XII ssJEE 2024 FST-12 DATED 16-01-24.pdf

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1. JEEMAIN 2024 pave6orz02 |
nen MAX.MARKS: 100
SECTION -1

PHYSICS (SINGLE CORRECT ANSWER TYPE)

This section contains 20 multiple choice questions Each question has À options (1), (2), (3) and (4) fr ts answer,
out of which ONLY ONE option can be corea.

Marking scheme: +4 for corect answer, Of no atempted and-1 if not correct.
1, Two charged spherical conductors of radius 2, and R, are connected by a wire. Then the

ratio of surface charge densities of the spheres (0,/0,)is :

2 R
ak Be oa

2. The velocity of a small ball of mass M and density d, when dropped in a container fl

d

ss bancs oa ti den lant Las

‘the viscous force acting on the ball will be :

aie B) Me or Da

3. A dipole is placed in an electri field as shown. In which direction will it move ?

A) towards the left as its potential energy will increase.
B) towards the right as its potential energy will decrease.
©) towards the left as ts potential energy will decrease.

D) towards the right as is potential energy will increase

4. A lens of large focal len

Ih and large aperture is best suited as an objective of an

astronomical telescope since
AA) a large aperture contributes to the quality and visibility of the images.

B) a large area of the objective ensures better light gathe:

power.
O) a large aperture provides a better resolution.
D) all of the above,

2. Ifa particle starts from rest under uniform acceleration of 2 m/s2, then distance travelled
in 3 seconds will be
A) 1 meter B) 4 meter C)9 meter D) 6 meter

Colu

1 - I gives certain physical terms associated with flow of current through a

‘metallic conductor, Column - II gives some mathematical rel

quantities, Match Column - I and Column - IL with appropriate relations

Column 1 Column — 11
A) Drift Velocity
B) Electrical Resistivity

©) Relaxation Period

D) Current Density

A) (AAR), (BAS), (CH(P), DO) BAR), (BIS) CQ. (D>P)
CHAR) BHP). CHS). DQ D) (AMR). BQ). (CMS). (DIAP)

‘The weight of a body on the earth is 400 N. Then weight of the body when taken 10 a
depth half of the radius of the earth will be

A)300N B) 100 N C) Zero D) 200 N

For a plane electromagnetic wave propagating in x-direction, which one of the following
combination gives the correct possible directions for electric field (E) and magnetic field

(B) respectively ?

A Joh je B)-j+f, -7-£
Oj 7-8 D) jek jek

A parallel plate capacitor has a uniform electric field ‘7° in the space between the plates.
the distance between the plates i “d” and the area of each plate is “A”, the energy

density in the capacitor is: (¢, = permittivity of free space)

mir mak O lara y Hl

3. 2

1.

14.

15,

‘The equivalent capacitance of the combination shown in the figur
$
HH]

Ly
¢

A)3C B)20 9er D)3C2
A particle is released from height $ from the surface of the Earth. At a certain height its
kinetic energy is three times its potential energy. The height from the surface of earth at
that instant is

s s

o LE

5 s
43 3 2

ICE and G respectively denote energy and gravitational constant, then 2 has the

dimensions of

ay pere Jr B)(m][e"][r-]

opatelr DT Tr]
ee ee a Mo gs
bo,

ayaa mi 92% Dar

Inside a capacitor the value of displacement current depends on
A) Rate of change of electric flux B) Magnetic field in the region

©) External resistance D) Speed of light

‘The intensity of magnetic field due to a long wire carrying current Lata distance r is
given by

ni DE o at Dal

An electromagnetic wave of wavelength "2' is incident on a photosensitive surface of
negligible work function. If‘m’ mass is of photoelectron emitted from the surface has
de-Broglie wavelength Athen:

2m): _{2me) _f2me\ 9s _ (2m
wae re De)

a ad

4. 18.

19,

20,

If force [ F], acceleration [ A ] and time [ T ] are chosen as the fundamental physical
quantities, Find the dimensions of energy

a [elta] DID
OFT) Der

‘Two conducting circular loops of radii R, and R, are placed in the same plane with their

centres e

the mutual inductance M between them will be directly

neiding. IFR, >> R,

proportional to

y Rt ES
On DR
A point object is placed at distance of 60 em from a convex lens of focal length 30 em.
Ifa plane mirror were put perpendicular to the principal axis of the lens and at a distance

‘of 40 cm from it, the final image would be formed at a distance of :

0m 40 em
A) 20 cm from the lens, it would be a real image

1B) 30 om from the lens, it would be a real image.

C)30 om from the plano mirror, it would be a virtual image.
D) 20 em from the plane mirror, it would be a virtual image.

A particle of mass ‘mis projected with a velocity = #7, (k<1) from the surface of the

earth. (U, escape velocity)

Ihe maximum height above the surface reached by the particle is:
per ey

aa) De)

CES »

Tse Tel

5. SECTION
(NUMERICAL VALUE ANSWER TYPE)

"This section contains 10 questions. The answer to ch question is o Numerical value I he Answer in the

deémels, Mark neares Integer only. Have to Answer any 5 only aut of 10 questions and question vil be

‘evaluated according tthe fellowing marking scheme:

[Marking scheme: +4 for correct answer, -1 in all other ei

21. Twenty seven drops of same size are charged at 220 V each. They combine to form a
bigger drop. Calculate the potential of the bigger drop (in Vo).
22. A uniform rod of length 200 em and mass 500 g is balanced on a wedge placed at

40 n and another unknown

ark, A mass of 2 kg is suspended from the rod at 20

mass “mn” is suspended from the rod at 160 cm mark as shown in the figure.

‘The value of m’ (in Kg) such that the rod is in equilibrium is 1 kg Find x (g=10 m/s")

0_20em 40cm 160 em

Ex =

23. From a circular ring of mass ‘M? and radius “R’ an are corresponding to a 90"sector is

removed. The moment of inertia of the remaining part of the ring about an axis passing

through the centre ofthe ring and perpendicı
=

24. À step down transformer connected to an ac mains supply of 220 V is made to operate a

lar to the plane of the ring is

yes “MR”. Then the value of 4K"

11 V, 44 W lamp. Ignoring power losses in the transformer, the current in the primary

cuit is 1 A. Find x

25. A sorew gauge gives the following readings when used to measure the diameter of a
Main scale reading : 0 mm

Circular scale reading : 52 divisions

6. 27.

28,

2.

Given that 1 mm on main scale corresponds to.

100 divisions on the circular scale. The diameter

of the wire from the above data In (em) is xx10

‘A nucleus with mass number 240 breaks into two fragments each of mass number 120,

the bin js 7.6 MeV while that of

ng energy per nucleon of unfragmented nuel

fragments is 8,5 MeV. The total gain in the Binding Energy in the process in MeV is
Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine, The losses
due to frictional force are 10% of the input energy. How much power is generated by the

turbi

in KW to the nearest integer is 2(g = 10m

The numberof photons per second on an average emite bythe source of
monochromatic light of wavelength 600 nm, when it delivers the power of 33:10” watt
willbe 10% (= 66 04)

An inductor of industanceL, a capacitor of capacitance Cand a resistor of resistance #R°
are connected in series to an ac source of potential difference “Y” vols as shown in
figure Potential difference across L, Cand R is 40 V, 10 V and 40 Y, respectively. The
amplitude of eurent lowing through LCR series circuits 10V34.The impedance of the
cireit in Ohm is

hows

|—s0v—+—10 Y 40 V—|

7. 30. A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds

to the same height. The magnitude of Impulse (in Kgm/s)

pparted to the ball is

Ce =10 m/s*)to the nearest

CHEMISTRY MAX.MARKS: 100

SECTION -1
(SINGLE CORRECT ANSWER TYPE)

This section contains 20 multiple choice questions, Each question hat 4 options (1, (2) (3) and (4) for Ms answer,

‘ut of which ONLY ONE option car be correa.

[Marking scheme: +4 for correct answer Of not atempted and -1 H not correc

31 STATEMENT I:

Lighest oxidation state of Mn is shown with Oxygen rather than

Fluorine
STATEMENT II: The oxidation of Mn in KMnOu is 17
A) Both STATEMENT I and STATEMENT IL are correct

B) Both STATEMENT I and STATEMENT II are incorrect
TATEMENT Lis correct and STATEMENT I

D) STATEMENT Lis incorrect and STATEMENT IL is correct
32. The IUPAC name ofthe given compound is

er
a
A) 2-Chloro-3-bromopentane 1) 3-Bromo -2-chloropentane
€) 2-Bromo -3-chloropentane D) 3-Chloro-2-bromoy
33. Which ofthe following are the example of double salt?
1) FeSO, [NA], SO,6H,0 2) [Cu(NH,), 80,
3) K¿SO, Al,(SO,), 241,0 4) K,UFe(CN),1

Choose the correct anser
A)Land3only B)land2only C)1, 2and 4 only D)2 and 4 only
34, Glucose does not react with
A) HEN B)Br water C)HNOs D)24-DNP

8. 35.

36.

37.

38,

39,

Which of the following relations are correct?

DAW = AU + PA 2) AG=AH-TAS 3) as = Le

4) AH = AU anRT

Choose the most appropriate answer from the options given below
A)3 and 4only B)2and 3 only ©) Land 2only — D)L2and 3 only

‘The correct order of C-CI bond lengths of x, y and z in the given compounds are

EAN
Hao x Hoo y =
a a
a
Masyz Baay>ax Oxosy D) yazox

Which of the following has zero dipole moment

A) Cis~2~butene B)L3
e
a
a
9 D)

Choose the incorrect option
A) Bond Energy order Cl, > Br, > & >

B) Thermal stability order HF > HCI> Hr > Hr
©) Bond Angle order NH, < PH, < sit, < abi,

D) Boiling point order 11,0 > HSe> 11,1

Hs
Which carboxylic acid gives Hell — Volhard — Zelinsky reaction?
A) Formie acid B) Bthanoie acid
©)2,2-Dimethyipropanoicacid D) Benzoie acid

Which one of the following sets of ions represents a collection of isoelectronic species?
Number : F : 9, CI : 17, Na= 11, Mg = 12, Al= 13, K = 19, Ca — 20, Se

(Given: As
-21)
w(K

B) (Ba? Sr” .K",Ca®)

9. 41

42

43.

of

Choose the most acidic compound among the given
on 008 go
B) N o
In which of the following is not a gaseous element?

AP BH OBn D)Ck

‘The best reagent used for the following conversion is

°
2
me "m

es) Dar,

fa’ Mg" Ca

a a py os

A) LAI, B) Zug; Con. HCL
Cy MN D) Balls
Match List I with List IL
Tist—T EE
P. | vant Hoff factor, 1 LJ Gryoscopie constant
o Tr 1. |Tsotonie solutions
R. | Solitons with same osmotic | Il. | Normal colligative property
are Abnormal colligative property
=| Azeotropes TV, [Solutions with same composition of
vapour above it

Choose the correct answer from the options given below
AP-ILQ@-LR-ILS-IV Bp-ULQ-ILR-LS-V
OP-ULQ-LR-IV,S-I DJP-LQ-HLR-I,S-IV

10. 45.

47.

48,

49.

‘The atom or group “Z” in the given reaction sehen

Hol, (Kor
+ rasero tanos
A) -o1 B) -ocH, oa D) =,

The effect oF increase in pressure tothe following reaction in equilibrium state, is :
PCI(g)=PCh(g)+Ch (2)

A) the equilibrium will shift in the forward dirceti

and more of Cl and PCI, gases
Will be produced

BB) the equilibrium will go backward due to suppression of dissociation of PCI,

€) No pressure effect on equilibrium

D) the equilibrium will go backward due to increase of dissociation of PCI,

Which reactant is used to get the required product in a given reaction scheme?

à) Bthanolic NaCN
Reactant 7 ET yet,

5 NAH FLO
Hye.
yaa Ba
CH
Hee
one a D) a

‘of HCI & NaOH Methyl orange is used as indicator Ihe colour change

is observed

A) before the end point
B) before the equivalence point

C) afterthe equivalence point

D) No colour change is observed

Rate constant of the reaction 241,0, >2H1,0+0, is 2.3x 10 ‘sec * order of reaction is

A) Zero BL 92 D)3

SRIT COS Page NOT

11. 50. The major end product of the given reaction is

Ms sac
Bt ip NANO¿MICI, 273K
DEPOBOA
HD EMNO,
No
En Cook
ee 8
à à B) OH
Hy
Coon oh
Be
o D) 4

SECTIONAL
(NUMERICAL VALUE ANSWER TYPE)

This seien contains 10 questions. The answer 1 each questions a Numerical volve. IF the Arswer nthe

decimals, Mark neores Integer only. Have to Answer any 5 only out of 10 questions and question vil be

‘evaluated eccoreing 1 the following marking scheme:

‘Marking scheme: +4 for corec answar,-1 in ll other cases.

31. No. of elements in the 5" period of periodic table Is "x" and atomic number of fist
noble gas in the periodic table is “y”. Then the value of (x + y) is

52. The number of SP? carbon atoms present in aromatic hydrocarbon obtained in the given

reaction is
Ho i) Excess of NaNH,
"Aromatic Hydrocarbon
E fi) Ag, NHC
ii) Red hot Fe tube

53. Total numberof moles of AgC! precipitated on addition of excess of AgNO, to one
mole each ofthe following complexes
[co(vit,),ch] [x1(41,0),]c1, [Pwit,), Ch] and [Pa(N#,),]Ch is.

12. 54

ss.

s6.

57

58.

so.

60.

Oxidation state of “S"in 1,80, is

How many moles of hydrogen iodide is consumed in a given reaction (for one mole of

reactant)?
on
He He
Ho be
or on
A first order reaction has the rate constant, & = 6.9310" 5"'. Half life time of the

reaction is see
‘The spin only magnetic moment of [Mn(,0), |" complexes is BM. (Nearest

integer) (Given : Atomic no. of Mn is 25)

‘The volume (in ml) of 0.01MHCI, required to completely neutralise 40ml 0.1M NaOH

is ...10 ml (Nearest Integer)

‘The number of water molecules required for complete hydrolysis of the given peptide is

ne
by

AL298K
HPO, = H,PON + H°,K,

HPOS = HPO +H

HPO? = POP +HK,

Based on above equilibria, thee
HPO, = PO +3H0,K is 10% (Nearest

13. MATHEMATICS MAX.MARKS: 100
SECTION -1
(SINGLE CORRECT ANSWER TYPE)
This section contains 20 multiple choice questions Each question has 4 options (1), (2), (3) and (4) fr Ms answer,
out of which ONLY ONE option can be corea.
[Marking scheme: +4 for core answer, Of not atempted and-1 if not correct.

61. The set of all the values of *a* for which the point (a? the parabola

2) lies i

yas, is

E fs)
weh)»

2. WR={33),166).09).12

OR D) R-(9}

5,6)}isarelation on the set

A={3,69.12}. The relation is
Ay an equivalence relation
B) reflexive and symmetric
reflexive and transitive
D) only reflexive

63. la faz and 5 are the angles made by a straight line with the diagonals ofa cube, then
sin’ a sin Gin y sin" 5 is equal to

1

vi mi CE D) None of these

64. The radin ofthe circle passing though the foi ofthe ellipse +21 and having its

center at (0, 3) is

a3 B)4 OF DE

65. Oll is leaking at the rate of 16cm /s from a vertically kept cylindrial drum containing

oil. Ifthe radius of the drum is 7 em and its height is 60 em, Then, the rate at which

the level ofthe oil is changing when oil level is 18cm, is
=16 -16 16 =16
a B c D
> 497 ) sr D 29m » x
66, the lines a:+2y-+1=0,be+3y-+1=0,er+-4y=1=0 are concurrent, hen a,b, are in

AAP B)GP our D) None of these

14. 67.

68.

69,

70.

mn

7.

B.

74,

(AS | ds equal

1

at By a o!

e solution of Bra is
The solution of © +1
A) et axec=0 B) eco

Cer sree: D) et? 2H

o

‘The value of J,

Nr = ir Di
TE is mal to
A Jeoslan(3 ze

Oper)

D):

A) (02) B) (20.0) C){-)-(0) Dina)

‘The ratio of the coefficient of x to the term independent of x in the expansion of
A)7:16 B)7:64 ©)1:4 D)1:32

Ifthe function 7(x)=aw""has a local maximum at the point (2,10), then

A) a=50,5=1 B) a=

Oa-s-t D)a-5-l

15. 75.

Z
length of AD is

of. Ifihe internal angular bisector of =.

»! a

76, Fortwo events À and B, if P=
3 3 1
A) P(An 5) à B)P(anB) à 4

7. The area bounded by the curves y = cos x and y = sin x between the ordinates

3-0 and x=, is
4

AEA B) 242 O4 1 D) Wa

78 ‘hen the vector Bsatisfying 248 2-6 and a
DEEE B) ai jak
ori j Dirj-

79, Let cos(a+ß)= Sand sin(a-P)= À. where 0 a, p<. Then tan2a=

as ss » 2»
= Oy

80. For two data sets each of size 5, the variances are given to be 4 and S and the

sans are given to be 2 and 4, respectively. T
combined data set is

variance of the

as mil os DE

SECTIONAL
(NUMERICAL VALUE ANSWER TYPE)

This sean contains 10 quests. The answer to ach question is 6 Numerical value. Fhe Answer in the

decimals, Mark nearest Integer only. Have to Answer any 5 only out of 10 questions and question will be

‘evaluated according 10 the fellowing marking scheme:

[Marking séhomes +4 for cores answer

8. Leaf fe [YoY 9.3.) then the number of one-one mappings om

Ato Bsuch that /(x,)-yVi-12345

16. 82

$,
$4,
85.

87.

88,

If system of equations x=ey+bz,y

solutions, then a? +8 =e! +2abe is equal to

The number of complex numbers z such that 2-1]

If as and Pare the roots of the equation x*—x-+1=0, thom a + 9%"

Ifthe latusrectum of a hyperbola through one focus substends 60° angle at the other

focus, then the square of its ecentricity eis.
1 1

1 sa, then the value of 3 is equal to
50207 Bono wi

Let x e[-1:1] for #=1,23.......24, stich that sin "xy sin + sim "u 128, then

the value of +25, +355 ont tp is

Ir 4+8=%, them (Inn) + tan) =

The number of integral values of 2 for which the equation x'+y*-22x+22y=14=0

represents a circle whose radius cannot exceed 6, i

arthemetic means are inserted between 7 and 49 and their sum is found to be 364,

then nis