MODE TI#

JEE ADVANCED
PART TEST SERIES

EARS NARAYANA
I1T-JEE ACADEMY-INDIA
Sec: SR.IIT *CO-SC(MODEL-A) &APEX Date: 01-09-24
Time: 3 Hrs Max. Marks: 186
01-09-24_SR.IIT_STAR cO-sC(MODEL-A)&APEX_JEE ADV_PTA-5_SYLLABUS
MATHEMATICS: PRESENd WEEK(100%): Areas: appliation of definite integrals to the
determination of areas involving simple curves.
Differential Equations: Solution of homogeneous differential equations,
separation of variables method Formation of ordinary differential
equations, linear first order differential equations.

PHYSICS: PRESENT WEEK(100%]:COM, Momentum ôs Collision: Systems of

particles; Centre of mass and its motion; Conservation of linear
momentum, Impulse; Elastic and inelastic colisions.

CHEMISTRY: PRESENT WEEK(100%): Aldehydes and Ketones: Preparation of

aldehydes and ketones from acid chlorides and nitriles; aldehydes from
esters; benzaldehyde from toluene and benzene; Reactions: oxidation,
reduction, oxime and hydrazone formation; Aldol condensation,
Cannizzaro reaction; Haloform reaction; Nucleophilic addition reaction
with RMgX, NaHSO3, HCN, alcohol, amine.
Carboxylic Acids: Physical properties; Preparation:from nitriles,
Grignard reagents, hydrolysis of esters and amides; Preparation of
benzoic acid from alkylbenzenes; Reactions: reduction, halogenation,
formation of esters, acid chlorides and amides.
Narayana llT Academy 01-09-24 SR.STAR CO-SC(MODEL-A) JEE-ADV PTA-5 QP
Max.Marks:62
PHYSICS
SECTION-|
(SINGLE CORRECT CHOICE TYPE)
Ihis section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its onswer,
out of which ONLY ONE is correct.
Marking scheme +3 for correct answer ,Oif not attempted and -1 in all other cases.
19. From a uniform cireular disc of radius a, an isosceles right angled triangle with the
hypotenuse as the diameter of the disc is removed. The distance of the centre of mass of
the remaining portion from the centre of the circle is

A)3(7-a) B (7-1)a C) D)
3(r+1)
20. A uniformly thick plate in the shape of an arrowhead has dimensions as shown. The
centre of mass lies at a point.

6 cm

3 6
Cm

A) 1.5 cm to the right of 0 B)3 cm to the right of O

C)O itself D) 1cm to the right of O

21. A ball of mass m falls vertically from a height h and collides with a block of equal mass

mmoving horizontally with a speed v ona surface. The coefficient of kinetic function
between the block and the surface is 0.2, while the coefficient of restitution e between
the ball and the block is 0.5 There is no friction acting between the ball and the block.
The velocity of the block decreases by: (Assuming time of collision is very short and
block does not come to rest)

02

A) 0 B) 0.142gh ) 0.342gh D) depends on v'

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Narayane liT Acode my sR.STAR Co sC(MODEL-A) JEE-ADV
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22. In the fig. shown, the two identical balls0109-24
of mass Mand radius Reach are placed in
Comtact wth cach other on the fricionless borizontalsurface. The third ballof mass M
and radius *5 coming down ventically and has avelocity v, when it simultaneously
ts he two balls and itself coes to ost 1hen eehof the two bigger balls will move
after collision with a spced
equal to:

A)
SECTION-I|
(MULTIPLE CORRECT CHOICE TYPE)
Ihis section contains 8 multiple choice
AYA D)y

out of which ONE OR MORE is/ are qvestions, Each auestion has 4 choices (A), (B), (C) and (D) for its answer,
correct.
Marking scheme +4 for correct answer,O if not atempted and -1.in all other cases.
23. A two particle system of masses 2 kg and 3 kg present at (15,0) and (0,20) in a x,y plane
then its centre of mass lies on lines:

"A) y=2x B) 12 24
=1 C) 3x-2y=-6 D) y=x
24. A stationary light smooth pulley can rotate about a fixed horizontal axis. A light
rope
passes over the pulley:One end of the rope supports a ladder with a man and other end
supports counter weight of mass M. Mass of the man is m. Initially the system is
stationary and the centre of mass of the counter weight is at aheight h from that of the
man as shown in the figure. If the mass starts to climb up slowly such that his centre of
mass reaches at the final level with that of the counter weight.

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Narayana IT Acade 01-09-24 SR.STAR CO-SCIMODELA) EE-ADV PTA-5
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A) Distance moved by counter weight relative to mh
ground is 2( M-m)

B)Distance moved by counter weight relative to mh

ground is (M -m)

C) Distance moved by man relative to ladder is

(M-m)

D) Distance moved by man relative to ladder is Mh

(M-m)

25. Two particles, each of mass m, are moving inside a fixed horizontal circular tube of
radius Rwith the same constant speed v. Figure shows their positions at time t= 0. The
system consists of particles. Mark the CORRECT statement(s) for any time t before the
collision:

A)Acceleration of the centre of mass is R sin(

2my?
B) Net external force acting on the system is R

C) Force acting on left particle is mv

D) Force acting on right particle is -

26. Aball is projected with velocity of 20/2m /s at angle of 45° with horizontal and at the
same instant another plate is rotating with constant angular velocity ö(|a =z/4rad Isec)
along z-axis as shown in the figure. The mass of the plate is much larger than the mass
of the ball. The plate is initially in horizontal position and collision of ball with plate is
perfectly elastic. Then choose the correct statement(s). (Given that the lengthy of plate
is 30 m)
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Naroyana llT Acedemy 01-09-24 SR.STAR CO-sC(MODEL-A)_ JEE-ADV

4D m

A) Time when the ballcollides with the plate is 2 (SI unit)

B)Velocity of the ball just after collision with the plate is 10(2+) (SI unit)
C) Position of ball when it again collides on the ground surface from the projection point
20z (Sl unit)

D)Maximum height achieved by the ball is 20 (SI unit)

27. Two balls B, and B, moving in opposite directions with speed 20m/s and 1Om/s
respectively are colliding, impulse due to collision acts on both at 150° from their
original direction of motion. After impact ball B, is observed to be moving at an angle
120° and 60° from it's initial direction of mo tion in centre of mass frame of two ball
system and in ground frame respectively. If mass of ball B, =Ikg.
A) Mass of ball B, is 3kg B) mass of ball B, is 2kg
1
C) Coefficient of restitution e= D) Coefficient of restitution e=1

28. The system shown with smooth, and light pulleys and light inextensible threads is
initialy in equilibrium in vertical plane. Block Chas mass m. This block is given an
impulse J in downward direotion, Then(Assume duration of impulsive force is small)

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Ngrayana lT Academy
O1-09-24 SR STAR Co-$C(MODEL-A) JEE-ADV PTA-S_QP
A) velocity ofC immediately afierwards is 8J
9 m

B) velocity of Aimmediately
afterwards is Om

C)velocity of Bimmediately afterwards in

2m

D)Impulse imparted by the system to the cciling is 5J

29. Particle of mass 'm' placed on a horizontal surface surrounded by walls as shown in
figure. Coefficients of restitution for collision with walls AB,BC,CD are
e=1,e=1/2,e=1/4 respectively. Particle Ist collide with wall AB as shown in figure.
After collision from wall BC &CD respectively if again return to same position.
Relation between 0,,0, &0 will be:

I B

A) tan , =2tan B) tan &, =2 tan C) tan , =2 cot0 D) 4 cot , =tan ,

30. In which of the following cases the cèntre of mass of arod is certainly not at its centre?
A) the density continuously increases from left to right
GROUP
B) the density continuously decreases from left to right
C) the density decreases from left to right upto the centre and then increases
D) the density increases from left to right upto the centre and then decreases.

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 SC{MODEL-A) JEE-ADV PTA-5 O
Narayane IIT Acode my o1-00.24 SR.STAR CO
SECTION- ||
(NUMERICAL VALUE ANSWER TYPE )
tomprising of positive or
This section contains 6 questiens, The rntwer t ekestinn is o Numerical values
to Hundredihs place).
negative decimal numbers (ploce volve rongine hom Thousonds Plote
Eg: 1234.56, 123.45, -123.45, -1234.56, -0.12,0.12 etc.
Marking scheme : +3 for coect onswet, Oin ll other coses.
an angle of 30' with the horizontal The
31. An object is projected with a speed 10n's at
Object breaks down inot n coual fraements during its motion. One fragments is found to
projection in the same azimuthal
strike the ground at a distance of /m from the point of
theremaining fragments
planc, in which the object is projected. Ifthecentre of mass of
thc value of n
strikes the ground at distance of 7Wim from the point of projection, then
is (Assume all fragnments reach the ground simulataneously)
v along
32. Inside a dust storm of unifom density pcach particle is moving with velocity
ratio of force nceded to
Same direction. A sphere is kept at rest inside the storm. Find the
keep the sphere at rest if collision of particles is perfectly elastic to if it is perfectly
inelastic. Ignore any change in size when particles stick to sphere and gravity is assumed
to be absent.
with
33. In the figure shows block A is of mass 1kg and B is of mass 2 kg. A moves
velocity 3 m/s and rises on B. All the surfaces are smooth. Assume no loss of kinetic
energy of (4+ B) due to collision between A and B. By the time A reaches to its
maximum height on B, find the work done (in joules) by A on B. Wedge is sufficiently
long.

3mls
AB

34. '5' identical balls placed on smooth horizontal surface. If 1% ball moving with velocity
u-2mls horizontally collide with 2nd ball, and 2md ball collide with 3rd ball and so on
collisions take place. If the velocity of 5th ball after collision is(1.5)'. Find the value of

n(coefficient of restitution e=1/2)

u= 2m/sec

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 PTA-5 QP
Narayana llT Academy 01-09-24 SR.STAR CO-SC(MODEL-A) JEE-ADV_
35. Two particles A and B each of mass m are attached by a light inextensible string of
length 2/.The whole system lies on a s)0oth horizontal table with B initially at a
distance/ from A. The particle at end B is projcctcd across the table with spced u
the value of
perpendicular to AB. Velocity of ball Ajust after the string is taut is 4

ris...
A

RAMAY

36. On a spring block

mass. After 10s,
system
velocity
shown
of
instant is xx10m/s .Find x?
3kg
in figure,
,mass is 30
a time
AYATH
verying force F=5t N is applied on 2kg
m/sec. The velocity of 2kg mass at this

are smooth)
(Intially spring is relaxed and all surfaces
m 3kg m=2 kg
k F=5t Nt

THE NARAYANÂ GROu

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