Answer: [A, D] or [D]
JEE (Advanced) 2022
Paper 2
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>) *77 ('"%/ &*$%$Q.1
Let
./%(
and
be real numbers such that
!
"
,
" ! $. If %&'( ) * + -
"#"
and
0
-
* + , then the greatest integer less than or equal to
%&'
$
./%
)
./%
%&'
)
./%
%&'
)
$
%&'
./%
0
is 1111111111111.
Q.2
If ( * is the solution of the differential equation
(
and the slope of the curve
Q.3
0
*
+ #$$$2/3$$$ 4 #5$$$$$$$$ ( * + 5
+ ( * is never zero, then the value of
#$
$ $ is 1111111111111.
The greatest integer less than or equal to
0
8
6/7 0 (
-
) *
(
$ )$
,
*$
,
is 1111111111111.
Q.4
The product of all positive real values of
(,9(
satisfying the equation
:
*
9;$
:
*
+
,9
is 1111111111 .
1/8
JEE (Advanced) 2022
Q.5
Paper 2
If
Let
) ((
%&'0
0*
* %&'
$5
is 11111111111.
then the value of
Q.6
-*
(
+ 6&<
be a real number. Consider the matrix
#
+ $
If
Q.7
>
(
*
$=$
is a singular matrix, then the value of
9
is 11111111111.
Consider the hyperbola
0
$$
0
+
##
with foci at and , , where lies on the positive -axis. Let be a point on the hyperbola, in the
first quadrant. Let
and
, + 5 ?&@A$ " 0 . The straight line passing through the point
having the same slope as that of the tangent at to the hyperbola, intersects the straight line , at
be the distance of from the straight line , , and + , . Then the greatest integer
, . Let
less than or equal to
Q.8
8
$%&' 0 is 1111111111111.
Consider the functions 5
defined by
E E
( *+
0
)
5
E E
$5
$$$$$$$$$$$$$$$$$$B'C$$$$$$$$$$$$$ ( * +
$$
D #$5$$$$$$$$$$$$$$$$$$$$$$$$$$$$E E 4 $=
If
is the area of the region
( 5 *
then the value of
F
$E E
$$5$$$#
<&' ( *5 ( *G$ $5
is 1111111111111.
2/8
JEE (Advanced) 2022
Q.10
Paper 2
Let
%&'0
+
$$=
,
Let$$
H#5 I
be the function defined by
( *+
(,
)
*
$$=
Then, which of the following statements is/are TRUE ?
(A) The minimum value of ( * is
(B) The maximum value of ( * is
(C) The function
)
( * attains its maximum at more than one point
(D) The function ( * attains its minimum at more than one point
Q.11
Let denote the complex conjugate of a complex number
which both real and imaginary parts of
($ $*0 )
0
If
is a non-zero complex number for
$
are integers, then which of the following is/are possible value(s) of E E ?
(A)
!- - 0
0
(B)
>
(C)
8
(D)
>
9
!
-!
,9
4/8
JEE (Advanced) 2022
Q.12
Q.13
Paper 2
Let be a circle of radius
4 #. Let , 5 0 5 J 5
be circles of equal radius 4 #. Suppose
each of the circles , 5 0 5 J 5
touches the circle externally. Also, for + 5 5 J 5
, the
circle
touches
touches , externally. Then, which of the following
, externally, and
statements is/are TRUE ?
(A) If
+ , then (
(B) If
+ , then $ "
(C) If
+ , then (
(D) If
+
, then
* "
*$ "
$
)
$ 4
Let , $B'C$ be the unit vectors along the three positive coordinate axes. Let
$$ + )
$5$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$ + ) 0 ) - $5$$$$$$$$$$$$$$$ 0 5 $5
$$$ + , ) 0 ) - $5$$$$$$$$$ , 5 0 5 be three vectors such that
0 -
$ + # and
4 #,
$#
$$ 0
-
#
$$$ , $
$$$
0
,
0
$$$#
-
$$$
+ $$$
,
0
$=
-
Then, which of the following is/are TRUE ?
(A)
$+ #
(B)
+#
(C)
$>$
#
(D) E E
5/8
JEE (Advanced) 2022
Q.14
For
Paper 2
, let the function ( * be the solution of the differential equation
$
)
+ ./%
5$$$$$$$$ (#* + #$=
Then, which of the following statements is/are TRUE ?
(A) $ ( * is an increasing function
(B) $ ( * is a decreasing function
(C) There exists a real number
infinitely many points
such that the line
+
intersects the curve
+ ( * at
(D) $ ( * is a periodic function
6/8
JEE (Advanced) 2022
Paper 2
!"#$%&' H )*+,-./. .+0123 (46
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*)$.%/0(/ %*&" +,%$'#()1 &"(($% '"% (3'#() &(//%$3()4#)2 '( '"% &(//%&' *)$.%/:)$.%/ '( %*&" +,%$'#() .#77 ;% %6*7,*'%4 *&&(/4#)2 '( '"% <(77(.#)2 5*/8#)2 $&"%5%=
= ) >< &';G '"% &(//%&' (3'#() #$ &"($%)?
= # >< )()% (< '"% (3'#()$ #$ &"($%) A#-%- '"% +,%$'#() #$ ,)*)$.%/%4B?
=
>) *77 ('"%/ &*$%$Q.15
Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are
distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each
box at least one red ball and one blue ball are chosen ?
(A) 21816
Q.16
(B) 85536
$$$0
(D) 156816
-
$$$0
If $
+ $$
(A)
$
$$$ #
#
$$$ #
#
(B)
$
#
#
#
#
(C)
$
$$$ #
#
$$$ #
#
(D)
$
$$$ #
#
$$$ #
$
# #
0
(C) 12096
,$$$
0
$, then which of the following matrices is equal to
0 00
$?
$
$
$
7/8
JEE (Advanced) 2022
Q.17
Paper 2
Suppose that
Box-I contains 8 red, 3 blue and 5 green balls,
Box-II contains 24 red, 9 blue and 15 green balls,
Box-III contains 1 blue, 12 green and 3 yellow balls,
Box-IV contains 10 green, 16 orange and 6 white balls.
A ball is chosen randomly from Box-I; call this ball . If is red then a ball is chosen randomly
from Box-II, if is blue then a ball is chosen randomly from Box-III, and if is green then a ball is
chosen randomly from Box-IV. The conditional probability of the event one of the chosen balls is
white given that the event at least one of the chosen balls is green has happened, is equal to
(A)
(C)
Q.18
,
0 9
0
(B)
,9
(D)
,
;
For positive integer , define
( *+
)
0
)
)
0
)
0
)
)
0
0
)
0
)
0
)$
$)
0
$$$=
Then, the value of 6&< ( * is equal to
!
-
(A)
) 6/7
(C)
!
6/7
-
>
-
(B)
6/7
!
(D)
) 6/7
>
-
!
8/8
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3.23.
JEE (Advanced) 2022
Paper 2
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$&/%%) 6#/',*7 ),5%/#& 8%93*4 #) '"% 37*&% 4%$#2)*'%4 '( %)'%/ '"% *)$.%/:)$.%/ '( %*&" +,%$'#() .#77 ;% %6*7,*'%4 *&&(/4#)2 '( '"% <(77(.#)2 5*/8#)2 $&"%5%=
=
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=
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Q.1
Concentration of H2SO4 and Na2SO4 in a solution is 1 M and 1.8 × 10 2 M, respectively. Molar
solubility of PbSO4 in the same solution is X × 10 Y M expressed in scientific notation . The value
of Y is
[Given: Solubility product of PbSO4
= 1. × 10 2]
Q.2
= 1.6 × 10 8. For H2SO4
is very large and
An aqueous solution is prepared by dissolving 0.1 mol of an ionic salt in 1.8 kg of water at 35 ºC.
The salt remains 90% dissociated in the solution. The vapour pressure of the solution is 59.724 mm
of Hg. Vapor pressure of water at 35 ºC is 60.000 mm of Hg. The number of ions present per
formula unit of the ionic salt is _______.
1/8
JEE (Advanced) 2022
Q.3
Paper 2
Consider the strong electrolytes ZmXn , UmYp and VmXn . Limiting molar conductivity (
2
) of
-1
UmYp and VmXn are 250 and 440 S cm mol , respectively. The value of (m + n + p) is _______.
Given:
Ion
2
n+
-1
Z
50.0
p+
U
25.0
n+
V
100.0
m-
X
80.0
(S cm mol )
is the limiting molar conductivity of ions
The plot of molar conductivity ( ) of ZmXn
Q.4
c1/2 is given below.
The reaction of Xe and O2 F2 gives a Xe compound . The number of moles of HF produced by the
complete hydrolysis of 1 mol of
Q.5
m-
Y
100.0
2 or 4 or 6
is _______.
Thermal decomposition of AgNO3 produces two paramagnetic gases. The total number of electrons
present in the antibonding molecular orbitals of the gas that has the higher number of unpaired
electrons is _______.
2/8
JEE (Advanced) 2022
Paper 2
Q.6
The number of isomeric tetraenes (
containing -hybridized carbon atoms) that can be
formed from the following reaction sequence is ________.
Q.7
The number of -
(methylene) groups in the product formed from the following reaction
sequence is ________.
Q.8
The total number of chiral molecules formed from one molecule of
(O3, Zn/H2O) is ________.
on complete ozonolysis
3/8
JEE (Advanced) 2022
Q.10
Paper 2
The correct option(s) about entropy (S) is(are)
[R = gas constant, F = Faraday constant, T = Temperature]
+
(A) For the reaction, M( ) + 2H (
the reaction is R
)
2+
H2( ) + M ( ), if
=
, then the entropy change of
assume that entropy and internal energy changes are temperature
independent .
+
(B) The cell reaction, Pt( ) | H2( , 1bar) | H (
+
, 0.01M) || H (
, 0.1M) | H2( , 1bar) | Pt( ), is an
entropy driven process
(C) For racemization of an optically active compound, S > 0
2+
(D) S > 0, for [Ni(H2O)6] + 3 en
Q.11
2+
[Ni(en)3] + 6H2O (where en = ethylenediamine)
The compound(s) which react(s) with NH3 to give boron nitride (BN) is(are)
(A) B
(B) B2H6
(C) B2O3
(D) HBF4
Answer: [B, C] or [A, B, C]
Q.12
The correct option s related to the extraction of iron from its ore in the blast furnace operating in
the temperature range 900 1500 K is are
(A) Limestone is used to remove silicate impurity.
(B) Pig iron obtained from blast furnace contains about 4% carbon.
(C) Coke (C) converts CO2 to CO.
(D) Exhaust gases consist of NO2 and CO.
5/8
JEE (Advanced) 2022
Q.13
Paper 2
Considering the following reaction sequence, the correct statement(s) is(are)
(A) Compounds and are carboxylic acids.
(B) Compound decolorizes bromine water.
(C) Compounds and react with hydroxylamine to give the corresponding oximes.
(D) Compound reacts with dialkylcadmium to give the corresponding tertiary alcohol.
Answer: [A, B, C] or [A, C]
Q.14
Among the following, the correct statement(s) about polymers is(are)
(A) The polymerization of chloroprene gives natural rubber.
(B) Teflon is prepared from tetrafluoroethene by heating it with persulphate catalyst at high
pressures.
(C) PVC are thermoplastic polymers.
(D) Ethene at 350-570 K temperature and 1000-2000 atm pressure in the presence of a peroxide
initiator yields high density polythene.
6/8
JEE (Advanced) 2022
Paper 2
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*)$.%/0(/ %*&" +,%$'#()1 &"(($% '"% (3'#() &(//%$3()4#)2 '( '"% &(//%&' *)$.%/:)$.%/ '( %*&" +,%$'#() .#77 ;% %6*7,*'%4 *&&(/4#)2 '( '"% <(77(.#)2 5*/8#)2 $&"%5%=
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=
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Q.15
Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The
packing efficiency (in %) of the resultant solid is closest to
(A) 25
Q.16
(C) 55
(D) 75
The reaction of HClO3 with HCl gives a paramagnetic gas, which upon reaction with O3 produces
(A) Cl2O
Q.17
(B) 35
(B) ClO2
(C) Cl2O6
(D) Cl2O7
The reaction of Pb(NO3)2 and NaCl in water produces a precipitate that dissolves upon the addition
of HCl of appropriate concentration. The dissolution of the precipitate is due to the formation of
(A) PbCl2
(B) PbCl4
(C) [PbCl4]
2-
(D) [PbCl6]
2-
7/8
JEE (Advanced) 2022
Q.18
Paper 2
Treatment of D-glucose with aqueous NaOH results in a mixture of monosaccharides, which are
(A)
(B)
(C)
(D)
8/8