FIITJEE JEE (MAIN)-2020

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BATCHES : Two Year CRP (1820) AB LOT

PHYSICS, CHEMISTRY & MATHEMATICS

PHASE – IV

INSTRUCTIONS

1. Immediately fill in the particulars on this page of the Test Booklet with Blue/Black Ball Point Pen. Use of

pencil is strictly prohibited. 2. The test is of 3 hours duration. 3. The Test Booklet consists of 90 questions. The maximum marks are 360. 4. There are three parts in the question paper A, B, C consisting of Physics, Chemistry & Mathematics and

having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response.

5. Candidates will be awarded marks as stated above in instruction No. 4 for correct response of each question.

(1/4) (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet.

6. There is only one correct response for each question. Filling up more than one response in any question will be

treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 5 above.

Atomic No.: H=1, He=2, Li=3, Be=4, B=5, C=6, N=7, O=8, F=9, Na=11, Mg=12, Al = 13, Si = 14, P = 15, S = 16, Cl = 17, Ar =18, K=19, Ca=20,Cr=24, Mn=25, Fe=26, Co=27, Ni=28, Cu=29, Zn=30, As=33, Br = 35, Ag = 47, Si = 21, Sn = 50, Ti = 22,I = 53, Xe = 54, Ba = 56, Pb = 82, U = 92, V = 50. Atomic masses: H =1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16, F=19, Na=23, Mg=24, Al=27, Si=28, P=31, S=32, Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn = 65.4, As = 75, Br = 80, Ag = 108, Sn = 118.7, I = 127, Xe = 131, Ba = 137, Pb = 207, U = 238.

Name of the Candidate :____________________________________________________

Batch :____________________ Date of Examination :___________________________

Enrolment Number :_______________________________________________________

FIITJEE JEE (MAIN)-2020

Paper Code

SET-A

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IT2020Two Year CRP (1820) AB-LOT-PH-IV-JEE MAIN-PCM (SET-A)2

PPhhyyssiiccss PART – I

Straight Objective Type This part contains 30 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. A charged particle moves through a magnetic field perpendicular to its direction then: (A) The momentum changes but the kinetic energy is constant (B) Both momentum and kinetic energy of the particle are not constant (C) Both momentum and kinetic energy of the particle are constant (D) Kinetic energy changes but the momentum is constant. 2. Two thin wire rings each having a radius R are placed at a distance d apart with their axes

coinciding. The charges on the two rings are + q and q. The potential difference between the centres of the rings is:

(A) 20

qR4 d

(B) 2 2

0

q 1 12 R R d

(C) Zero (D) 2 2

0

q 1 14 R R d

3. Two concentric coils each of radius equal to 2 cm are placed at right angles to each other. 3A and 4A are the currents flowing in each coil respectively. The magnetic induction in Wb/m2 at the centre of the coils will be:

(A) 12 × 105 (B) 105 (C) 5 × 105 (D) 7 × 105 4. A wire shown in the figure carries a current of 40 A. If r = 3.14cm, the

magnetic field at P will be : (A) 1.6 × 103 T (B) 3.2 × 102 T (C) 4.8 × 103 T (D) 6.0 × 104 T

P

90° r r

5. The equivalent resistance between points A and B of an

infinite network of resistance, each of 1 connected as shown is :

1 1 1

1 1 1

A

B

(A) Infinite (B) 2 (C) 1 52

(D) zero

6. In a potentiometer experiment the balancing with a cell is at length 240 cm. On shunting the cell with a resistance of 2, the balancing length becomes 120 cm. The internal resistance of the cell is:

(A) 1 (B) 0.5 (C) 4 (D) 2 Space for Rough Work





7. An electric dipole is placed at an angle of 30° to a nonuniform electric field. The dipole will experience:

(A) A translational force only in the direction of the field (B) A translational force only in a direction normal to the direction of the field (C) A torque as well as translational force (D) A torque only. 8. A particle of mass m and negative charge q is thrown in gravity free

space with speed u from the point A on the large non-conducting charged sheet with surface charge density ‘’. The maximum distance from A on sheet where the particle will strike the sheet is:

(A) 2

02m u cos2q

(B) 2

02m u sin2q

(C) 2 2

0u cos mq

(D) 2 2

0u sin mq

+

+

+

+

+

‘’

u

A 9. A point charge Q is located below the disc of radius R at ‘a’ distance from

the plane of the disc. If one fourth (1/4th) of the flux from the charge passes through the disc, then find the relation between a & R.

(A) a 1R 2 (B) a 1

R 4

(C) a 1R 3 (D) a 3

R 2

R

a Q

10. In a meter bridge with standard resistance of 5 in the left gap, the ratio of balancing lengths

of meter bridge wire is 2 : 3. The unknown resistance is: (A) 1 (B) 15 (C) 10 (D) 7.5 11. The field lines shown above indicate that

(A) 2 16Q Q

7

(B) 2 16Q Q7

(C) 2 17Q Q

6

(D) 2 17Q Q6

Q1

Q2

Q3

12. A charge q is placed at the corner of a cube of side ‘a’. Find the flux through the cube. (A) q/80 (B) 4q/0 (C) q/0 (D) 3q/80

Space for Rough Work





13. Find equivalent capacitance between points A and B in given figures. Each plate is having area a and distance between plate is d.

(A) 05 a2d

(B) 05 a

d

(C) 0ad (D) 0a

5d

A

B

14. Two rods each of length 6L carry charge Q are placed as shown in figure. Find magnitude of electric field at point P, which is at a distance of 5L from centre of each rod.

(A) 20

1 3 Q.64 L

(B) 20

5 Q4 L

(C) 20

1 Q.2 L

(D) 20

3Q5 L

Q, 6L

Q, 6L

60° 5L P

5L

15. In the given circuit, with steady current, find the potential drop

across the capacitor. (A) V/3 (B) V/5 (C) 2V/9 (D) 4V/3

R V

V

2V 2R

C

16. In the circuit shown in the figure key (k) is open. The

charge on capacitor C in steady state is q1. Now key is closed and at steady state charge on C becomes q2. Find the ratio of charges q1 / q2.

(A) 5/9 (B) 9/5 (C) 5/3 (D) 3/5

C E

R2 =3

R1 =2 k

17. A charged particle is projected in a magnetic field 2ˆ ˆB (3i 4 j) 10 T.

The acceleration of

the particle is found to be jyi38(a

) m/s2. Find the value of y.

(A) 2 (B) 3 (C) 4 (D) 5 18. A circular loop of radius R = 20 cm is placed in a uniform

magnetic field B

=2T in x-y plane as shown in figure. The loop carries a current i=1.0 A in the direction shown in figure. Find the magnitude of the torque acting on the loop.

(A) 0.35 N-m (B) 0.25 N-m (C) 0.55 N-m (D) 2.5 N-m

y

x

B

B

450






19. Current shown in figure is: (A) 7A (B) 2A (C) 5A (D) 3A

15V 2V 5V 10V 5V

2 3 5 5

20. The angle of dip at the magnetic pole is: (A) Zero (B) 90° (C) 45° (D) 180° 21. A particle of specific charge (charge/mass) starts moving from the origin under the action

of an electric field 0ˆE E i

and magnetic field 0

ˆB B K.

Its velocity at (x0, y0, 0) is ˆ ˆ(4i 3 j). The value of x0 is:

(A) 0

0

E132 B (B) 0

0

16 EB (C)

0

252 E

(D) 0

52B

22. Two particles X and Y having equals charges, after being accelerated through the same

potential difference, enter a region of uniform magnetic field and describe circular paths of radii R1 and R2 respectively. The ratio of the mass of X to that of Y is:

(A) 1/21 2R / R (B) 2 1R / R (C) 21 2R / R (D) 1 2R / R

23. A battery of internal resistance 4 is connected to the network of

resistance as shown. In order that the maximum power can be delivered to the network, the value of R in should be

(A) 4/9 (B) 2 (C) 8/3 (D) 18

6R

R R

R 4R

R R

E

4

24. A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The

separation between its plates is ‘d’. The space between the plates is now filled with two

dielectrics. One of the dielectrics has dielectric constant K1=3 and thickness d3

while the

other one has dielectric constant K2=6 and thickness 2d.3

Capacitance of the capacitor is

now: (A) 1.8 pF (B) 45 pF (C) 40.5 pF (D) 20.25 pF 25. Three identical metal plates with large surface area are kept parallel to each

other as shown in the figure. The leftmost plate is given a charge Q, the rightmost a charge – 2Q and the middle one remains neutral. Find the charge appearing on the outer surface of the rightmost plate.

(A) Q2

(B) – 2Q (C) Q4

(D) – 4Q

Q –2Q






26. Maximum power developed across variable resistance R in the circuit shown in figure is

(A) 50W (B) 75W (C) 25 W (D) 100W

1

1

R

10V

10V

27. A rectangular loop carrying current i is situated near a long straight

wire such that the wire is parallel to one of the sides of the loop and is in the plane of the loop. If a steady current I is established in the wire as shown in figure the loop will

i

i

(A) Rotate about an axis parallel to the wire (B) Move away from the wire (C) Move towards the wire (D) Remain stationary 28. Magnetic permeability is maximum for: (A) ferromagnetic substances (B) diamagnetic substances (C) paramagnetic substances (D) all of these 29. A current carrying circuit in which current splits to pass through

two parallel resistors of resistance R and 2R is shown in the figure. The resistors form the vertical arms of the square part of the circuit of side L. The arrangement is in the plane of a uniform horizontal magnetic field of flux density B produced by two pole pieces. The circuit is hinged along the yy’ direction such that it can freely rotate about yy’ axis. The moment of inertia of the loop about yy’ axis is 2mL , where m is the mass of the square and is a constant. Then,

L R

y I

I y’

L

2R S N

L/2

(A) Angular acceleration of the loop at the instant shown is Bm

(B) Angular acceleration of the loop at the instant shown is B6 m

(C) Angular acceleration of the loop at the instant shown is zero (D) The loop would start rotating in such a way that the right part of the loop would move

outward. 30. The net capacitance of the shown infinite

network across A and B, if each capacitor has a capacitance of C, is

(A) 3 1 C4

(B) 3 1 C4

(C) 5 1 C4

(D) None of these

A

B

C C C C

C C C C C C

C C C

C C C C






CChheemmiissttrryy PART – II

Straight Objective Type This part contains 30 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. The reagents used to convert

C CH CH3

O

are:

(A) i. O3/Red. ii. AlCl3 iii. MeCOOH (B) ii. H2SO4 + HgSO4 ii. H2O, heat (C) i. O3/Zn - AcOH ii. H2SO + HgSO4 iii. H2O, heat

(D) i. CH3COOH ii. H2O2 + 2OH/ H O

2. When methyl D-glucopyranoside is treated with HIO4 its number of mole consumed per

mole of the sugare is (A) 2 (B) 3 (C) 4 (D) 5 3.

3H O3

(1mole)CH MgBr A B

O

CH3 Product B is

(A) CH3CH2OH (B) 3 2 3

OH|

CH CH CH CH

(C) 3 2 3

Br|

CH CH CH CH (D) O O

4. The major product of following elimination reaction will be

?EtO

Me

H

Cl

H

(A)

(B)

(C)

(D) Reaction not possible

space for Rough Work





5. CH3COOH

4LiAlH H3 2(A), (A) CH COOH (B) H O

In the above reaction ‘A’ and ‘B’ respectively are: (A) CH3COOC2H5, C2H5OH (B) CH3CHO, C2H5OH (C) C2H5OH, CH3CHO (D) C2H5OH, CH3COOC2H5

6. Which of the following reacts with HBr at faster rate? (Assuming substitution)

(A) OH

(B)

OHCH3

(C) OH

CH3 (D)

OH

CH3 7. What is the major product (Y) in the reaction given below?

3 2 2CH CH OH SOCl (1 equivalent)HCl(g), X Y

OH

COOH

(A)

OEt

OH

O

(B)

Cl

OEt

O

(C)

OEt

Cl

O

(D)

OEt

O

8.

2moist Ag O HA B

CH3

Cl

CH3

Cl The product ‘B’ is

(A) CHO

CH3

H

CH3

(B)

CH3

O CH3

(C)

CH3

CH3 O H H

O

(D) CH2

CH3

CH3 space for Rough Work





9. The structure of aspartic acid is given below:

3

2 1 2 3

NH|

(HOOC CH CH COOH) (A) The pKa ,pKa and pKa of (A) respectively, are

1.88, 3.65 and 9.60. pKa1 and pKa2 corresponds to the ionization of the COOH group. pKa3 corresponds to the ionization of NH3

+ ion. What is the pH at isoelectric point?

(A) 1 2pKa pKa2

(B) 1 3pKa pKa2

(C) 2 3pKa pKa2

(D) 1 2 3pKa pKa pKa3

10.

NH2 C

CH3

H

C

O

NH CCH2OH

HC OH

Oa b c d

Which bond (s) will cleaved by acid hydrolysis? (A) a (B) b (C) c (D) d 11. Aspartame is an artificial sweetener having peptide bond in its structure given below:

NH2

CH2COOH

O

NH COOCH3

C6H5

It contains the following groups: (I) Amino, (II) Carboxylic (III) Ester (IV) Amide (V) Allyl (select the correct answers) (A) I, II, III, IV, V (B) I, II, III, IV (C) I, II, III (D) I, II, IV, V 12.

2O H3 6A B C (C H O)

CH3

CH3 ‘B’ will be

(A) Phenol (B)

OH

(C) CH3

CH3

H

OH

(D) Carboxylic acid






13. Which is maximum basic in nature?

(A) N

H

(B) NH

(C) NH2

(D)

NH

14. Which one of the following esters is obtained by the esterification of propan2ol with

ethanoic acid? (A) (CH3)2CHCOOCH3 (B) CH3COOCH2CH3 (C) CH3COOCH(CH3)2 (D) (CH3)2CHCOOCH2CH3

15. In the following sequence of reactions, what is D?

CH3

3 24 NHKMnO KOH/BrA B C D

(A) primary amine (B) an amide (C) phenyl isocyanate (D) a chain lengthened hydrocarbon 16. In the reaction

EtONa /EtOH3 3 heat

CH COCH X

the product (X) is

(A)

CH3CH3

(B) OH

CH3CH3

(C) CH3

CH3

(D)

OH

CH3 CH3

OH 17. Consider the following sequence of reactions

O

2 4

2 4 2

H SONaCNH SO H O, heatA B

The major product (B) is

(A)

OH

COOH

(B)

OH

CN

(C)

CN

(D)

COOH






18. In the following reactions :

Br

Ph MeAlc. KOH

Ph + HBr

Br

Ph CD3

Alc. KOHPh CD2 + DBrII.

I.

The rate of reaction of (I) is faster than of (II). Both reactions proceed by which mechanism? (A) E1 (B) E2 (C) E1cb (D) -elimination 19. On monochlorination of 2 – methylbutane, the total number of chiral compounds formed is (A) 2 (B) 4 (C) 6 (D) 8 20. Which is the correct order of dipole moment of following compounds?

Cl

Cl

Cl

Cl

ClCl

(III)(II)(I)

(A) I > II > III (B) I > III > II (C) I < II < III (D) III > I > II 21. The product formed in following reaction sequence

will be CH2

B2H6 H2O2

OH-

(A) H

H2C OH

H

H

(B) H

OH

H

CH3

(C) H

H

OH

CH3

(D) None of these

22.

22

4

Hg OAc ,H OY

NaBH 3

2 2

BH ,THF XNaOH,H O

The products (X) and (Y) of above reaction exhibit (A) chain isomerism (B) position isomerism (C) functional isomerism (D) ring-chain isomerism






23. The compound which undergoes NS 1most rapidly:

Br Br

CH2 Br Br

(A) (B)

(C) (D)

24. What will be the product of the following reaction?

CH2Cl

Cl

MgEt2O

?

(A) CH2MgCl

Cl (B)

Cl

MgCl (C)

(D)

CH2Cl

MgCl 25.

COOH

CH2OH ,COOH

CHO

COONa

CH2OH

,

COONa

COONa

COONa

CH2OH

COONa

COOH

COOH

COOH

COOH

COOH

,

,

(A)

(C)

(B)

(D)

26. A -hydroxy carbonyl compound is obtained by the action of NaOH on : (A) R3CCHO (B) C6H5CHO (C) CH3CHO (D) HCHO 27. Cannizzaro reaction is not given by : (A) Trimethyl acetaldehyde (B) Acetaldehyde (C) Benzaldehyde (D) Formaldehyde


COOH

CHO

46% NaOHA + B. A & B will be :2





28. Product ‘A’ will be :

CH3 OH

(A) (B)

(C) (D)

29.

N

CH3

CH2 CH3

CH3

Product (Alkene). The major alkene produced will be

Ag2O / moist

(A) N

Me

MeEt

(B) N

Me

NeEt

(C) CH2 CH2 (D) None of these

30. NH2

and

NH2

can be differentiated by:

aniline cyclohexanamine (A) Hinsberg Test (B) Iso-cyanide test (C) NaNO2, HCl, then -Napthol (D) NaOH


CH2 NH2HNO2 'A' +

OH

+ CH2 CH CH CH3

OH48% 47% 5%





MMaatthheemmaattiiccss PART – III

Straight Objective Type This part contains 30 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

1. Let

x x

2

e e x , x 0xf x3 , x 02

then the value of for which f(x) is a continuous function at x = 0 will be (A) 1 (B) 0 (C) 4 (D) 2

2. If 3 3x acos , y asin , then the value of 2dy1

dx

is equal to

(A) 2tan (B) 2sec (C) sec (D) sec 3. The values of k for which the function 3 2f x kx 9x 9x 3 x R is an increasing

function will be (A) k > 3 (B) k > 1 (C) k 2 (D) k 1 4. The points on the curve 3y x 3x at which the normals are parallel to the line 2x 18y 9

are (A) (2, 2), 2, 2 (B) 2, 2 , 2, 2 (C) 2, 2 , 2, 2 (D) (2, 2), 2, 2

5. Let f be a real valued invertible function such that 3x 5f 100x 15, x 2x 2

. Then find the

value of f-1(2015).

(A) 2016 (B) 60342015

(C) 52

(D) 25

6. Number of onto function f : A B , that can be defined if A = {1, ,2, 3, 4, 5} and B = {a, b, c}

is (A) 243 (B) 153 (C) 150 (D) 147

Space For Rough Work





7. If K = e2015, then, K

1

cos( lnx)I dx

x

is

(A) 0 (B) (C) 2015 (D) 2015

8. Maximum distance of any point on the curve 5x2 – 2xy + 5y2 =1 form origin is (A) 5 (B) 2 (C) 1/2 (D) 1/5

9. 2 2 2n

1 2 3 1lim ....n 1n 1 n 2 n 3

(A) 0 (B) 1/2 (C) 1 (D) 2 10. If 6(8a + c) = 16b + 3d, then, the f(x) = ax3 + bx2 + cx + d has at least one root in (A) (-3, 0) (B) (-4, 0) (C) (-4, -3) (D) (0, 2)

11. The value of 1/44

5

x x dx

x

is equal to

(A) 54

3

1 11 c15 x

(B) 54

3

4 11 c15 x

(C) 54

3

1 11 c4 x

(D) 54

3

3 11 c4 x

12. If the tangent at (p, q) to x3 + y3 = 2015 meets the curve again at (a, b), then a bp q

(A) -1 (B) 0 (C) 1 (D) None of these

13. 4

1/4

1 1sin x dx

x x

(A) 15sin4

(B) 15sin

4

(C) 154

(D) 0

14. The value of

2x

2

x 1e dxx 1

is equal to

(A) x x 1e cx 1

(B) x x 1e cx 1

(C) xe x 1 c (D)

xe cx 1






15. If f(x) is a function such that f’’(x) + f(x) = 0 and g(x) = (f(x))2 + (f’(x))2 and g(3) = 3, then g(8) is

(A) 0 (B) 3 (C) 5 (D) 8

16. If

5 3(x 5x 4x)sin120

f(x)x!

, then Range of f(x) is

(A) {0} (B) I (C) Q (D) R

17. The value of 2

3

dx

x 1 x is equal to

(A) 3

3 3

x 13 ln c1 x 1 x

(B)

33

3

x3 ln 1 x c1 x

(C) 3

3 3

1 x 13 ln cx 1 x

(D)

33

3

1 x3 ln 1 x cx

18. The curves 2 2 2 24x 9y 72 and x y 5 at (3, 2) (A) touch each other (B) cut orthogonally (C) intersect at 45º (D) intersect at 60º 19. Evaluate

xlim x( x 8 x)

(A) 0 (B) 4 (C) 8 (D) Not defined

20. The value of

/2

40

sinxcos x dx1 sin x

is equal to

(A) 2 (B)

4 (C)

6 (D)

8

21. Let f be continuous and differentiable function such that f(x) and f’(x) have opposite signs

everywhere. Then, (A) f is increasing (B) f is decreasing (C) |f| is increasing (D) |f| is decreasing

22. If

3(x x)sin6

f(x)| x | !

, then period of f(x) is

(A) Not defined (B) f(x) is not periodic (C) 2 (D) 1






23. The value of

2

21

dxx 1 ln x is equal to

(A) 1 (B) ln2 (C)

ln21 ln2

(D) 1 ln2ln2

24. If nX 8 7n 1: n N and Y 49 n 1 : n N , then

(A) X Y (B) Y X (C) X Y (D) None of these

25. Let f : R R be defined as f x 2x sinx . Then f is (A) One -one and onto (B) One-one but not onto (C) Onto but not one-one (D) Neither one-one nor onto 26. The domain of the function f x x 1 6 x is (A) 1, (B) , 6 (C) [1, 6] (D) , 1 6,

27. The value of

2 415

2 40

sin x cos x . x dx

cos x sin x

is equal to

(A) 13

(B) 14

(C) 16

(D) 15

28. If 2A x : x 5x 6 0 , B {2, 4} & C {4, 5} , then A B C is (A) {(2, 4), (3, 4)} (B) {(4, 2), (4, 3)} (C) {(2, 4), (3, 4), (4, 4)} (D) {(2, 2), (3, 3), (4, 4), (5, 5)}

29. The value of x 0

ln 1 ax ln 1 bxlim

x

is

(A) a b (B) a + b (C) ab (D) a/b

30. The function

2

2

2

x , 0 x 1a

f x a, 1 x 2

2b 4b , 2 xx

is continuous for 0 x , then which of the following is true? (A) a = 1, b = 1 (B) a 1, b 1 2 (C) a 1, b = 1 (D) a 1, b 1






FIITJEE COMMON TEST

BATCHES : Two Year CRP (1820) AB LOT PHASE TEST-IV

JEE MAIN ANSWER KEY

SECTION – I (PHYSICS) SECTION – II (CHEMISTRY) SECTION – III (MATHS) 1. A P120313 2. B P120105 3. C P120302 4. D P120302 5. C P120508 6. D P120208 7. C P120113 8. B P120104 9. C P120108 10. D P120210 11. A P120107 12. A P120108 13. A P120114 14. A P120104 15. A P120216 16. C P120216 17. A P120305 18. B P120309 19. D P121512 20. B P112901 21. C P120305 22. C P120313 23. B P121517 24. C P120117 25. A P121424 26. A P121510 27. C P120306 28. A P112908 29. B P120307 30. C P121421

1. B C121401 2. D C122901 3. B C121807 4. A C124601 5. D C122807 6. B C121802 7. B C121802 8. A C121802 9. D C121208 10. C C121207 11. B C121210 12. A C121205 13. B C121208 14. C C121207 15. C C121208 16. C C121206 17. D C121206 18. B C121201 19. B C121201 20. A C121202 21. A C121203 22. B C121203 23. B C121201 24. A C121201 25. B C121206 26. C C121206 27. B C121206 28. D C121203 29. C C121208 30. C C121208

1. D M120404 2. D M120510 3. A M120604 4. D M120602 5. C M113411 6. C M113409 7. A M120802 8. C M120608 9. B M110613 10. B M120613 11. B M120701 12. A M120601 13. D M120802 14. B M120709 15. B M120616 16. A M120317 17. A M120713 18. B M120603 19. B M110605 20. D M120802 21. D M120604 22. D M120322 23. C M120802 24. A M120303 25. A M120310 26. C M113416 27. C M120802 28. A M113403 29. B M110609 30. C M120404

Paper Code

SET-A





BATCHES : Two Year CRP (1820) AB LOT PHASE TEST-IV

JEE MAIN HINT & SOLUTIONS

SECTION–I : PHYSICS

1. A P120313 Charge particle moves in circular path with constant speed. 2. B P120105

2 2

0

qV4 R d

3. C P120302

2 2

2 2 0 1 0 21 2

i iB B B2R 2R

4. D P120302 5. C P120508 6. D P120208

1

2

r 1 R

7. C P120113 1 2F q(E E ) 8. B P120104

2u sin2R

a

; 0

qa2 m

9. C P120108

0

q 1 cos2

10. D P120210

5 2x 3 x = 7.5.

11. A P120107 No. of fields lines proportional to charge. 12. A P120108 By symmetry flux passing through the cube = q/80

13. A P120114

CAB = C +C + C/2 = 5C/2 = 05 A2d

.

A B

2

2 3 3 4 4 5

1





14. A P120104

E due to rod =

6L

200

1 Q dx.4 6L 8L x

= 20

1 Q64 L

Enet = 2 E cos 30°.

x

Q, 6L

5L E

dx

15. A P120216 In steady state no current will pass through the capacitor. In the outer loop, 2V – 2iR – iR – V = 0 i = V/3R For the upper loop, V – VC – iR – V = 0 |VC| = iR = V/3

R V

V

2V 2R

C

i

i

16. C P120216 When key is open q1 = CE

when key is closed q2 = C

2

21R

RRE

)RR(

CERCE

qq

2122

1 = 2

21

RRR

= 35 .

17. A P120305 Fm B a B a.B 0

ˆ ˆ ˆ ˆ( 8 / 3i yj).(3i 4 j) 0 y 2.

18. B P120309 | | = MBsin = niAB sin = (0.04) (2) sin 900 = 0.25 N-m 19. D P121512 20. B P112901 21. C P120305

0 01qE x m 25 .2

22. C P120313

mvrqB

23. B P121517 4 = 2R; R = 2. 24. C P120117

0AC 9 pF

d

0e

1 2

AC 40.5 pFd 2d3K 3K

25. A P121424 26. A P121510

1R2

10i1

2P i R 50 . 2P i R 50W.

27. C P120306 28. A P112908 29. B P120307

Torque 22I L I L I BLLB LB

3 2 3 2 3 2 ;

2

2IL B IB

6 mL 6 m

.

30. C P121421





CH3 CH

CH3

CH2 CH2 Cl2u.v CH2

Cl

C

H

CH3

CH2 CH3*

+

CH C

Cl

HCH3

CH3 CH3*

+ 2 other products

CHEMISTRY 1. B 2. D 3. B

3CH Mg Br

O

CH3

3H O

CH3

OMgBr

CH3

CH3

OH

CH3 4. A 5. D 6. B 3 alcohols react faster with HBr due to more stable 3 carbocation 7. B

3 2CH CH OHacid

OH

COOH

OH

COOC2H5

2SOClCl

COOC2H5

8. A 9. D 10. C 11. B 12. A 13. B 14. C 15. A 16. C 17. D 18. B C – D bond is stronger than C – H bond. In E2 the RDS is step in which C–H or C–D bond is

broken. 19. B Total number of chiral compounds will be four (including d&l) 20. A Dipole moment depends upon the angle between the vectors. In ortho substituted product

the angle is minimum hence is maximum.

C l C l C l C l 2 cos , where 2

is the vector moment and is the angle between two

vector moments. 21. A 22. B Hygroboration oxidation gives anti markownikoff’s product where are oxymercusation de

mercuration gives markownikoff’s product. 23. B





The carbocation formal will be most stable due to conjugation. 24. A Alkyl halide is more reactive than aryl halide. 25. B In Cannizaro’s reaction –CHO is oxidised to give –COOH and –CHO is reduced to form –

CH2OH. In presence of NaOH, –COOH group will turn into salt. 26. C Aldol reaction is given by the aldehyde having H atom only. 27. B For Cannizaro’s reaction, aldehyde should not contain H atom. 28. D

CH2 NH2

+ HNO2

NaNO2+HClCH2 N N]Cl

-

CH2 OHH2O

2CH

29. C In cope reaction, the alkene formed will be less substituted (not saytzeff product but

Hofmann elimination product). 30. C





MATHEMATICS 1. D M120404

x x x x

2x 0 x 0

2 x x 2

x 0

e e x . e e 1lim lim

2xx . e e 1lim

2 2

2

21 3 1 3 22 2

2 is not possible 2 2. D M120510

2

2

22

dy a . 3sin . cos tandx a . 3cos . sin

dy 1 1 tan secdx

3. A M120604

2 2f ' x 3kx 18x 9 3 kx 6x 3

f ' x 0, x Rif k 0 & 36 12k 0 k 3

k 3

4. D M120602

2 2dy 3x 3 3 x 1dx

Slope of the line 2 118 9

Since normal is parallel to the given line

2 2 2 3 x 1 9 x 1 3 x 4 x 2

y 8 6 , 8 6 2, 2

(2, 2) & 2, 2 are required points

5. C M113411

1 3x 5f (100x 15)x 2

Put x = 20 1 3 20 5 5f (2015)20 2 2

6. C M13409 Number of functions from A to B is 35 = 243 Number of functions from A to {a, b} is 25 = 32 Number of onto functions from A to {a, b} is = 32 – 2 = 30 Number of functions from A to {a} is 1 Number of onto function from A to B is = 243 – 3 × 30 – 3 = 150 7. A M120802

2015

20150

0

Put lnx t I cos t dt [sin t] 0

8. C M120608 Put x r cos , y r sin

2 2 2 15r r sin2 1 r5 sin2

r is maximum, when 5 sin2 is minimum





2min max max

1 15 sin2 | 4 r | r |4 2

9. B M110613

If n 2 2 2

1 2 nS ....n 1 n 2 n n

1 2 nT T ... T

r 2

rTn r

Now, if r = 1, 2,...n 2 2 2n 1 n r n n.

2 2 2

1 1 1n n n r n 1

2 2 2

r r rn n n r n 1

n2 2

n(n 1) n(n 1)S

2(n n) 2(n 1)

n 2n n n

1 n(n 1)lim lim S lim

2 2(n 1)

n nx n

1 1 1lim S lim S2 2 2

10. B M120613

If 4 3 2ax bx cxg(x) dx e

4 3 2

4 3 21 (3ax 4bx 6cx 12dx 12e)12

1g( 4) (3.256a 256 96c 48d 12e)12

1 (16(48a 16b 6c 3d) 12e)12

= e = g(0) g(x) satisfies Rolle’s Theorem in [-4, 0] g(x) has at least one root in (-4, 0) 11. B M120701

14

13 4

5 3 4

1x 11 1xI dx 1 . dx

x x x

14

3 4

5 54 4

3

1 1 3z dz, put 1 z dx dz3 x x

1 z 4 1c 1 c53 15 x4

12. A M120601

2

2(p,q)

dy pdx q

Slope of line joining (a, b) and (p, q) : 2

2

q b pp a q

2 2 2

2 2 2

q a p ap a pp a q bq b q

a bpq (pb qa) 1

p q

13. D M120802





Put 2

1 1x dx dtt t

1/4

24

1 1I t sin t . dt

t t

1/ 4

4

1 1sin t dt I

t t

I 0 14. B M120709

2x

2

x 1 2xI e dx

x 1

x2

x x2

x x2

2xe 1 dxx 1

x 1 1e 2 e dx

x 1

1 1e 2 e dxx 1 x 1

x

x

x

x

ee 2 cx 1

x 1 2e cx 1

x 1e cx 1

15. B M120616 g'(x) 2f(x).f '(x) 2f '(x).f ''(x) 0 g(x) is constant function. 16. A M120317 For x! to be defined, x must be a whole number. 5 3 2 2x 5x 4x x(x 1)(x 4) (x 2)(x 1)x(x 1)(x 2) Since, product of any 5 consecutive integers is a multiple of 5!. 5 3x 5x 4x 120K, K I

sin(K )f(x) 0 x Dom (f(x))x!

17. A M120713 Put 3 2x z dx 3z dz

2

2 23

3z dz dz I 3z 1 z z z 1

2

1 1 13 dzz z 1 z 1

z 13 ln cz 1 z 1

3

3 3

x 13 ln cx 1 x 1

18. B M120603





For, 2 2

(3,2)

dy 4x dy 24x 9y 72,dx 9y dx 3

For 2 2

(3,2)

dy x dy 3x y 5,dx y dx 2

the curves cut orthogonally 19. B M110605

xlim x( x 8 x)

x x

8 x 8lim limx 8 x 81 1

x

84

1 1 0

20. D M120802 Put 2sin x t 2sinxcos xdx dt

1

1 120 0

1 dt 1 1 I tan t 02 2 2 4 81 t

21. D M120604

f(x), f(x) 0| f(x) |

f(x), f(x) 0

f '(x), f(x) 0dy | f(x) |f '(x), f(x) 0dx

d | f(x) | 0dx

|f| is decreasing. 22. D M120322 fDom I f(x) = 0 fx Dom Period of f(x) = 1 23. C M120802

2

21

dxIx 1 ln x

Put 11 lnx t dx dt

x

1 ln2 1 ln2

211

dt 1tt

1 ln211 ln2 1 ln2

24. A M120303

nn

2

n n n n 22 3 n

8 7n 1 1 7 7n 1

n n 11 7n . 7 .......... 7n 1

2!

49 C C . 7 ....... C . 7

n 8 7n 1 will be multiple of 49 for n 2 X Y 25. A M120310

f x 2x sinx

f ' x 2 cos x 0

f x is one-one 1 cosx 1





Also, fR R f(x) is one-one and onto function 26. C M113416 f(x) will be real if x 1 & x 6 f D 1, 6 27. C M120802

2 415

22 20

11 12 4 65 5

4 20 0 0

1 cos x cos xI . x dx

cos x 1 cos x

1 cos x cos x x 1 . x dx x dx6 61 cos x cos x

28. A M113403

A 2, 3

B 2, 4 , C 4, 5

B C 4

A B C 2, 4 , 3, 4

29. B M110609

x 0

ln 1 ax ln 1 bxlim

x

x 0

1 1a . b1 ax 1 bx

lim1

a 1 b 1 a b

30. C M120404 At x = 1, LHL = 1/a, RHL = a

21LHL RHL a a 1 a 1a

At 2

22b 4bx 2, LHL a, RHL b 2b2

LHL = RHL 2a b 2b

2b 1 a 1

b 1 a 1 2, 0

b 2 1, 1


Two Year CRP (1820) AS LOT-PH-IV JEE MAIN

Chemistry QUESTIONS

Errata Question/ Line No

Q.NO. 2

Q. No. 9

In answer Answer should be 'A

In answer Answer should be 'A

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