixing

> 0

(B) The curve shows positive deviation from Raoult’s law

(C) Y has higher boiling point than X

(D) The two liquids could be ethanol and cyclohexane



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

inclusive.





1. Consider following compounds :

H2S, MnO

2, PbO

2, Pb

3O

4 , acidic sol. KMnO

4, NaClO, O

3, SO

2. How many of these can oxidize

HCl to Cl2 ?

2. Find the total number of sulphide ppt that dissolve in dil. HCl among the following

ZnS , Ag2S , CaS , CuS , FeS , HgS

3. Find the total number of species which are polar and optically active

XeF4, ClF

3, SO

2, S

2Cl

2 , H

2O

2 , BrF

5 , BI

3 , NF

3


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4. Find the number of correct statement from the given

(i) Compound O can form stable hydrate.

(ii) Compounds

OH

&

OH

can be differentiated by NaOH + I2.

(iii) Compounds

OH

&

OCH3

can be differentiated by using cerric ammonium nitrate test.

(iv) Compounds Ph & Ph can be differentiated by using Bayers reagent.

(v) Compounds

OH

OH

&

OH

OH can be differentiated by using HIO4 followed by

treatment with AgNO3.

(vi) Compounds Cl & Cl can be differentiated by aqueous AgNO3.

(vii) Acetaldehyde and Benzaldehyde can be differentiated by Tollen’s test

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Y


*1001CT102116075* (1001CT102116075)


5. How many of the following compounds on hydrolysis produce glucose?

(i) Sucrose (ii) Lactose (iii) Maltose (iv) Ribose

(v) Starch (vi) Glycogen (vii) Cellulose

6. In how many of the following reactions correct product formed?

(i)

O14

14

OH

T > 100ºC (ii) CH Cl(excess)/Anhy.AlCl3 3

CH3

(iii) C–NH2

O

Br /KOH2

NH2 (iv) NO2 Sn/HCl

NH2

(v) CH Cl2

Mg/dry ether CH MgCl2

HOHO

(vi)

ClCl

ClCl

4Na/dry ether


CHEM

ISTR

Y

E-29/32*1001CT102116075* (1001CT102116075)

7. Consider the galvanic cell (H0 = –247.25 kJ , S0 = –20 J/K ; Ksp

of AgCl = 1.8 × 10–10 , Kf of

Ag(NH3)2

+ = 1.7 ×107) that utilizes the following half reaction

Anode : Zn(s) + H2O(l) ZnO(s) + 2H+(aq) + 2e–

Cathode : 2Ag+(aq.) + 2e– 2Ag(s)

If ionic product of AgCl in a solution prepared by mixing 50 ml of 0.1 M AgNO3 and 50 ml of

4M NH3 and adding 10 ml of 0.22M NaCl solution in cathodic compartment is x × 10–y and

standard emf of cell is z then calcualte value of y- 4z.

8. A salt BCl is dissolved in water having concentration 5000 ppm which depresses the freezing

point of the aqueous solution by 0.155K. If distance of next nearest neighbour for Cl– is x pm

then calculate value of x

200 2.

Given that BCl forms NaCl type crystal and density of BCl crystal is 1.25 gm/cc. Degree of

dissociation of BCl is 60% and density of water is 1gm/ ml


E-30/32

CHEM

ISTR

Y


*1001CT102116075* (1001CT102116075)

9. 'n' factor of PCl5 when it reacts with NaOH is x

'n' factor of SO2Cl

2 when it reacts with KOH is y

'n' factor of H2C

2O

4.2NaHC

2O

4.2K

2C

2O

4.3Al

2(C

2O

4)

3.4FeC

2O

4.5SnC

2O

4

when it reacts with KMnO4 is Z, then calculate value of

1(Z X.Y)

4

10. pH of 0.1M NH4Cl solution (K

b = 1× 10–5).



E-31/32*1001CT102116075* (1001CT102116075)



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

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

QUESTION PAPER FORMAT AND MARKING SCHEME :

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

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 0One or more If only the bubble(s) In all

I correct10

corresponding—

other— 30option(s) to all the correct cases

option(s) is(are)darkened

+3 0Single digit If only the bubble In all

IV Integer 10 corresponding — other — 30(0-9) to correct answer cases

is darkened

Your Target is to secure Good Rank in JEE 2017 *1001CT102116075* (1001CT102116075)E-32/32

1.

2. (ORS)

3.

4.

5. 32 20

6.

7.

8.

9.

:

10.

11.

12. :

13.

14.

15. g = 10 m/s2

PAPER – 1

SCORE(ADVANCED)

JEE (Main + Advanced) : LEADER & ENTHUSIAST COURSE

Paper Code : *1001CT102116075* (1001CT102116075)

CLASSROOM CONTACT PROGRAMME(Academic Session : 2016 - 2017)

Time : 3 Hours Maximum Marks : 180

HIN

DI

Test Type : FULL SYLLABUS Test Pattern : JEE-Advanced

TEST DATE : 26 - 04 - 2017


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,

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 =

20

1

c

Planck constant h = 6.63 × 10–34 J–s

H-2/32 *1001CT102116075* (1001CT102116075)


MAT

HEM

ATIC

S

H-3/32*1001CT102116075* (1001CT102116075)

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

-1 : –I : ( : 30)

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

: +3

: 0

1. y2 = 8x

(A) 8 (B) 9 (C) 12 (D) 15

2. z 1 i 1 z 1 i 1 2

(A) 3zz z z 1 0 (B) 3zz 7z 7z 15 0

(C) zz z z 3 0 (D) 3zz z z 1 0

3. ' S ',

cos3 + sin3 + (2sin2 – 3) (sin – cos) > 0 ' S '

(A) 3

2n ,2n4 6

, n I (B) 2n ,2n

3 4

, n I

(C) 3

2n ,2n4 4

, n I (D)

3 52n ,2n

4 4

, n I

H-4/32

MAT

HEM

ATIC

S


*1001CT102116075* (1001CT102116075)

4. 1 x

1 xg(x) t f '(t) dt

f(x) (a, b)

y = f '(x) x = 1

(A) x R g(x) (B) x > 1 g(x)

(C) g'(x) (D) g'(x), x = 2

5.

2

x 1, x [0,1]

2xf (x) , x (1,2)

x

x 3x 3, x [2,3]

({·} )

(A) f(x) [0, 3]

(B) f(x) 3

(C) f(x), x = 2

(D) f '(x) [1, 4)

6. i 1

(A) i (B) 3 i

2

(C)

3 i

2

(D)

i 3

2

7. ƒ 1 1ƒ(x) ƒ(y) x, y R {0}

x y

3 5

4

2

3(ƒ(x)) ƒ(x) 1 2dx log

1 (ƒ(x)) 2 3

(A) (B) < 17

(C) 1 1tan sec5

(D) ()


MAT

HEM

ATIC

S

H-5/32*1001CT102116075* (1001CT102116075)

8. IITJEE ADVANCED A, B C

3 1

,10 2

2

5 A

m

n (m, n N) (m + n)

(A) 10 (B) 20 (C) 40 (D) 80

9. n

nk

k 0

2kf (n) C cos

n

n 1n 1

kk 0

2kg(n) C cos

n

(A) f(6) (B) g(8)

(C) f(n) = 2g(n + 2) (D) f(n) = 2g(n)

10. 10 Hi

i Am m

(A) H4 H

8(B) A

1 A

9(C) H

3 A

4(D) H

2 A

5

–II : & –III :

II III

H-6/32

MAT

HEM

ATIC

S


*1001CT102116075* (1001CT102116075)

–IV : ( : 30)

0 9

: +3

: 0

1.2 2

nlimsin 4(n!) 4(n!) 1

2

, (n N)

2. M, ABC AB 2 P

BC 'AP + PM ' 'AP + PM ' b 'b'

3. 1 n

n 2012

0

xI dx

x 1

1 n

n 2013

0

xJ dx

x 1

n N A = [aij]

3×3

2012 i i

ij

I I , i ja

0 , i j

B = [b

ij]

3×3, 2016 j j 3

ij

J J , i jb

0 , i j

1 11det(B ) 2trace(A )

10


MAT

HEM

ATIC

S

H-7/32*1001CT102116075* (1001CT102116075)

4. 4

R 8R

13

5. 2 4

0

32 dx

(1 x )

H-8/32

MAT

HEM

ATIC

S


*1001CT102116075* (1001CT102116075)

6. g : R R x R x.g(0) + g(x) = ex–1g'(1) +2x

2

g(x)

[ : e ]

7. ' a ' f(x) = 5sin2x – 2cos2x + 3ax – 4, x R

8. ' n ' (x, y, z )

(0, 0, 0), (8, 0, 0), (0, 8, 0) (0, 0, 8) n

7


MAT

HEM

ATIC

S

H-9/32*1001CT102116075* (1001CT102116075)

9. x 2 22 2

1 1 2 1x x xcos sin (x 6x 8) sin (2k 1)

2 2 12 2 4

k

10. (x2y2 – 1) dy + 2xy3dx = 0 (1, 1) (k, 2)

(8k2)

H-10/32

PHYS

ICS


*1001CT102116075* (1001CT102116075)

-2 : –I : ( : 30)

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

: +3

: 0

1. r O P OO v

O P

v

(A) 2 2 2

v

4r v t(B)

v

2r(C) 2 2

v

2r v t(D)


PHYS

ICS

H-11/32*1001CT102116075* (1001CT102116075)

2. A a h

A

a .3

h

(A) gh

m/s4

(B) 2gm/s

8

(C) g

3 m/s2 (D)

3. L 4

A a

A :-

P Q

A a

L

L2

L2

(A) Q a = 3g

(B) Q a = 2g

(C) Q L

t3g

(D) Q L

t2g

H-12/32

PHYS

ICS


*1001CT102116075* (1001CT102116075)

4. AB CD B C ABC , AB ( )

DC

B

A

(A) tan (B) tan

2

(C) 2

tan

2 tan

(D) 2

tan 2

tan

5.

X =50C X =100L V=100 2 sin (377t)

R=100 X =100L

(A) 1

2 (B)

(C) (D) 100 W


PHYS

ICS

H-13/32*1001CT102116075* (1001CT102116075)

6.

vapp

t

(A)

(B)

(C)

(D)

7.

B

A

(A) A B

(B) () A 2

w

1

w =

(C) 2

1

2

3sin

4 1

(D)

H-14/32

PHYS

ICS


*1001CT102116075* (1001CT102116075)

8. A B 1 B C

2

t = 0 A B 2 N0 N

0 t = t

0 B

B 03N

2

(A) 10

1 2

1 4t n

3

(B)

10

2 2

1 4t n

3

(C) t = t0 0 2

A

1

3NN

2

(D) t = t

0 0 2

A

1

2NN

3

9.

4

PQR PSR 4 8

× ××× ×

× ××

××

×

××

×

××

××

××

×

R

S Q

P

(A) 48 V

(B) P R 24 V

(C) P R 8 V

(D) P R


PHYS

ICS

H-15/32*1001CT102116075* (1001CT102116075)

10. ABCD AB

B

CD

A

(A) sin cot

(B) 45º

(C) 2

(D)

–II : & –III :

II III

H-16/32

PHYS

ICS


*1001CT102116075* (1001CT102116075)

–IV : ( : 30)

0 9

: +3

: 0

1. M x- 253MR

40X x

Ox

R/2R/2


PHYS

ICS

H-17/32*1001CT102116075* (1001CT102116075)

2. AC 100 cm X

4 Y Y

A 40 cm Y 100ºC

12 Y

2x 10 SI x

lA C

G

D

x =4 Y

3. L

x T = T0x2/L2

E 0E T

n

n

L

x

x

Temperature

T

H-18/32

PHYS

ICS


*1001CT102116075* (1001CT102116075)

4. 9m v0 = 2 m/s X X X v0 :-

C

X

v = 2 m/s0

5.

6.1

Z


PHYS

ICS

H-19/32*1001CT102116075* (1001CT102116075)

6. 2f f

gSA ;fn 30º x Nf

3 N

=30° x

y

2f

90°

H-20/32

PHYS

ICS


*1001CT102116075* (1001CT102116075)

7. 1kg 1C

B = 2T g = 10 m/s2

8. v 18 m/s = 60° m (m/s ) :

v

m


PHYS

ICS

H-21/32*1001CT102116075* (1001CT102116075)

9. d h

djk;k tkrk gSA dks.kh; osx 4d

8hX

X

Liquid

Fixed surface

10. X- 10 kV 20 kV X-

K

H-22/32

CHEM

ISTR

Y


*1001CT102116075* (1001CT102116075)

-3 : –I : ( : 30)

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

: +3

: 0

1.

(A) [Fe(C2O

4)

3]3–

(B) [Fe(CN)6]4– Fe Fe

18 –4

(C) [Co(en)3]3+ (Fac) (Mer) en, H

2N-CH

2CH

2-NH

2

(D)

2.

(A) FeSiO3

(B) CO2(g) + C(s) 2CO(g)

(C) FePO4

(D) S, P, C, Si Fe Fe

3. Al2O

3 :-

(A) Al(OH)3

(B) AlCl36H

2O

HCl

(C)

(D) NaOH


CHEM

ISTR

Y

H-23/32*1001CT102116075* (1001CT102116075)

4.

2CH COOH3

Ca(OH)2 X (Y).

Y

(A) Y 2, 3--2-

(B) Y

(C) Y H2SO4

(D) Y, NH2OH(pH = 4.5 )

5.

OO

O

HO3+

X + Y ( )

(A) X Y,

(B) Y, p-

(C) (Protection)

(D) Y

6.

(A) CH – CH = CH – CH – CHD – CH = CH – CH3 2 3(B)

CH = CH – CH = CH2

Et

(C)

Et

CH CH2 3

Cl

(D) H – C C– CHD – CH = CCH – CH2 3

CHClBr

H-24/32

CHEM

ISTR

Y


*1001CT102116075* (1001CT102116075)

7.

O

(A)

OH

KMnO /H4

+

(B)

OH

MnO2 (C)

CH2

O3

Zn/H O2

(D) HIO4

OHOH

8.

(A) B B

A A B

7 3 /64

(B) FCC 4.8 Å

1.7 Å. [ 1.5 1.2 , 3 1.7 ]

(C) 3.4Å 1.37 gm/cc [ 3 1.7 ]

(D) 2

13


CHEM

ISTR

Y

H-25/32*1001CT102116075* (1001CT102116075)

9.

Li+/Li = –3.05V Na+/Na = –2.71V K+/K = –2.93V

(M = )

2M +H2O 2MOH + H

2

Li (gently)

(A) G

(B)

(C) K

(exponential)

(D) Li K

10. X Y

X = 100%Y = 0%

X = 0%Y = 100%

Molarcomposition

Vapour pressure (mm of Hg)

(A) Hmixing

> 0

(B)

(C) X Y

(D)

–II : & –III :

II III

H-26/32

CHEM

ISTR

Y


*1001CT102116075* (1001CT102116075)

–IV : ( : 30)

0 9

: +3

: 0

1.

H2S, MnO

2, PbO

2, Pb

3O

4, KMnO

4, NaClO, O

3, SO

2. HCl Cl

2

2. HCl :

ZnS , Ag2S , CaS , CuS , FeS , HgS

3.

XeF4, ClF

3, SO

2, S

2Cl

2 , H

2O

2 , BrF

5 , BI

3 , NF

3


CHEM

ISTR

Y

H-27/32*1001CT102116075* (1001CT102116075)

4.

(i) O

(ii) OH

OH

NaOH + I2

(iii) OH

OCH3

(iv) Ph Ph

(v)

OH

OH

OH

OH HIO4 AgNO3

(vi) Cl Cl AgNO3

(vii)

H-28/32

CHEM

ISTR

Y


*1001CT102116075* (1001CT102116075)

5.

(i) (ii) (iii) (iv)

(v) (vi) (vii)

6.

(i)

O14

14

OH

T > 100ºC (ii) CH Cl(excess)/Anhy.AlCl3 3

CH3

(iii) C–NH2

O

Br /KOH2

NH2

(iv) NO2 Sn/HCl

NH2

(v) CH Cl2

Mg/dry ether CH MgCl2

HOHO

(vi) Cl

Cl

ClCl

4Na/dry ether


CHEM

ISTR

Y

H-29/32*1001CT102116075* (1001CT102116075)

7. (H0 = –247.25 kJ , S0 = –20 J/K

AgCl Ksp = 1.8 × 10–10 , Ag(NH3)

2

+ Kf = 1.7 ×107) :

Zn(s) + H2O(l) ZnO(s) + 2H+(aq) + 2e–

: 2Ag+(aq.) + 2e– 2Ag(s)

50 ml 0.1 M AgNO3 50 ml 4M NH

3 10 ml of 0.22M NaCl

AgCl x × 10–y emf z

y- 4z

8. BCl 5000 ppm 0.155K

Cl– xÅ x

200 2

BCl NaCl BCl 1.25 gm/cc BCl

60% 1gm/ ml

H-30/32

CHEM

ISTR

Y


*1001CT102116075* (1001CT102116075)

9. PCl5 NaOH 'n' x

SO2Cl

2 KOH 'n' y

H2C

2O

4.2NaHC

2O

4.2K

2C

2O

4.3Al

2(C

2O

4)

3.4FeC

2O

4.5SnC

2O

4 KMnO

4 'n'

Z 1(Z X.Y)

4

10. 0.1M NH4Cl (K

b = 1× 10–5) pH


H-31/32*1001CT102116075* (1001CT102116075)


16. 17.

____________________________

____________________________

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

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

+3 0

I 10 — — 30

+3 0

IV (0-9)

10 — — 30

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 2017 *1001CT102116075* (1001CT102116075)H-32/32

JEE (Main + Advanced) : LEADER & ENTHUSIAST COURSE · 2019-11-13 · E-6/32 MATHEMATICS Target :...

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