12th JEE

Advanced

Test-01
DURATION ::180
DURATION Minutes
90 Minutes DATE : 30/06/2024 M.MARKS : 180

Topics covered
Physics: Electric Charges and Fields Electrostatic Potential and Capacitance, Current Electricity
Chemistry: Solutions Electrochemistry Chemical Kinetics, Organic 11th – Revision, GOC & Hydrocarbon,
Haloalkanes and Haloarenes
Mathematics: Determinants Matrices Basic Mathematics Relations and Functions, Inverse Trigonometric
Functions

General Instructions:
1. Immediately fill in the particulars on this page of the test booklet.
2. The test is of 3 hours duration.
3. The test booklet consists of 54 questions. The maximum marks are 180.
SECTION-1 (Maximum Marks: 24)
This section contains EIGHT (08) questions.
• The answer to each question is NUMERICAL VALUE.
• For each question, enter the correct integer corresponding to the answer using the mouse and the onscreen virtual
numeric keypad in the place designated to enter the answer. If the numerical value has more than two decimal places,
truncate/round-off the value of TWO decimal places.
• Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct integer is entered;
Zero Marks : 0 In all other cases.

SECTION-2 (Maximum marks: 24)

• This section contains SIX (06) questions.
• Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are)
correct answer(s).
• For each question, choose the option(s) corresponding to (all) the correct answer(s).
• Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 ONLY if (all) the correct option(s) is(are) chosen;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : –1 In all other cases.

SECTION-3 (Maximum marks: 12)

• This section contains FOUR (04) Matching List Sets.
• Each set has ONE Multiple Choice Question.
• Each set has TWO lists: List-I and List-II.
• List-I has Four entries (I), (II), (III) and (IV) and List-II has Five entries (P), (Q), (R), (S) and (T).
• FOUR options are given in each Multiple Choice Question based on List-I and List-II and ONLY ONE of these
four options satisfies the condition asked in the Multiple Choice Question.
• Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 ONLY if the option corresponding to the correct combination is chosen;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : –1 In all other cases.
[1]
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[2]
 IMPORTANT CONSTANTS

Speed of light in free space, : 3.00 × 108 ms–1

Permeability of free space, : 4 × 10–7 Hm–1
Permittivity of free space, : 8.85 × 10–12 Fm–1
The Planck constant, : 6.63 × 10–34 Js
Rest mass of electron, : 9.1 × 10–31 kg
Rest mass of proton, : 1.67 × 10–27 kg
Molar gas constant, : 8.31 JK–1 mol–1
The Avogadro constant, : 6.02 × 1023 mol–1
The Boltzmann constant, : 1.38 × 10–23 JK–1
Gravitational constant, : 6.67 × 10–11 N m2kg–2
Acceleration of free fall : 9.8 ms–2
Rydberg Constant : 1.097 × 107 m–1
Atomic mass unit : 1.67 × 10–27 kg
Charge on proton : 1.6 × 10–19 C

IMPORTANT VALUES

2 = 1.414 ln 10 = 2.303
3 = 1.732 log102 = 0.3010
5 = 2.236 log103= 0.4770
 = 3.142 log107 = 0.845
e (Euler’s constant) = 2.718

* Use above values unless otherwise specified in a question.

❑❑❑
 PART-I (PHYSICS)
SECTION-1 shell A, then the final charge on the shell B is
Numerical Value Type Questions: 8Q
equal to − . Find x.
1. Two parallel plate capacitors with area A are x
connected through a conducting spring of natural
length l in series as shown. Plates P and S have
fixed positions at separation d. Now the plates are
connected by a battery of emf E as shown. If the
extension in the spring in equilibrium is equal to
the separation between the plates, the spring
270 AE 2
constant k is . Find x.
x(d − l )
3 5. A network shown in the figure consists of a
battery and five unknown resistors. When an ideal
ammeter is connected between the terminals A and
B, its reading is 4 A and when a resistance of 3 
is connected in series with the ammeter its reading
becomes 2 A. Now the ammeter and the resistance
are disconnected and an ideal voltmeter is
2 connected between the terminals A and B. What
2. A small ball of mass 1 kg and charge μC is would the voltmeter read in volts?
3
placed at the centre of a uniformly charged sphere
1
of radius 1 m and charge mC. A narrow smooth
3
groove is made in the sphere from centre to
surface as shown in figure. The sphere is made to
rotate about a diameter perpendicular to the
6. A positively charged small disc is released on the
1 top of fixed hemispherical frictionless dome in
groove at a constant rate of revolutions per
2 presence of a uniform horizontal electric field. If
second. Find the speed w.r.t. ground (in m/s) with the disc leaves the dome after an angular
which the ball slides out from the groove. Neglect displacement θ = sin–1 (3/5), find ratio of
any magnetic effect. gravitational and electrostatic forces on the disc.
Assume that the dome does not exhibit any
electrical property.

3. Find the magnetite of uniform electric field E in 7. A right pyramid of square base and height H has
N/C (direction shown in figure) if an electron uniform charge distributed everywhere within its
entering with velocity 100m/s making 300 volume. Modulus of electric field and potential at
comes out making 600 (see fig.), after a time the apex P of the pyramid are E0 and V0. A
numerically equal to m/e of electron.
H
symmetrical portion of height h = from the
2
apex has been removed. The modulus of electric
field and potential at the apex P of this truncated
pyramid is xE0 and yV0 respectively. Find x + y.

4. Figure shows a system of three concentric metal

shells A, B and C with radii a, 2a and 3a
respectively. Shell B is earthed and shell C is
given a charge Q. Now if shell C is connected to

[4]
8. Six plates each of area A are arranged as shown in
 10 
figure. The separation between adjoining plates is (A) t2 − t1 =  log e   (C) t1 + t2 = 2 log e (3)
9
d. The equivalent capacitance between points A
x A  10 
and B is 0 . Find x. (B) t1 + t2 = 2 log e  (D) t2 − t1 = 2 log e (3)
d  3
12. Mark the correct statement(s) for the situation
shown:

SECTION-2
One or More Than One Correct Type Questions:
9. Two concentric shells A and B have radii R and (A) If a point charge 𝑞 is placed inside the
3V cavity but not at centre, then potential
2R, charges qA and qB and potentials 2V and 𝑞
2 of the conductor is 4𝜋𝜀 𝑅0
respectively. Now, the shell B is earthed and the (B) If a point charge 𝑞 is placed at the
new charges on them become q A' and qB' . Then centre of cavity, then potential of the
conductor will be zero.
(C) If a point charge 𝑞 is placed inside the
cavity but not at centre, then potential
of the conductor will be
𝑞 1 1 1
4𝜋𝜀 𝑅
[ +𝑟−𝑟 ]
qA 1 q A' 0 1
(A) = (B) =1 (D) If a point charge 𝑞 is placed inside the
qB 2 qB'
cavity but not at centre, then potential
(C) Potential difference between A and B after at the center of the conductor due to
3V charges on the outer surface of
earthing becomes 𝑞
2 conductor is 4𝜋𝜀 𝑅
0
(D) Potential difference between A and B after
13. Nine wire each of resistance r are connected to
V
earthing becomes make a prism as shown in figure. The equivalent
2
resistance of the arrangement
10. In the given figure the capacitance of capacitor
is 𝐶. The left plate of the capacitor is given
charge 𝑄 and right plate is uncharged. Then
choose the correct statement(s):
6
(A) across terminals A and D is r
15
8
(B) across terminals A and D is r
15
3
(C) across terminals A and B is r
5
4
(D) across terminals A and B is r
5
(A) The amount of charge that will flow 14. An ideal dipole of dipole moment P is placed
through the battery till the steady state in front of an unchanged conducting sphere of
is reached when the switch 𝐾 is closed radius R as show.
𝑄
will be 𝐶𝜀 + 2
(B) The charge appearing on the inner face
of the left plate at steady state is 𝐶𝜀 KP
(A) The potential at point A is
(C) The charge appearing on the interface ( r − R )2
of the right plate at steady state is 𝐶𝜀 KP
2𝑄 (B) The potential at point A is
(D) If 𝜀 = 𝐶 , then work done by cell after
r2
3𝑄 2
closing the switch is (C) The potential due to diploe at point B
𝐶
11. A capacitor charges from a cell through a KP
is
resistance. The time constant is τ. The capacitor ( r + R )2
collects 10% of its final charge in a time t1 and (D) The potential due to diploe at point B
after a time t2, the charge on the capacitor KP
is 2
becomes 10% less than its final charge. Then r
[5]
 SECTION-3 I II III IV
Matrix Match Type Questions: (A) P P Q Q,S
15. With reference to the circuit diagram shown (B) P P Q,S Q
match the following (C) Q Q,S P P
(D) Q,S Q P P

17. n identical drops of a liquid each having charge q

and radius r coalesce. Match the unfilled places in
List-I with their respective fills given in List-II. In
List-I, E, V, C and  represents electric field at
surface, potential at surface, capacitance and
List I List II
surface charge density respectively.
I Potential difference, in volt, P zero List I List II
across A and D
I Ebig = …..Esmall P n1/3
II Potential difference, in volt, Q 9
across capacitor II Vbig = …..Vsmall Q n3
5
III Cbig = …..Csmall R n2/3
III Value of Y, in ohm, for R 1
which no energy is stored 5 IV big = ……small S n–1/3
across capacitor

IV Steady state current, in S 14 T n5/3

ampere, in the branch
I II III IV
containing the capacitor is
(A) P R P P
T 14 (B) P Q R T
3 (C) T P R R
(D) S R P Q
I II III IV
(A) Q R T P 18. Match List-I with List-II
(B) R Q S P List I List II
(C) Q R P S
(D) R Q T S I 1 P At large distance from
E
16. The diagram shows a circuit with zero identical r centre of the dipole
resistors. The battery has a negligible internal
resistance. What will the effect on the ammeter and II 1 Q At large distance from the
voltmeter be if the switch S is closed? E
r2 centre, at the axis of a
uniformly charged ring.

III 1 R Due to an infinite charged

E
r3 conducting plate.

IV 1 S At a radial distance x
List -I List -II E
r0 from the axis of a infinite
Ammeter
I. P. Increases thin conducting charged
reading
cylinder (x > R, R is the
Voltmeter
II.. Q. Decreases radius of cylinder)
reading
Equivalent T At a distance r from the
III.
. resistance of R. Does not change axis of a infinite uniform
circuit
line charge
Power dissipated
IV.
. across R in right S. Becomes zero I II III IV
branch (A) P, S Q R S, T
T. Cannot be determined
(B) R, S S Q R, T
(C) S, T P Q P, R
(D) S, T Q P R

[6]
 PART-II (CHEMISTRY)
SECTION-1
Numerical Value Type Questions:
19. Among the following, how many solutions show (iii)
positive deviation from raoult’s law?
(i) n-Hexane + n-Heptane (iv)
(ii) Acetone + carbon disulphide (v)
(iii) Carbon tetrachloride + chloroform
(iv) Chloroform + benzene 23. Cadmium amalgam is prepared by electrolysis of
(v) Benzene + toluene CdCl2 using mercury cathode. How long (in
(vi) Acetone + aniline seconds) should a current of 6 A is passed in
(vii) Acetic acid + pyridine order to prepare 12% by mass Cd-Hg amalgam
(viii) Acetone + ethanol on a cathode of 3.3 g Hg? [Atomic mass: Cd =
(ix) Chlorobenzene + bromobenzene 112.4; Hg = 200.60]
(x) n-Butyl chloride + n-Butyl bromide
(xi) Acetone + chloroform 24. nA → B is a 1st order reaction, whose
(xii) Chloroform + diethyl ether concentration versus time curve is given below.
(xiii) HCl + water
(xiv) Acetone + benzene
(xv) Ethyl alcohol + water

20. How many species out of the following are

aromatic?
If the half-life for the reaction is 24 minutes, then
(i) (ii) the value of n is _________ .

(iii) (iv) 25.

(v) (vi)
Consider the solutions given below with
mentioned concentrations and find the value of
P
(vii) (viii) , where P is the number of solutions having
Q
characteristics of “sol-1” and Q is the number of
solutions having characteristics of “sol-2”.
[Given Kf = 2 kg K mol–1. Assume all
(ix)
electrolytes undergo complete ionization.]
(i) 0.5 molal urea solution
21. In the reaction A → Products, the rate is (ii) 0.5 molal NaCl solution
doubled when the concentration of 'A' is (iii) 0.5 molal K3[Fe(CN)6] solution
quadrupled. If 50% of the reaction occurs in (iv) 0.1 molal Ca3(PO4)2 solution
8 2 h, then how long (in hours) would it take 1
(v) molal CaCl2 solution
for the completion of next 50% of reaction? 6

22. Among the following free radical bromination 26. Consider the following unbalanced redox
reactions how many will produce 2° halide as the reaction
major product? Hg 22+ + NO3− + H + Hg 2+ + HNO2 + H 2 O
(1M) (1M) (1M) (1M)
(i) [Concentration of ionic species are given at
equilibrium]
If E ocell of the given reaction is 0.09 V, then
(ii)
calculate the minimum pH required to reach
equilibrium.
 2.303RT 
Take = = 0.06,log 2 = 0.3
 F 
[7]
 SECTION-2 (C) H2C = CH — CH = CH2
One or More Than One Correct Type Questions:
27. Which of the following will give same (D)
product with HBr in presence or absence of
peroxide. 31. If total vapour pressure of an ideal binary
(A) Cyclohexene solution of liquids A and B at particular
(B) 1-methylcyclohexene temperature is represented as P = (150 + 100 xA)
(C) 1,2-dimethylcyclohexene mm Hg, then Select the correct option(s).
(D) 1-butene  P 
(A) lim 
x A →0 x
 = 150 mm Hg
 B
28. During preparation of cyclohexene by Kolbe's
 P 
electrolytic method from compound X, inert (B) lim   = 250 mm Hg
x A →0 x
electrodes are used. The option(s) representing  B
incorrect statement(s) is/are 3
(C) If xB = 0.5, then yA =
8
(A) 5
(D) If xA = 0.5, then yA =
8
(B) Reductive ozonolysis of cyclohexene will
produce adipic acid 32. Ionic conductance at infinite dilution of Al3+ and
(C) pH of the reaction mixture increases SO42– ions are 60 and 80 –1 cm–2 eq–1,
progressively as the reaction proceeds respectively.
(D) pH of the reaction mixture remains same The correct option(s) regarding Al2(SO4), is/are
throughout the reaction (A) The molar conductance is 140 –1 cm–2 mol–1.
(B) The equivalent conductance is 140 –1 cm–2
29. Consider an elementary chemical reaction: eq–1.
A→B (C) The molar conductance is 840 –1 cm–2 mol–1.
This reaction is studied by a chemist who (D) The molar conductance is 23.33 –1 cm–2
obtained the following three graphs for the mol–1.
experiments done at different temperatures SECTION-3
Matrix Match Type Questions:
33.

Column-I Column-II

A. p.
Select the correct statement(s) based on the
following graph.
(A) Line 2 and line 3 represent experiment done B. q.
at different temperatures but with the same
initial concentration of [A].
C. r.
(B) Line 3 represents lower temperature than
line 2.
(C) Line 2 represents lower temperature than line
D. s.
3.
(D) Line 1 and line 2 represent experiment done
at same temperature.
I II III IV
30. Which of the following compound(s) evolve(s) (A) R S Q P
CO2 gas, on undergoing oxidative ozonolysis? (B) P Q R S
(C) Q P S R
(D) S R P Q
(A)

(B)

[8]
34. Match the List-I with List-II I II III IV
List-I List-II (A) P S,Q Q P,R,S
(Major electrolysis (B) P,T P,Q P P,R,S
product using inert
(C) P P,R R P,R,S
electrodes)
(D) P,T Q,R S P,R,S
I Dilute aq. P O2 evolved at
solution of anode 36. Match the List-I with List-II
HCl List-I List-II
II Dilute aq. Q H2 evolved at I P Graph between
solution of cathode half-life v/s initial
NaCl Concentration for
III Concentrated R Cl2 evolved at 1st order reaction
aq. solution anode
II Q Graph between
of NaCl half-life v/s initial
IV AgNO3 aq. S Ag deposited at Concentration for
solution cathode second order
T NO2 is evolved at reaction
anode III R Graph between
I II III IV half-life v/s initial
(A) P,Q P,Q Q,R P,S Concentration for
Zero order reaction
(B) P,R P,R Q,R S,T
IV S Graph between
(C) P,S P,R Q,R S,T
degree of
(D) P,Q P,Q R,S S,Q dissociation and
time for a first
order reaction
35. Match the List-I with List-II
T Graph between
List-I List-II C0 − C
I P -bond and time
C
involved in for a second order
conjugation reaction, where C0
II Q Every lone is the conc. of
H 2 N CH = CH − C  CH pair present reactant at time
in molecule t = 0, C is
involved in the concentration
resonance of reactant at time t
III R 2  bonds I II III IV
CH 2 = CH − O − CH3
involved in (A) Q S,T P S
conjugation (B) S R,T Q P
IV CH3CH = CHCH = CH2 S - (C) Q P,T S R
conjugation
(D) Q R,S P P
T aromatic

PART-III (MATHEMATICS)
SECTION-1 e x − e− x
38. Let f ( x) = and if f(g(x)) = x then
Numerical Value Type Questions: 2
37. Suppose a matrix A satisfies A2 – 5A + 7I = O. If
1  e1002 − 1 
A8 = aA + bI, then a/253 is g  is equal to
167  2e501 

[9]
39. Let f: [0, 4] → [0, ] be defined by 47. It is given that x = 9 is a solution of the equation
f(x) = cos–1 (cos x). The number of points x  [0,
10 − x
( )  8ax 
log e x 2 + 15a 2 − loge (a − 2) = log e 
a−2
 ,
4] satisfying the equation f ( x) = is
10 then
(A) a = 3
40. If f(x) is a polynomial function satisfying f(x)f(y) (B) a = 3 /5
= f(x) + f(y) + f(xy) – 2 for all real x and y and f(3) (C) other solution is x = 15
= 10, then f(4) – 8 is equal to (D) other solution is x = 3/5
48. Let g(x + y), g(x).g(y) and g(x – y) are in A.P. For
41. If 0    /2, then number of roots of all x, y  R and g(0)  0. Then
cos 2 cos 4 cos 6
2 2 2
(A) g(2) = 1
() = sin 2 sin 4 sin 6 is (B) the graph of g is symmetry about y-axis
1 1 1 (C) g is an odd function
42. If f(x) = sin2x + sin2 (x + /3) + cos x cos(x + /3) (D) g(0) = 1
1 49. 2 tan–1 (–3) is equal to
and g(5/4) = 1298 then g o f (x) is equal to.
59 (A) –cos–1 (–4/5)
(B) – + cos–1 (4/5)
x − 2 ( x − 1) 2 x3 (C) –/2 + tan–1 (–4/3)
43. If ( x) = x − 1 x2 ( x + 1)3 then the (D) cot–1 (4/3)
x ( x + 1) 2 ( x + 2)3 50. Let f : A → B and g : B → C be two function
absolute value of coefficient of x in (x) is and gof : A → C is defined. Then which of the
following statement(s) is(are) incorrect?
(A) If gof is onto then f must be onto
x 2 − x − 2 (B) If f is into and g is onto then gof must
44. If −3   2 for all x  R, then how
x2 + x + 1 be onto function
(C) If gof is one-one then g is not
many integral values of  exist? necessarily one-one
(D) If f is injective and g is surjective then
SECTION-2 gof must be bijective mapping
One or More Than One Correct Type Questions: SECTION-3
Matrix Match Type Questions:
45. Let f ( x ) = cot −1 (sgn ( x ) ) + sin −1 ( x − x) 51. Let A and B be two non-singular matrices such
which of the following is(are) correct? that (AB)k = Ak Bk for three consecutive positive
(A) Domain of f ( x ) is [−1,2)
integral value of k.
(B) f ( x ) is an even function x  −1,1
List-I List-II
(C) f ( x ) is bounded
(D) Number of solution of the equation I ABA–1 P A2

f ( x ) = is zero II BAB–1 Q B
2
[Note: {y} and sgn (y) denotes fractional part of y
and signum of y respectively.] III AB2A–1 R A

IV BA2B–1 S B2
46. let A be 4 × 4 matrix with real entries such that
determinant of every 2 × 2 submatrix is 0, then T BA
(A) adj(A) = O I II III IV
(B) det(A) = 0 (A) Q R S P
(C) A = O (B) Q P T S
(D) AX = O has infinite number of solution (C) Q P S R
(D) Q T P Q
[10]
  − x4  sec 2  1 1
52. Consider, f ( x ) = x − sin x, g ( x ) = cos −1  e 2 
  s () = cos  cos  cosec 2 
2 2

 
−1  2 x  cos 2  cot 2 
and ( )
h x = tan  
1
 1 + x2  Match the functions in List-I with their range in
List-II.
Column
Column-I List-I List-II
-II
f ( x) − g ( x) I p() P [0, 1]
lim is equal
A. x→0 x 2 p. −1
II q() Q [0, 2 2 ]
to
g ( x ) − xh ( x ) III r() R [–2, 2]
lim is equal −2
B. x→0 x 2 q.
3
to
IV s() S [− 5 − 2, − 5 + 2]

lim
f ( 2 x ) − h x3 ( ) is −1 T [–1, 3]
C. x→0 3 r.
x 2 I II III IV
equal to (A) T Q S P
cot −1 ( h ( x ) ) − 2 g ( x ) (B) Q R R P
lim (C) Q S R P
x→   1  1
D. cos−1  x 1 − cos   s. (D) R S Q T
  x  2
is equal to 54. Column
Column-I
-II
I II III IV
1 + tan x − 1 + sin x
(A) P P Q P A. lim = p. 0
(B) Q P P P x→0 x3
(C) Q R P S tan ( x ) + 2sin 2 ( x ) + 5 x 4 1
B. lim = q.
(D) S Q P R x→0 3sin ( x ) − x 2 + x3 2
1
53. Let
e −1 1
2
x
C. = r.
− 2 sin  cos  lim 3
x→  − 2 tan −1 x 2
p() = 1 cos  sin  ,
      1
−1 sin  − cos  D. lim cos   .cos  = s.
x→1  x + 1   x −1 4
sin 2 1 1
q () = 2 cos 2 2 3 I II III IV
(A) S R Q P
cos 2 3 5 (B) P Q S R
cos  sin  cos  (C) Q S R P
r () = − sin  cos 
sin  and (D) R P S Q
− cos  − sin  cos 

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