PAPER - 1 : PHYSICS, MATHEMATICS & CHEMISTRY - Vidyalankar Classes

MRF

Test Booklet Code

B

PAPER - 1 : PHYSICS, MATHEMATICS & CHEMISTRY

Do not open this Test Booklet until you are asked to do so. Read carefully the Instructions on the Back Cover of this Test Booklet.

Important Instructions:

1. Immediately fill in the particulars on this page of the Test Booklet with only Black Ball Point Pen provided in the examination hall.

2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer Sheet and fill in the particulars carefully.

3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum marks are 360.

5. There are three parts in the question paper A, B, C consisting of, Physics, Mathematics and Chemistry having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for each correct response.

6. Candidates will be awarded marks as stated above in instruction No. 5 for correct response of each question. 1/4 (one fourth) marks of the total marks allotted to the question (i.e., 1 mark) 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.

7. 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 6 above.

8. For writing particulars/ marking responses on Side-1 and Side-2 of the Answer Sheet use only Black Ball Point Pen provided in the examination hall.

9. No candidates is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc., except the Admit Card inside the examination room/hall.

10. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This space is given at the bottom of each page and in four pages (Pages 2023) at the end of the booklet.

11. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room / Hall. However, the candidates are allowed to take away this Test Booklet with them.

12. The CODE for this Booklet is B. Make sure that the CODE printed on Side2 of the Answer Sheet is same as that on this Booklet. Also tally the serial number of the Test Booklet and Answer Sheet are the same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the invigilator for replacement of both the Test Booklet and the Answer Sheet.

13. Do not fold or make any stray marks on the Answer Sheet.

Name of the Candidate (in Capital letters) : ______________________________________________

Roll Number : in figures

: in words ______________________________________________________________

Examination Centre Number :

Name of Examination Centre (in Capital letters) : ____________________________________________

Candidate's Signature : ______________________

1. Invigilator's Signature : _________________

2. Invigilator's Signature : _________________

(Pg. 1)

JEE-MAIN 2018 : Question Paper and Solution (2)

Read the following instructions carefully :

1. The candidates should fill in the required particulars on the Test Booklet and Answer Sheet (Side-1) with Black Ball Point Pen.

2. For writing/marking particulars on Side-2 of the Answer Sheet, use Black Ball Point Pen only. 3. The candidates should not write their Roll Numbers anywhere else (except in the specified space) on the

Test Booklet/Answer Sheet. 4. Out of the four options given for each question, only one option is the correct answer. 5. For each incorrect response, ? (one-fourth) of the total marks allotted to the question (i.e., 1 mark) will

be deducted from the total score. No deduction from the total score, however, will be made if no response is indicated for an item in the Answer Sheet. 6. Handle the Test Booklet and Answer Sheet with care, as under no circumstances (except for discrepancy in Test Booklet Code and Answer Sheet Code), another set will be provided.

7. The candidates are not allowed to do any rough work or writing work on the Answer Sheet. All calculations/writing works are to be done in the space provided for this purpose in the Test Booklet itself, marked `Space for Rough Work'. This space is given at the bottom of each page and in four pages (Pages 20 ? 23) at the end of the booklet.

8. On completion of the test, the candidates must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.

9. Each candidate must show on demand his/her Admit Card to the Invigilator. 10. No candidate, without special permission of the Superintendent or Invigilator, should leave his/her seat. 11. The candidates should not leave the Examination Hall without handing over their Answer Sheet to the

Invigilator on duty and sign the Attendance Sheet again. Cases where a candidate has not signed the Attendance Sheet second time will be deemed not to have handed over the Answer Sheet and dealt with as an unfair means case. The candidates are also required to put their left hand THUMB impression in the space provided in the Attendance Sheet. 12. Use of Electronic/Manual Calculator and any Electronic Item like mobile phone, pager etc. is prohibited. 13. The candidates are governed by all Rules and Regulations of the Examination body with regard to their conduct in the Examination Hall. All cases of unfair means will be dealt with as per Rules and Regulations of the Examination body. 14. No part of the Test Booklet and Answer Sheet shall be detached under any circumstances. 15. Candidates are not allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, electronic device or any other material except the Admit Card inside the examination room/hall.

(Pg. 2)

(3) VIDYALANKAR : JEE-MAIN 2018 : Question Paper and Solution

PART- A : PHYSICS

ALL THE GRAPHS/DIAGRAMS GIVEN ARE SCHEMATIC AND NOT DRAWN TO SCALE

1. It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional

loss of its energy is pd; while for its similar collision with carbon nucleus at rest, fractional loss of energy is pC. The values of pd and pc are respectively:

(1) (0, 0)

(2) (0, 1)

(3) (89, 28)

(4) (28, 89)

1. (3)

L.M.C mv1 + 2m V2 = mV0

V1 + 2V2 = V0 e = V2 V1 1

V0

V2 V1 V0

...(1) ...(2)

v0

m

2m

rest

v1

v2

m

2m

On

solving

V2

2v0 3

and

V1

V0 3

Final KE of neutron =

1 2

mV12

1 2

m

V0 3

2

1 9

1 2

mV02

Loss

in

KE

=

8 9

1 2

mV02

Fractional loss

Pd

8 9

0.89

Similarly collision between N and C

mV1 + 12m.V2 = mV0

V1 + 12V2 = V0

V2 V1 = V0

On

Solving

V2

2V0 13

...(1)

...(2)

and

V1

11V0 13

Final

KE

1 2

m

11V0 13

2

121 169

1 2

mV02

Loss

in

KE

=

48 169

1 2

mV02

Fractional

loss

Pc

=

48 169

0.28

2. The mass of a hydrogen molecule is 3.32 1027 kg. If 1023 hydrogen molecules strike, per

second, a fixed wall of area 2 cm2 at an angle of 45 to the normal, and rebound elastically with a

speed of 103 m/s, then the pressure on the wall is nearly:

(1) 2.35 102 N/m2

(2) 4.70 102 N/m2

(3) 2.35 103 N/m2

(4) 4.70 103 N/m2

2. (3)

P1 = 2 mv cos 45 = 2 mv

Force F =

P t

= n P1

Where n no. of molecules incident per unit time

(Pg. 3)

Pressure P = Force Area

n 2mv P =

A

1023 2 3.321027 103

P =

2104

P = 3.32 103 = 2.35 103 N/m2 1.41

JEE-MAIN 2018 : Question Paper and Solution (4)

Vcos45

m

v

Vcos45

4 45 45

3. A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in

a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering

entire cross section of cylindrical container. When a mass m is placed on the surface of the piston

to

compress

the

liquid,

the

fractional

decrement

in

the

radius

of

the

sphere,

dr r

,

is:

(1) mg 3Ka

(2) mg Ka

(3) Ka mg

(4) Ka 3mg

3. (1)

Bulk modulus

K

=

dP dV / V

dV dP =

V K

dV mg =

... (1)

r

V Ka

V = 4r3 3

dV dr = 3

Vr

... (2)

From eq. (1) and (2)

dr mg r 3Ka

4. Two batteries with e.m.f. 12 V and 13 V are connected in parallel across a load resistor of 10 .

The internal resistances of the two batteries are 1 and 2 respectively. The voltage across the

load lies between.

(1) 11.4 V and 11.5 V (3) 11.6 V and 11.7 V 4. (4)

(2) 11.7 V and 11.8 V (4)11.5 V and 11.6 V

E1 E 2

Eeq =

r1 r2 1 1

r1 r2

=

12 13 12 1 1

=

37 3

12

req

1 2

=

=

1 2

2 3

12 V 13 V

10 10 2

(Pg. 4)

(5) VIDYALANKAR : JEE-MAIN 2018 : Question Paper and Solution

37

i =

Eeq R req

3 10

2

=

37 amp

32

3

V = iR = 37 10 = 185 = 11.56

32

16

5. A particle is moving in a circular path of radius a under the action of an attractive potential

U

=

k 2r2

.

Its

total

energy

is:

(1) Zero

(2)

3 k 2 a2

(3)

k 4a 2

(4)

k 2a 2

5. (1)

U

=

k 2r2

F =

du dr

= +

k 2

2 r3

F

=

k r3

mv2 k Centripetal force r = r3

mv2

k = r2

kE

=

1 2

mv2

k 2r2

Total Energy E = K + U = O

6. Two masses m1 = 5 kg and m2 = 10 kg, connected by an

inextensible string over a frictionless pulley, are moving

as shown in the figure. The coefficient of friction of

horizontal surface is 0.15. The minimum weight m that

should be put on top of m2 to stop the motion is:

(1) 43.3 kg

(2) 10.3 kg

(3) 18.3

(4) 27.3 kg

6. (4) at equilibrium

m

T

fr = T = m1g

m2

frmax = (m2 + m)g (10 + m) g = 5 g

fr 10 kg

5 10 + m =

0.15

100 10 + m =

3

70 m = kg = 23.3 kg. The minimum weight in the options is 27.3 kg.

3

T m1 5 kg

m1g

7. If the series limit frequency of the Lyman series is L, then the series limit frequency of the Pfund

series is:

(1) L/16

(2) L/25

(3) 25 L

(4) 16 L

(Pg. 5)

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