REVIEW TEST-24-P2-(JEE ADV.)PCM Physics PART – I

REVIEW TEST-24-P2-PCM-JEE ADV.-2020

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RREEVVIIEEWW TTEESSTT--2244--PP22--((JJEEEE AADDVV..))PPCCMM PPhhyyssiiccss PART – I

SECTION – A

(One or More than One Options Correct Type) This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct. 1. A spherical shell of volume mass density , thickness t and radius R(R>>t) is

placed concentrically inside another shell of radius 2R having same thickness and of same material as shown in the figure. The circumferential stress developed in the outer shell is

(A) compressive in nature (B) Tensile in nature

(C) 3GRt2 (D) 3 2

GRt2

t t

R

2R

2. An 168O nucleus is spherical having radius R, surface area A and volume V. According to

empirical observations, the volume of the 12850Sn nucleus assumed to be spherical is V, radius

R and surface area A. Then (A) R = 8R (B) A = 8A (C) V = 8V (D) R = 2R 3. Two objects of the same mass slide down on two

different smooth inclined plane of same height but of different angles. When they reach the bottom, then I1 and I2 are the impulses of the weights of the first and the second object during the motion, P1 and P2 are the powers developed by the weights of the first and the second objects.

1 2

h

(A) 1 2

2 1

I sinI sin

(B) 1

2

I 1I

(C) 1 1

2 2

I sinI sin

(D) 1 1

2 2

P sinP sin

Space for Rough work



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4. The ends of a long bar are maintained at different temperatures and there is no loss of heat from the sides of the bar due to conduction or radiation. The graph of temperature against distance from the hot end of the bar at steady state is shown in the diagram. From this we can conclude that

(A) The cross-sectional area of the bar may be increasing as the distance from the hot end increases.

(B) The cross sectional area of the bar may be decreasing as the distance from the hot end increases.

Distance from hot end

Tem

pera

ture

T

x

(C) The thermal conductivity of the bar may be increasing as the distance from the hot end increases.

(D) The thermal conductivity of the bar may be decreasing as the distance from the hot end increases.

5. In the figure shown, sound waves A and B, both of

wavelength are initially in phase and travelling rightward as indicated by the two rays. Wave A is reflected from four parallel surfaces but ends up travelling in original direction. The possible value(s) of distance L in terms of wavelength in figure which put A and B exactly out of phase with each other after all the reflections is/are

(A) /2 (B) 3/2 (C) 3/4 (D)

A

L

L

B

6. A current carrying circuit in which current I 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 mL2, where m is the mass of the square loop and is a constant. Then,

L I

I

N S R 2R L

y

y

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

(B) Angular acceleration of the loop at the instant shown is IB6 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.




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7. A helicopter has a mass m and maintains height by imparting a downward momentum to a column of air defined by the slipstream boundary as shown in the figure. The propeller blades can project a downward air speed v, where the pressure in the stream below the blades is atmospheric and the radius of the circular cross section of the slip stream is r. Neglect any rotational energy of the air, the temperature rise due to air friction and any change in air density ().

v r

(A) 1 mgvr

for equilibrium (B) 2 mgvr

for equilibrium

(C) Power of engine = mg mg2r

for equilibrium (D) Power of engine = mg mgr

for equilibrium

8. Incompressible liquid of negligible viscosity is

pumped at total volume flow rate Q through two small holes into the narrow gap between closely spaced parallel plates as shown. The liquid flowing away from the holes has only radial motion. Assume uniform flow across any vertical section.

Q/2

Q/2

r

(A) flow velocity is proportional to 21r

(B) flow velocity is proportional to 1r

(C) pressure difference between the centre and any radial point is proportional to 21r

(D) pressure difference between the centre and any radial point is zero.




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9. Consider the circuit shown below. SI is constant

current source, meaning that no matter what device is connected between points A and B, the current provided by the constant current source is always SI the same.

IS A B

4R 2R

4R

2R

2R

4R

(A) If an ideal voltmeter is connected between A and B, the reading of voltmeter is ISR (B) If an ideal voltmeter is connected between A and B, the reading of voltmeter is 2ISR

(C) If an ideal ammeter is connected between A and B, the reading of ammeter is SI9

(D) If an ideal ammeter is connected between A and B, the reading of ammeter is SI6

10. We have two equal size boxes A and B . Each box contains gas that behaves as an ideal gas.

Thermometers are inserted into each box and it is found that the gas in box A is at a temperature of 50C, while the gas in box B is at 10C. Which of the following statements(s) is/are true?

(A) The pressure in A may be higher than in B. (B) There may be more molecules in A and than in B. (C) The molecules in A have more average kinetic energy per molecule than those in B. (D) The molecules in A are moving faster than B.




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SECTION - B Matrix – Match Type

This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example: If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s and t; then the correct darkening of bubbles will look like the following:

p q r s

p q r s

p q r s

p q r s

p q r s

D

C

B

A t

t

t

t

t

1. A cylinder of volume V = 102 m3 made by non

conducting walls contains 8 gm of He gas. The cylinder is divided by a thin fixed membrane into two unequal parts. Volume of the left compartment

is V/3 and the right component has volume 2V3

.

The left compartment has an installed electric heater. Due to finite conductivity of the membrane,

heat passes from the left part into the right part. Heat transfer rate through the membrane is 0.2 watt per T = 1C temperature difference across the membrane. Initially the heater is off and both the parts are in thermal and mechanical equilibrium. The membrane can withstand maximum pressure difference of 103 Pa. The heater starts supplying heat slowly the left compartment at its maximum possible power such that the membrane remains intact (after long time of heating also). (Take R = 25/3 J/mol-K).

Column I Column II

(A) For the left compartment (p)

P

Pres

sure

of t

he s

yste

m

T Temperature of the system

(B) For the right compartment (q) Rate of transfer of heat is 0.20 watt (C) For the whole cylinder (r) Rate of transfer of the heat is 0.06 watt (D) Through the membrane (s) Rate of transfer of heat is 0.12 watt (t) Rate of change of internal energy is constant




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2. Match the following Column I (system) Column II (Property) (A) A conducting loop is placed on horizontal xy

plane in a uniform vertical magnetic field 20

2B ˆB T (k)t

where T is a constant. The radius

of the loop is increasing continuously as 0r trT

, where t is starting from a value t 0

(p) An induced current

x

y

(B) A fixed long conducting cylinder of length ,

radius R and thickness t (where >> R and R >> t) having an initial current I0.

(q) An electrostatic field

I R

t

(C) A non conducting solid cylinder of length ,

radius R (R << ) having uniform volume charge density is rotating about its central axis with constant angular velocity by some external agent.

(r) An induced electric field

R

(D) An infinite sheet of surface charge density placed on xy plane and moving with velocity

0ˆv v i

and a conducting loop is fixed just

above the sheet.

(s) A steady magnetic field

x

y

z

v

(t) No induced current




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SECTION – C

(One Integer Value Correct Type) This section contains 8 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). 1. Two small solid spheres each of mass m = 1 kg are

thrown at the same time with same initial velocity v = 2003 m/s and angle = 30 with the horizontal. Sphere 2 is thrown at a height h = 1 m above sphere 1 as shown in the figure. Counting the gravitational force ground

2

1

h

between the two spheres, calculate the change of distance h( 108m) between the two spheres

at the moment sphere -1 hits the ground. You may take the distance between the two spheres as

constant h in your derivation for the gravitational force because h<< h. ( 1120G 103

Nm2/kg2

and g = 10 m/s2) 2. A uniform hemisphere with radius R = 10 m is placed on a

horizontal smooth surface. Its centre of mass C is below the centre O. An object ‘A’ is placed on the flat surface of the hemisphere at point O. The mass of the object is 1/8th of mass of the hemisphere. The coefficient of friction between the object and the surface of the hemisphere is = 0.2. Now the object ‘A’ is displaced slowly along the flat surface of the hemisphere towards its outer rim. Find the maximum distance (in m) of the object from the centre O without slipping on the hemisphere.

O

C

A

3. Two identical particles A and B each of mass M are fixed on the two

ends of a uniform rigid rod of length = 207

m and same mass M. The

upper mass A is restricted to move on a smooth horizontal rail and the rod is free to swing along the rail. Take g = 10 m/s2. Find the angular frequency of oscillation (in rad/s) of the system, if it is displaced slightly from its equilibrium position and released.

A

B




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4. Intensity of light due to the slits of Young’s double slit experiment are I and 4I. If the distance of the point from the centre of the bright fringe, where the intensity becomes equal to the average intensity on the screen is equal to /k ( is the fridge width). Find k.

5. The upper end of a 76 cm long glass tube is closed and the open

lower end is just touching the mercury in the cup. The tube is partly filled with mercury with 102 moles of a mono atomic gas enclosed in the upper end as shown in the figure. How much heat (in Joule) is released by the enclosed gas while its temperature is slowly reduced by 30C. The external atmosphere can balance 76 cm of

the mercury column and take ideal gas constant 25R3

J/molK.

(neglect the effect of surface tension)

6. Two identical carts A and B each with mass m are

connected via a spring with spring constant K. Two additional springs identical to the first, connect the carts to the fixed points. The carts are free to oscillate under the effect of the springs in one dimensional frictionless motion. Under suitable initial condition, the two carts will oscillate in phase according to

Cart A Cart B

A 1 Bx (t) A sin t x (t) where xA and xB are the positions of carts A and B relative to their respective equilibrium

positions. Under other suitable initial conditions, the two carts will oscillate exactly out of phase according to

A 2 Bx (t) A sin t x (t)

Determine 2221

.




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7. Figure shows a non-conducting sprayer

having a non conducting liquid of volume V, volume charge density and surface tension T. It is being sprayed into a gravity free room forming very large no of identical charged small liquid drops each of radius R. Ignore any type of inter-drop forces, find the equilibrium radius of the drops (in

millimetre) given 902

T3.6 10

m3 for

the drop.

Gravity free room

8. The vertical displacement of light rays parallel to the axis of a lens is measured as a function of

the vertical displacement h of the incident ray from the principal axis as shown in figure (a). The data is plotted in figure (b). The distance D from the lens to the screen is 1.0 m. If the focal length of the lens (for paraxial rays) is (10) K cm, then what is K?

d h

D lens

Figure (a)

Screen

2 1 0 1 2

2

0

2

h (cm)

d(cm

)

Figure (b)




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CChheemmiissttrryy PART – II

SECTION – A

Straight Objective Type This section contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which One or More than One is/are correct. 1. Which of the following graph(s) is/are correct?

0 1

0 1

[HA] [A ]Given : [HA] [A ] [HA] [A ]

1

(A)

1.00.80.60.40.2

0 2 4 6 8

0 1

pH

(B)

[NaA]log[HA]

1.2 0.8

0 1

0.4 0 0.4 0.8

Buffe

r cap

acity

(C)

A

B

C

Concentration

pH

A-Buffer B-Weak acid

C- Strong acid

0.0

10-2 10-3 10-4 10-5

1.0

2.0

3.0

4.0

5.0

10-1

(D)

A

B

C

Concentration

pH

A-Buffer B-Weak acid

C- Strong acid

0.0

10-2 10-3 10-4 10-5

1.0

2.0

3.0

4.0

5.0

10-1

Space for rough work



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2.

O

CH3

C

O

CH3

3 2 2AlCl /CS i) CaOClii)A Pr oducts

Product(s) is/are

(A)

OH OHO

CH3 CH3

(B)

OH

CH3

COOH

(C) CHCl3 (D) CaCO3

3. Find out the correct statements (A) Chemisorption increases with increase of temperature whereas physisorption decreases with

increase of temperature (B) 3 2 52

CH CH COOC H can give the Claisen reaction with NaH.

(C) Nitration of

NH2

gives para product more than meta.

(D) Glyptal is a polymer of ethylene glycol and sebacic acid.




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4. In which of the following are the ‘Ei’ mechanism involve in any step? (A)

OC

CH3

O

(B)

2

3

i CSii CH Briii

Alkene

HO

R

(C)

i OHii

CH3 C

O

CH3 CH3 C

CH3

CH C

O

CH3 (D) Base/Ph S

O

CH2

O

CH

F

CH3 Ph S

O

CH CH CH3

O 5. In a closely packed face centred unit cell with all lattice positions occupied by ‘A’ atoms, body-

centred octahedral hole is occupied by atom ‘B’ having appropriate size. Choose the correct statement (s) regarding such crystal:

(A) void percentage is 24.6 (B) percentage space occupied is 80.3 (C) formula of the compound is A4B (D) formula of the compound is AB 6. Which of the following trend(s) is(are) correct? (A) Boiling point PH3 < AsH3 < NH3 < SbH3 (B) Melting point B > Al > Ga < In < Tl (C) Equatorial radii PF5 < SF4 < ClF3 < BrF3 (D) Nucleophilic order N2H4 > NH3 7. Which of the following is/are give laughing gas on heating? (A) NH4NO3 (B) NaNO3 + NH4Cl (C) (NH4)2Cr2O7 (D) NO2 + H2S




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8. Which of the following form (s) the same osazone derivative? (A) D-glucose (B) D-fructose (C) D-mannose (D) D-galactose 9. Which of the following polymer (s) has cross linked three dimensional network? (A) Urea – formaldehyde resin (B) Bakelite (C) Amylopectin (D) Melamine-formaldehyde 10. The – COOH group is not present in (A) Picric acid (B) Aspirin (C) Ascorbic acid (D) Barbituric acid




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SECTION-B (Matrix Type)

This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example:

If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s and t; then the correct darkening of bubbles will look like the following:

p q r s

p q r s

p q r s

p q r s

p q r s

D

C

B

A t

t

t

t

t

1. Match the following reagent (in Column – I) with the cations in Column – II which can be

precipitated: Column – I Column – II

(A) AgNO3 (p) Cl (B) FeCl3 (q) Br (C) BaCl2 (r) I (D) Pb(CH3COO)2 (s)

3CH COO (t) 2

3CO 2. Match the Column – I with Column - II:

Column – I Column – II (A) Kohlraush law (p) o

mm / (B) m (q) 1

R A

(C) Kappa (r) om 3 4 2Ca PO o 2 o 3

43 Ca 2 PO

(D) (s) 1000M

(t) 1000N




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SECTION –C Integer Answer Type

This section contains 10 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). 1. How many of the following gives red colour with neutral FeCl3 solution.

OH

3CH COONa, HCOONa, NaSCN,

OH

OH

OH

,

2. Number of NH3 molecule formed in osazone formation from one molecule of glucose.

3. The three pKa values of H2C

COOH

CH

NH3+

COOHare 1.89, 3.65 and 9.60, what is the PI(isoelectric

point) of this amino acid in nearest integer. 4. The magnetic moment of a metal ion is 24 B.M. Find out the number of unpaired electrons in it.




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5. Two radioactive elements A and B have half-life of t and 3t respectively. If we start with 1 mole of each of them after a time interval of 6t the (simple whole number) mole ratio (A/B) is m : n. Find the value of m n 1 .

6. How many of the following forms colourless soluble complex with NH3. Ag, Cu, Cd, Zn, Ni, Co 7. Number of – OH group bonded with ‘B’ in Na2B4O7.10H2O. 8. Number of structural isomers of C2H3N.




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MMaatthheemmaattiiccss PART – III

SECTION – A

Multiple Correct Choice Type

This section contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only ONE OR MORE THAN ONE is/are correct 1. Let A be the set of all possible positive integers r such that, m2 – n2 = r3 for some m, n I, then

(where N is set of natural numbers) (A) number of primes in A is finite (B) number of primes in A is infinite (C) A – N = (D) N – A = 2. ai, bi, ci, ….., fi (i = 1, 2, 3), gi (i = 1, 2, 3, ….. 6) are distinct

natural numbers less than 51. If the numbers closer to centre of the figure are larger, then number of ways of completing the figure is _____

(A)

5024 6

24! 1C 5!6!4! if we assume circular symmetry

(B) 45024

1C 6!6 if we assume circular symmetry

(C)

5024 6

24!C4!

without circular symmetry

(D) 45024C 6! without circular symmetry

g3 b1

b2 b3

a3 a2 a1 g2 g5 d1 d2 d3

g4

c1 c2

c3

g1

f1

f2

f3

g6

e1

e2

e3

3. Let f: [0, 1] R is a function satisfying x x

2 4

0 0

1 f ' t f ' t dt f t dt , f(0) = 0, then which of

the following is/are true

(A) 1 1fe e

(B) 2 2fe e

(C) 1 1fe e

(D) 2 2fe e




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4. Lines 9! x + 21 y – 1 = 0 and 331 x – 428 y + 1 = 0 divide the xy plane into four regions I, II, III and IV containing points A(1, 0), B(0, 1), C(0, 0), D(–1, 0) respectively. The point E(3, 2) lies in

(A) obtuse region (B) acute region (C) IInd region (D) IVth region

5. Let 3 5 7x x xf x x .....

1 3 1 3 5 1 3 5 7

and

2 4 6x x xg x 1 .....2 2 4 2 4 6

, then

(A)

2tx2

0

f xe dt

g x

(B) f(x) = x f(x) + 1

(C) 2x

2g x e (D) f(x) + g(x) = ex

6. Let 1

n 2

1Sn n!

and 2 3

1 1 1S .....3 3 3 3 3 3

. Then

(A) S1 is finite (B) S2 is finite (C) S1 is not finite (D) S2 is not finite

7. Let 2nf n 3 1 n N, then (where [.] is denotes the greatest integer function)

(A) 2nf n 1 f n 3 1

(B) f(n) = 8f(n – 1) – 4f(n – 2) (C) 2n 2n 2n 2 2n n

0 2 4 2nf n 1 2 C C 3 C 3 ..... C 3 (D) [f(n)] + 1 is divisible by 2n + 1 8. f(x) = x3 – ax2 + bx – c has three distinct real roots, (a, b, c R) x1, x2 and x3. If x1 < x2 < x3, then (A) a2 – 3b is positive (B) a2 – 3b < (x3 – x1)2

(C) a2 – 3b 23 13 x x4

(D) 223 1

3a 3b x x4

9. Let Dn = Number of ways of putting 2n distinct letters in 2n corresponding envelops such that no

letter goes in its correct envelope and Pn = Number of ways of drawing n chords joining 2n distinct points on a circle such that no two chords intersect inside or on the circle. Which of the following is/are correct?

(A) (2n – 1)! < Dn n (B) Dn > Pn n (C) Dn < (2n)! n (D) for n > 2, Pn < (2n – 1)! < Dn




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10. Let <an> and <bn> be two real sequences such that 2n k

k n 1a a

and n kk n 1

b b

, then

(A) ap + ap + 1 + ap + 2 ….. is never finite for any p (B) bp + bp + 1 + bp + 2 ….. is not finite for any p (C) either all or none of the terms in an are zero (D) either all or none of the terms in bn are zero

SECTION – B

(Matching List Type) This section contains 2 multiple choice questions. Each question has matching Column(s). The Column(s) have choices (A), (B), (C) and (D) out of which only ONE OR MORE THAN ONE is/are correct 1. sin i, cos i, tan i (i = 1, 2, 3, 4) are arranged in decreasing order. Let the order be a1a2a3 ….. a12,

then match the following Column-I with Column-II Column – I Column – II

(A) a4 is less than (p) tan 3 (B) a5 is greater than (q) tan 2 (C) a7 is not equal to (r) sin 4 (D) a10 is greater than (s) cos 1 (t) tan 4

2. Let f: N R be defined as f(1) = ln , f(2) = ln( – f(1)) and for n > 1

f(n + 1) = f(n) + ln( – f(n)) If

nlim f n

exist and is related to by nlim f n g

. Match the values of x in Column-I with

factors of g(x) in Column-II Column – I Column – II

(A) 21 (p) 4 (B) 25 (q) 7 (C) 31 (r) 2 (D) 36 (s) 3 (t) 5




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SECTION – C

(One Integer Value Correct Type)

This section contains 8 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). 1. If x3 – 3x2 – x + 4 = 0 and ax3 + bx2 + cx + 5 = 0 have one root common, if a, b, c Q, then the

value of 2b

ac is _____

2. Roots of equation x3 + 3x2 + 2x + 1 = 0 are , , and roots of equation ax3 + bx2 + cx + d = 0 are

2 + 2, 2 + 2, 2 + 2, then 3b c da is equal to _____

3. The value of 2 4 4 6 6 26 cos cos cos cos cos cos7 7 7 7 7 7

is _____

4. 2n

2 2n i 1

nlimi n

is equal to _____ (where [.] is denotes the greatest integer function)

5. Number of integral points lying on the curve y3 = x3 + 8x2 – 6x + 8 are _____ 6. Area enclosed by normal to the parabola y2 = 4x at P(t2, 2t) and the parabola is minimum. The

square of slope of normal to the parabola is _____ 7. Two circles C1 and C2 intersect at A and B. The arc AB of circle C2 divide circle C1 into two

regions of equal area. If radius of circle C1 is 1 and range of length of arc AB is (a, b), then [a + b] is _____ (where [.] is denotes the greatest integer function)

8. Let y = g(x) be a function such that kk

n 10

x f x dx g k f k f n

. Number of points of

discontinuity of y = g(x) in the interval (0, ) is _____ (where [.] is denotes the greatest integer function)


REVIEW TEST-24-P2-(JEE ADV.)PCM Physics PART – I

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Transcript of REVIEW TEST-24-P2-(JEE ADV.)PCM Physics PART – I