(Acade Ses : 2021 - 2022) JEE(M+Advance) : ENTHUSIAST ...

READ THE INSTRUCTIONS CAREFULLY

GENERAL :

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

5. After breaking the seal of the booklet, verify that the booklet contains 28 pages andthat all the 18 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 purposeon the ORS. Do not write any of these details anywhere else on the ORS. Darkenthe 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 correctway.

14. Darken the bubbles ONLY IF you are sure of the answer. There is NO WAY to eraseor "un-darken" a darkened bubble.

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

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

Time : 3 Hours Maximum Marks : 198

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)1001CJA102121006)(1001CJA102121006) Test Pattern

CLASSROOM CONTACT PROGRAMME(Academic Session : 2021 - 2022)

JEE(Main+Advanced) : ENTHUSIAST COURSE (PHASE : TNAS)

JEE(Advanced)REVIEW TEST

28-02-2021En

glis

h

PAPER-1

E-2/28

Target : JEE (Main + Advanced) 2022/28-02-2021/Paper-1

1001CJA102121006

ALLEN

Space for Rough Work

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 = 58Atomic 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 pe9

0

1 = 9×104

· 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 s = 5.67 × 10–8 Wm–2–K–4

· Wien's displacement law constant b = 2.89 × 10–3 m–K· Permeability of vacuum µ0 = 4p × 10–7 NA–2

· Permittivity of vacuum Î0 = 20

1

cm· Planck constant h = 6.63 × 10–34 J–s

Enthusiast Course/Phase-TNAS/28-02-2021/Paper-1ALLEN

E-3/281001CJA102121006

BEWARE OF NEGATIVE MARKINGHAVE CONTROL ¾® HAVE PATIENCE ¾® HAVE CONFIDENCE Þ 100% SUCCESS


PART-1 : PHYSICSSECTION–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 uniform thin circular rubber band of mass M and spring constant k has an original radius R.Now it is tossed into the air. Assume it remains circular when stabilized in air and rotates atangular speed w about its center uniformly. Which of the following gives the new radius of therubber band ?

(A) ( )

( )22 kR

2 k Mp

p - w(B)

( )( )2

4 kR4 k M

p

p - w (C) ( )

( )2

2 2

8 kR

8 k M

p

p - w(D)

( )( )

2

2 2

4 kR

4 k M

p

p - w

2. Two blocks, of masses M and 2M, are placed next to each other on a horizontal smooth surface.The blocks are connected by a light spring with force constant k. Initially, the blocks are at rest.Then block M is given a quick push directly away from block 2M so that it acquires velocity v.The displacement of block M by the next moment its velocity equals v again is :

(A) 2m2 v3k

p (B) 2 v 2m3 3kp

(C) v 2m

3 3kp

(D) 2mv3k

p

Target : JEE (Main + Advanced) 2022/28-02-2021/Paper-1ALLEN

E-4/28 1001CJA102121006


3. Cosider n moles of ideal Helium gas at a pressure P0, volume V0 and temperature T0 placedin a vertical cylindrical container of area A. A movable frictionless horizontal piston of massm. Initially the system is in equilibrium and the spring is unstretched. The frequency f ofsmall oscillation of the piston, when it is slightly diplaced from equilibrium position is :

(Given that spring constant 0

mgAkV

= . All the processes in gas are adiabatic.)

Spring

Piston

Gas

Vacuum

(A) 2

0

1 mg3nRTp (B)

2

0

1 2mg3nRTp (C)

2

0

1 2mgnRTp (D)

2

0

1 4mg3nRTp

4. A uniform cylindrical tube l m long and closed at bottom end is completely filled with water.Upper end is clamped & is stretched downward. Its found that length of tube increases by lt butthat of water column increases by lw. Obtain poisson's ratio :

(A) w

t2l

l(B) w

t

l

l(C) w

t

2ll

(D) w

t4l

l


E-5/281001CJA102121006


5. A block of wood of relative density 0.5 is placed 10m inside a vessel containing water. Thevessel is accelerated upward with an acceleration of 10 m/s2. If the block is released at someinstant, then the time taken by block to reach the surface of water from that instant is(g = 10 m/s2)(A) 0.5 sec (B) 1 sec (C) 2 sec (D) none of these

6. A symmetrical block of mass M having a notch of hemispherical shape of radius R is placed on ahorizontal surface. A small particle of mass m is placed inside the hemispherical notch and canslide without friction. Find the time period of small oscillation of the particle and the block. Theacceleration due to gravity is g.

mR

M

(A) R2mg 1M

pé ù+ê úë û

(B) R2

Mg 1m

pé ù+ê úë û

(C) R m2 1g Mé ùp +ê úë û

(D) R M2 1g mé ùp +ê úë û


E-6/28 1001CJA102121006

SECTION-I(ii) : (Maximum Marks: 24)� This section contains SIX questions.� Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of

these four option(s) is (are) correct option(s).� For each question, choose the correct option(s) to answer the question.� Answer to each question will be evaluated according to the following marking scheme:

Full Marks : +4 If only (all) the correct option(s) is (are) chosen.Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.Partial Marks : +2 If three or more options are correct but ONLY two options are chosen,

both of which are correct options.Partial Marks : +1 If two or more options are correct but ONLY one option is chosen

and it is a correct option.Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).Negative Marks : –2 In all other cases.

� For Example : If first, third and fourth are the ONLY three correct options for a question withsecond option being an incorrect option; selecting only all the three correct options will resultin +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options),without selecting any incorrect option (second option in this case), will result in +2 marks.Selecting only one of the three correct options (either first or third or fourth option), withoutselecting any incorrect option (second option in this case), will result in +1 marks. Selectingany incorrect option(s) (second option in this case), with or without selection of any correctoption(s) will result in –2 marks.

7. A spherical concave mirror of radius of curvature 40 cm is moving with a constant velocity2cm/s along positive x-axis as shown. A point object 'P' located at a distance 30 cm left to thepole of the concave mirror is also moving with a velocity of 4 cm/s along positive x-axis at aheight of 0.2 cm above the principal axis as shown in figure. Then choose the CORRECToption(s):

/////////////////////////////////////

Principalaxis2F

0.2cm

P 4cm/s

F O

30cm 2cm/s

R = 40cmy

x

(A) The velocity of image at this instant is 8 cm/s along negative x-axis.(B) The velocity of image at this instant is 6 cm/s along negative x-axis.(C) The velocity of image at this instant is zero along negative y-axis.

(D) The velocity of image at this instant is 2

25 cm/s along negative y-axis.



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8. A cylindrical tank having cross-sectional area A = 0.5 m2 is filled with two liquids of densityr1 = 900 kgm–3 and r2 = 600 kg m–3, to a height h = 60 cm each as shown in figure. A smallhole having area a = 5 cm2 is made in right vertical wall at a height y = 20 cm from thebottom. A horizontal force F is applied on the tank to keep it in static equilibrium. The tankis lying on a horizontal surface. Neglect mass of cylindrical tank comparison to mass ofliquids, (Take g = 10 ms–2)

h

hF

r2

r1 y

(A) The velocity of efflux is 4 ms–1.(B) Horizontal force F to keep the cylinder in static equilibrium, if it is placed on a smooth

horizontal plane is 7.2 N.(C) Minimum and maximum values of F to keep the cylinder in static equilibrium just after the

water starts to spill through the hole. If the co-efficient of static friction between contactsurfaces is 0.01 is 0 and 52.2 N respectively.

(D) Minimum and maximum values of F to keep the cylinder in static equilibrium just after thewater starts to spill through the hole. If the co-efficient of static friction between contactsurfaces is 0.01 is 7.2 and 52.2 N respectively.

9. A vertical cylinder contains ideal gas with the help of two pistons whose combined mass is M.Pistons are connected by an inextensible string. The difference in the area of pistons is A.Atmospheric pressure is P0. Initially the system is in equilibrium as shown in the figure. Nowheat is slowly supplied to the system. Mark the CORRECT statement(s) :

(A) Volume will increase (B) Pressure will remain constant(C) Temperature will increase. (D) Internal energy of gas will remain constant.



E-8/28 1001CJA102121006

10. A light, rigid sheet of triangular shape has a curved portion cut from it as shown in figure. Itfloats on the surface of water. Some soap solution is dropped as shown. Surface tension ofwater and soap film are T1 & T2 respectively. T1 = 1.5 T2. Choose the CORRECT option(s).

R R

R

x

y

Soap

(A) The frame experiences a net forces F = (T1 – T2)R in y < 0 direction.(B) The frame experiences force F = (T1 – T2)R in y > 0 direction.(C) The frame experiences force (T1 – T2) (2 – p)R in y > 0 direction.(D) Resultant force on wire frame is zero.

11. A plane minor is placed in y-z plane facing towards negative x-axis. The mirror is moving in thepositive y-direction with a speed of 2 cm/s. A point object 'p' is moving in front of the mirror with

a velocity (1cm/s) i + (1cm/s) j . Then which of the following statements is CORRECT ?

(A) The velocity of image is with ˆ ˆ( i j)- + cm/s.

(B) The velocity of image with respect to mirror is ˆ ˆ(i j)- + cm/s

(C) The velocity of image with respect to object is ˆ(2i)- cm/s

(D) The unit vector in the direction of reflected ray is ˆ ˆ(i j)

2+

.



E-9/281001CJA102121006

12. A block with very large mass M slides on a frictionless surface towards a fixed wall withspeed v0. The block strikes a particle with very small mass m (and negligible size), which isinitially at rest at a distance L from the wall. The particle bounces elastically off the blockand slides to the wall, where it bounces elastically and then slides back toward the block. Theparticle continues to bounce elastically back and forth between the block and the wall. (AssumeM >> m)

V0

L

(A) Minimum separation between block of mass M and wall is mLM .

(B) As the distance between block of mass M and wall decreases, speed of m decreases.(C) As the distance between block of mass M and wall decreases, speed of m increases.(D) None of these



E-10/28 1001CJA102121006

SECTION-II : (Maximum Marks: 24)� This section contains SIX questions.� The answer to each question is a NUMERICAL VALUE.� For each question, enter the correct numerical value (in decimal notation, truncated/rounded-

off to the second decimal place; e.g. 6.25, 7.00, –0.33, –.30, 30.27, –127.30, if answer is 11.36777.....then both 11.36 and 11.37 will be correct) by darken the corresponding bubbles in the ORS.For Example : If answer is –77.25, 5.2 then fill the bubbles as follows.

0 0 0

+

0

–

0 01 1 1 1 1 12 2 2 2 2 23 3 3 3 3 34 4 4 4 4 45 5 5 5 5 56 6 6 6 6 67 7 7 7 7 78 8 8 8 8 89 9 9 9 9 9

•

•

•

•

•

•

•

•

••

0 0 0

+

0

–

0 01 1 1 1 1 12 2 2 2 2 23 3 3 3 3 34 4 4 4 4 45 5 5 5 5 56 6 6 6 6 67 7 7 7 7 78 8 8 8 8 89 9 9 9 9 9

•

•

•

•

•

•

•

•

••

� Answer to each question will be evaluated according to the following marking scheme:Full Marks : +4 If ONLY the correct numerical value is entered as answer.Zero Marks : 0 In all other cases.

1. A car drives anticlockwise (counterclockwise) around a flat, circular curve at constant speed,so that the left, front wheel traces out a circular path of radius R = 9.60 m. If the width of thecar is 1.74 m, what is the ratio of the angular velocity about its axle of the left, front wheel tothat of the right, front wheel, of the car as it moves through the curve? Assume the wheelsroll without slipping.

2. A uniform solid right prism whose cross section is an isosceles right triangle with height h andwidth w = 2h is placed on an incline that has a variable angle with the horizontal q. What is theminimum coefficient of static friction so that the prism topples before it begins sliding as q isslowly increased from zero ?

q

h

w



E-11/281001CJA102121006

3. Imagine two concave spherical mirrors with a common axis, such that the mirrors are twoparts of a sphere with a radius r = 1m. When we place a point light source in the centre of thesphere, each mirror forms a reflected image of the source which coincides with the sourceitself. Find the distance of the source from the centre such that it coincide with its imageformed after three reflections (but does not coincide with the image formed after one reflection).Assume paraxial ray approximation.

4. A particle of mass 1 kg is released from point A. It collides with sphere of mass 2 kg kept onsmooth horizontal surface. After collision velocity of particle becomes horizontal. There is nofriction at any point of contact (Given AB = 20m, g = 20 m/s2). The coefficient of restitutionbetween particle and sphere is

R

A

B

R/2



E-12/28 1001CJA102121006

5. A bright source S is kept on the principal axis of a concave mirror of focal length f = 20 cm ata distance d = 30 cm from its pole. Find the distance D (in cm) in front of the concave mirrorwhere a plane mirror should be placed so that the ray after being reflected first at the concavemirror and then by the plane mirror return to the point S.

6. A is a fixed point at a height 2m above a perfectly inelastic smooth horizontal plane. A lightinextensible string of length 3m has one end attached to A and other is to a heavy particle.The particle is held at the level of A with string just taut and released from rest. Find theheight of the particle above the plane when its is next instantaneously at rest.

A

2m

3m



E-13/281001CJA102121006


PART-2 : CHEMISTRYSECTION–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 :


1. 2.08 kg of an equimolar mixture of ferrous oxalate (MW = 144) and ferric oxalate(MW = 376) require X moles of K2Cr2O7 in acidic medium for complete oxidation thenX is -(A) 16/3 (B) 6 (C) 32/3 (D) 10/3

2. Which of the following statement is CORRECT?(A) CH2 is relatively more stable than CCl2 and CF2

(B) CHF3 is more acidic than CHCl3(C) R3C–O–H is more acidic than R3Si–O–H

(D) 33 6B O- and B3N3H6 are aromatic in nature

3. Which of the following compound has / have Z-configuration :

(A) C CH

CH3

I

Br

(B) C CCHO

COOH

O

O

(C) C CBr

IH C3

Br(D)

Cl Cl


E-14/28 1001CJA102121006


4. 300 gm, 30% (w/w) NaOH solution is mixed with 500 gm 40% (w/w) NaOH solution. What is %(w/v) NaOH in final solution if density of final solution is 2 gm /mL :(A) 72.5 (B) 65 (C) 62.5 (D) 75

5. Which of the following order is NOT correct with respect to the given property?(A) NaF < NaCl < NaBr < NaI : Ionic character(B) SrC2O4 < BaC2O4 < BeC2O4 : Solubility in water(C) Ca3N2 < Mg3N2 < Be3N2 : Thermal stability(D) AgI < AgBr : covalent character

6.C – OC H2 5

O

OHH N2

BrCorrect IUPAC nomenclature and D.U. of given compound?(A) Ethyl, 2-amino-4, bromo-6-hydroxy benzoate, D.U. = 5(B) Ethyl-6-amino-4, bromo-2-hydroxy benzoate, D.U. = 5(C) Ethoxy-carbonyl 2-amino-4-bromo-6-hydroxy benzen, D.U. = 4(D) Ethyl 2-amino 4-bromo-6-hydroxy benzene carboxylate, D.U. = 5


E-15/281001CJA102121006








7. Select the correct option(s).(A) Fraction of molecule in the range Uavg ± f Uavg is same for SO2 and O2 at same

Temperature (0 < f < 1).(B) Fraction of molecule in the range Umps ± 100 (m/sec) is same for SO2 and O2 at same

Temperature.(C) Fraction of molecule in the range Uavg ± f Uavg is same for O2 at 300 K and at 200 K (0 < f < 1).(D) None of these

8. Which of the following statement(s) is/are CORRECT?(A) BiCl5 is more stable than BiF5

(B) PbCl2 is more stable than GeCl2 and SnCl2

(C) SiO2 is more acidic oxide than PbO2 and SnO2

(D) Tl+3 ion is more stable than Tl+1 ion


E-16/28 1001CJA102121006

9. Which of the following statement is/are correct about the given compound :-

Cl

H

NH–CO

CO–NH

H

Cl

(A) It has centre of symmetry (B) It has plane of symmetry(C) It is optically inactive (D) It can show optical isomerism

10. With respect to NaCl lattice of edge length of 5.6 Å. Correct option(s) is/are -(A) In lattice Na+ form fcc and Cl– occupy all octahedral voids(B) Distance between two nearest Na+ will be 3.95Å approximately(C) On increasing pressure of NaCl lattice may convert to CsCl type lattice(D) On heating NaCl lattice, schottky defects may formed.

11. Which of the following compound(s) have tendency to form dimer?(A) AlI3 (B) AlF3 (C) BF3 (D) AlH3

12. Select correct statement :

(A) HOOC

Ph COOH

PhH

H H

H is a optically inactive compound

(B) Chair form of cyclohexane is optically active

(C) Methane has both C2 and C3 axis of symmetry

(D)O

have 4 stereoisomers



E-17/281001CJA102121006


off to the second decimal place; e.g. 6.25, 7.00, –0.33, –.30, 30.27, –127.30, if answer is11.36777..... then both 11.36 and 11.37 will be correct) by darken the corresponding bubblesin the ORS.For Example : If answer is –77.25, 5.2 then fill the bubbles as follows.

0 0 0

+

0

–

0 01 1 1 1 1 12 2 2 2 2 23 3 3 3 3 34 4 4 4 4 45 5 5 5 5 56 6 6 6 6 67 7 7 7 7 78 8 8 8 8 89 9 9 9 9 9

•

•

•

•

•

•

•

•

••

0 0 0

+

0

–

0 01 1 1 1 1 12 2 2 2 2 23 3 3 3 3 34 4 4 4 4 45 5 5 5 5 56 6 6 6 6 67 7 7 7 7 78 8 8 8 8 89 9 9 9 9 9

•

•

•

•

•

•

•

•

••


1. In ZnS (density = 4 gm/ml) unit cell all following manipulations are done -(i) All ions along one body diagonal are removed(ii) After step (i) one Zn2+ is swapped by face centered s–2 ion.Find density of final unit cell if volume of unit cell remain unchanged ?

2. Consider the following species :(BeH2)n , I2Cl6 , Al2(C6H5)6 , Be2Cl4 , [Be(OH)2]n , B2H2(CH3)4 , Al2Cl6

(i) if the total number of species which contain 3c-2e1 bond = A(ii) if the total number of species which are non planar = B(iii) if the total number of species which contain 3c-4e1 bond = C

Then find the value of B C ?

A+

=



E-18/28 1001CJA102121006

3. How many chiral and resolvable molecules are present among the following compounds

(i) H

Cl

CH3

H(ii)

Cl Me

Br Et(iii)

O

O

(iv)

Br

Cl

(v) (vi) C = C = CCH3

H H

CH3

(vii) N

H

O(viii)

Cl Cl

Cl Cl

4. Temporary hardness in tap water is measured in terms of parts of CaCO3 per 106 part of water.

If 500 ml of the hard water having Ca(HCO3)2 was titrated against 2 41 MH SO20 for complete

neutralisation it requires 40 ml titrant, then temporary hardness in tap water (in ppm)



E-19/281001CJA102121006

5. Consider the following odd e1 species :-OF, CH3, CF3, ClO3, ClO2, NO2

(i) if the total number of species which undergoes dimerisation easily and loose planarity = 'X'(ii) if the total number of species which are non planar = 'Y'

Then find the value of X ?Y=

6. Number of compound can show G.I. and O.I. both?

(i) (ii) (iii)

Cl Cl

(iv)

(v) N

H(vi) N N

H H

(vii)

(viii) (ix)



E-20/28 1001CJA102121006


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 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 :


1. The number of ways in which the letters of the word 'TWITTER' can be arrange in the adjacentfigure such that no horizontal row is empty (each box contains at most one letter), is

(A) (10C3 – 9C2).7

3(B) ( )- -10 9

3 2

7C C 9 .

3

(C) ( )10 93 2

7C C 10 .

3- - (D) ( )10 9

3 2

7C C 8 .

3- -

2. The whole numbers x1, x2 & x3 when divided by 4 leaves a remainder of 0,1 & 2 respectively.The number of non-negative integral solution of the equation x1 + x2 + x3 = 35, is -(A) 45 (B) 55 (C) 105 (D) 190

3. If tan–1(x + 1) + cot–1(x–1) = 1 14 3sin cos

5 5- -+ , then possible value of x is

(A) 3

47

(B) 7

43

(C) -7

43

(D) 6 7


E-21/281001CJA102121006


4. Given that ƒ(x) is a function defined on ¡, satisfying ƒ(1) = 1 and for any x Î ¡, ƒ(x + 5) > ƒ(x) + 5and ƒ(x + 1) < ƒ(x) + 1. If g(x) = ƒ(x) + 5 – x, then g(2021) is equal to-(A) 3 (B) 4 (C) 5 (D) 6

5. If n n

n nr 0 r 0r r

(r 5) n

C C= =

+=å å , then the value of 'n' is -

(A) 6 (B) 10 (C) 14 (D) 186. The value of k (k > 0) such that the length of the longest interval in which the function

( ) ( )1 1sin sin cos cosf x kx kx- -= + is constant as 4p

, will be

(A) 3 (B) 4 (C) 5 (D) 6


E-22/28 1001CJA102121006








7. The number of distinct terms in power of x in the expansion of

(1 + x)(1 + x3)( 1+ x6)( 1+x12) (1+x24) . . . (1 + n3 2x ´ ) is (where n Î ¥ )(A) 512 for n = 8 (B) 512 for n = 7(C) 1 + 3 + 5 + ... +31 for n = 6 (D) 1 + 3 + 5 + ...+31 for n = 7


E-23/281001CJA102121006

8. Consider ƒ : ¡ ® ¡ satisfying the equation ƒ(x + y) = ƒ(x – y) + ƒ(x).ƒ(y) " x, y Î ¡.Identify the correct statement(s)

(A) ƒ(2014) + ƒ(2015) = ƒ(2016) (B) sin–1(ƒ(2)) + cos–1(ƒ(3)) = 2p

(C) ƒ(2014) – ƒ(2015) = ƒ(2016) (D) sin–1(ƒ(3)) + cos–1(ƒ(2)) = 2p

9. If 3 2f (x) 4x x 2x 1= - - + and ( ) ( ){ }min f t ; 0 t x ; 0 x 1g x

3 x ; 1 x 2£ £ £ £ì ü

= í ý- < £î þ, then which of the

following is (are) correct ?

(A) 1 1g4 2

æ ö =ç ÷è ø (B) 3 1g4 4

æ ö =ç ÷è ø

(C) 7 5g4 4

æ ö =ç ÷è ø (D) 3 1g4 2

æ ö =ç ÷è ø



E-24/28 1001CJA102121006

10. The values of x satisfying the equation 9 6 39 27 219x x x x 08 64 512

+ + - + = is -

(A) 1 13

4- +

(B) 12

- (C) 1 13

4- -

(D) 12

11. Let A be set of first 25 natural numbers and a, b, c are three distinct elements of set A,then number of unordered triplets (a, b, c) if :(A) a+b+c is divisible by 3, is 772 (B) a+b+c is an even number, is 1156(C) abc is an even number, is 2014 (D) abc is divisible by 3, is 1620

12. The coefficient of x324 in the expansion of (x + 1) (x – 2)2 (x + 3)3(x – 4)4.......(x – 24)24(x + 25)25

is-

(A) 325 (B) 8 4 2

8 4 2 5k s r 0

k 0 s 0 r 0

C 4. C C C= = =

æ ö+ + +ç ÷

è øå å å

(C) 12 – 22 + 32 – 42 +........ –242 + 252 (D) 11 + 22 + 33 + 44 +.......+2525 .



E-25/281001CJA102121006


off to the second decimal place; e.g. 6.25, 7.00, –0.33, –.30, 30.27, –127.30, if answer is11.36777..... then both 11.36 and 11.37 will be correct) by darken the corresponding bubblesin the ORS.For Example : If answer is –77.25, 5.2 then fill the bubbles as follows.

0 0 0

+

0

–

0 01 1 1 1 1 12 2 2 2 2 23 3 3 3 3 34 4 4 4 4 45 5 5 5 5 56 6 6 6 6 67 7 7 7 7 78 8 8 8 8 89 9 9 9 9 9

•

•

•

•

•

•

•

•

••

0 0 0

+

0

–

0 01 1 1 1 1 12 2 2 2 2 23 3 3 3 3 34 4 4 4 4 45 5 5 5 5 56 6 6 6 6 67 7 7 7 7 78 8 8 8 8 89 9 9 9 9 9

•

•

•

•

•

•

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•

••


1. Let A = {1, 2, 3, 4}, B = {1, 2, 3, 4}. The total number of functions ƒ : A ® B such that ƒ(x) ¹ x" x Î A and range of ƒ(x) contains exactly three elements, is

2. If [x]3 + [y]3 + [z]3 – 3[x] [y] [z] = 4; where x,y,z > 0 (where [.] denotes GIF); then minimumpossible value of (x + y + z) is

3. If N denotes the number of positive integral solutions of equation xy = 23.34.56.(x + y),then N is equal to



E-26/28 1001CJA102121006

4. Let -

=

=+ +å

n1

n 2k 0

49S tan

49k 63k 57 then ( )®¥ nn

cot lim S is equal to

5. The number of 5-digit numbers of the form abcde where a,b,c,d,e Î {0,1,2,...9} and b = a + c,d = c + e is

6. The area enclosed between the curve ƒ(x) = cos–1(cosx) and g(x) = sin–1(sinx) in pé ùÎ pê úë ûx ,2

2 is


Enthusiast Course/Phase-TNAS/28-02-2021/Paper-1

E-27/281001CJA102121006

ALLENSpace for Rough Work

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

+91-744-2757575 [email protected] www.allen.ac.in

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 instructionsand 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. .............................................

Target : JEE (Main + Advanced) 2022/28-02-2021/Paper-1

Your Target is to secure Good Rank in JEE 2022 1001CJA102121006E-28/28

ALLEN

Que. No. Category-wise Marks for Each Question MaximumSection Type of Full Partial Zero Negative Marks of the

Que. Marks Marks Marks Marks section+3 0 –1

I(i) Single If only the bubble If none In allcorrect option 6 corresponding to — of the other 18

the correct option bubbles is casesis darkened darkened

+4 +1 0 –2One or more If only the bubble(s) For darkening a bubble If none In all

I(ii) correct 6 corresponding corresponding to each of the other 24option(s) to all the correct correct option, provided bubbles is casesoption(s) is(are) NO incorrect option darkened

darkened darkened+4 0

Numerical If only the bubble In all II Value Type 6 corresponding — other — 24

(Up to second to correct answer casesdecimal place) is darkened

(Acade Ses : 2021 - 2022) JEE(M+Advance) : ENTHUSIAST ...

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