Class 12th JEE
MRJM/12
Milestone Test-0
Phase-2
DATE: 09/06/2024
M.MARKS: 300
DURATION: 180 Minutes
Topic Covered
Physics
:
Electric Charges and Fields
Chemistry
:
Solutions, Electrochemistry
Mathematics :
Determinants, Matrices
GENERAL INSTRUCTION
1.
2.
3.
4.
5.
6.
7.
8.
Immediately fill in the particulars on this page of the test booklet.
The test is of 3 hours duration.
The test booklet consists of 90 questions. The maximum marks are 300.
There are three sections in this question paper. Sections I, II and III, are of Physics, Chemistry and
Mathematics, respectively. Each section consists of 30 questions, of which the first 20 are mandatory and
are of Multiple Option type and the last 10 are of integer answer type. You need to attempt any 5 integer
type questions (out of 10) in each of the three sections.
There is only one correct response for each question.
Each correct answer will give 4 marks while 1 Mark will be deducted for a wrong response.
No student is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone,
any electronic device, etc. inside the examination room/hall.
On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the
Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.
SECTION-I (PHYSICS)
Single Correct Type Questions (1-20)
1.
A thin conducting ring of radius R is given a
charge +Q. The electric field at the centre O of the
5.
A comb run through one’s dry hair attracts small
bits of paper. This is due to
(1) Comb is good conductor
(2) Paper is good conductor
(3) The atoms in the paper get polarized by the
charged comb
(4) The comb possesses magnetic properties
6.
The electric field due to an electric dipole at a
distance r from its centre in axial position is E . If
the dipole is rotated through an angle of 90° about
its perpendicular axis, the electric field at the same
point will be
(Note: r is very larger than dipole length)
E
(1) E
(2)
4
E
(4) 2E
(3)
2
7.
Three infinitely large non conducting charged
sheets are placed as shown in figure. The electric
field at point P is
ring due to the charge on the part AKB of the ring
is E. The electric field at the centre due to the
charge on the part ACDB of the ring is
2.
3.
(1) E along KO
(2) 3 along
E
OK
(3) 3 along
E
KO
(4) E along OK
Two charges of equal magnitudes and at a distance
r exert a force F on each other. If the charges are
halved and distance between them is doubled, then
the new force acting on each charge is
(1) F /8
(2) F /4
(4) F /16
(3) 4 F
z
A pendulum bob of mass 30.7 × 10−6 kg and
carrying a charge 2 × 10−8 C is at rest in a
N
horizontal uniform electric field of 20000 . The
C
tension in the thread of the pendulum will be
(
approximately g = 9.8 m/s 2
4.
)
(1) 3 × 10−4 N
(2) 4 × 10−4 N
(3) 5 × 10−4 N
(4) 6 × 10−4 N
One of the following is not a property of field lines
(1) Field line between a positive and a negative
charge is a continuous curve without any
break.
(2) Two field lines cannot cross each other
(3) Field lines start at positive charge and end at
negative charge
(4) They form closed loop
8.
(1)
2σ
k̂
ε0
(2) −
2σ ˆ
k
ε0
(3)
4σ
k̂
ε0
(4) −
4σ ˆ
k
ε0
An electron is moving around the nucleus of a
hydrogen atom lying at rest at origin in a circular

orbit of radius r. The coulomb force F

experienced by electron ( r is position vector of
1
electron and K =
).
4πε0
(1) − K
e2
rˆ
3
(2) K
e2 
r
r3
(4) K
r
(3) − K
e2 
r
r3
e2
r3
rˆ
9.
10.

The torque acting on a dipole of dipole moment P

in an electric field E is
 
 
(1) P.E
(2) P × E
 
(3) Zero
(4) E × P
14.
Let there be a spherically symmetric charge
distribution with charge density varying as
5 r 
ρ(r ) =
ρ0  −  upto r = R, and ρ ( r ) = 0
4 R
for r > R, where r is the distance from the origin.
The electric field at a distance r (r < R ) from the
origin is given by
4πρ0 r  5 r 
(1)
 −  (2)
3ε0  3 R 
ρ0 r  5 r 
 − 
4ε0  3 R 
4ρ0 r  5 r 
 − 
3ε0  4 R 
ρ0 r  5 r 
 − 
3ε0  4 R 
(3)
11.
(3)
(4)
ρR
ε0
Zero everywhere
Non-zero and uniform
Non-uniform
Zero only at its centre
15.
Electric point charges 𝐴𝐴 and 𝐵𝐵 repel each other.
Electric point charges 𝐵𝐵 and 𝐶𝐶 also repel each
other. If 𝐴𝐴 and 𝐶𝐶 are held close together, they will
(1) Attract
(2) Repel
(3) Not affect each other
(4) None of these
16.
A thin glass rod is bent into a semicircle of radius
𝑟𝑟. A charge +Q is uniformly distributed along the
upper half and a charge –Q is uniformly distributed
along the lower half, as shown in Fig. The electric
field 𝐸𝐸 at 𝑃𝑃, the centre of the semicircle, is

The direction of electric field intensity E at a
( )
point on the equatorial line of an electric dipole of

dipole moment ( p ) is
(4) Perpendicular to the equatorial line and

parallel to ( p )
12.
(4)
A spherical portion is removed from a solid non
conducting uniformly charged solid sphere as
shown in the figure. The electric field inside the
empty space is
(1)
(2)
(3)
(4)
(1) Along the equatorial line towards the dipole
(2) Along equatorial line away from the dipole
(3) Perpendicular to the equatorial line and

opposite to ( p )
ρr
ε0
Three charges q1 = 1×10–6C, q2 = 2×10–6C and
q3 = –3×10–6 have been placed as shown. Then, the
net electric flux will be maximum for which of the
shown gaussian surface.
S2
S1
(1)
S3
q1
q2
q3
(1) S1
(3) S3
13.
(3)
(2) S2
(4) Same for all three
An insulated solid sphere of radius R has uniform
charge density ρ. The electric field at a distance r
from the centre of the sphere (r < R)
ρr
ρR
(2)
(1)
3ε 0
3ε 0
17.
Q
π ε0 r
2
2
4Q
π ε0 r
2
2
(2)
(4)
2Q
π ε0 r 2
2
Q
4π ε 0 r 2
2
Two point charges q1 (10µC ) and q2 ( −25µC ) are
placed on the x-axis at x = 1 m and x = 5 m ,
respectively. The electric field vector (in N/C) at


1
= 9 × 109 N − m 2 C−2 
origin.  Take,
4πε0


(1) −81 × 103 iˆ
(3) 27 × 103 iˆ
(2) 81 × 103 iˆ
(4) −27 × 103 iˆ
[3]
18.
19.
20.
Two charges, each equal to q, are kept fixed at
x = –a and x = a on the x-axis. A particle of mass
q
𝑚𝑚 and charge q0 = − is placed at the origin. If
2
charge q0 is given a small displacement y(y << a)
along the y-axis, the net force acting on the particle
is proportional to
(2) –y
(1) y2
1
1
(4) –
(3)
2
y
y
Statement 1: If a proton and an electron are
placed in the same uniform electric field. They
experience different acceleration
Statement 2: Electric force on a test charge is
independent of its mass
(1) Statement 1 is True, Statement 2 is True;
Statement 2 is correct explanation for
Statement 1
(2) Statement 1 is True, Statement 2 is True;
Statement 2 is not correct explanation for
Statement 1
(3) Statement 1 is True, Statement 2 is False
(4) Statement 1 is False, Statement 2 is True
between q1 and q3 is F13, the ratio of magnitudes of
forces
F12
is x. Find x.
F13
23.
If the linear charge density of a cylinder is 4µCm–1
of radius 2 cm then electric field intensity at point
3.6 cm from axis is n×106 NC–1. Find n.
24.
A point charge +q is placed at the centre of a cube
of side a. The electric flux emerging from the cube
x q
. Find x.
is
5 ε0
25.
Four charges +Q, −Q, +Q, −Q are placed at the
corners of a square taken in order. At the centre of
N
the square electric field is k . Find k.
C
26.
When the distance between two charged particles
is halved, the force between them becomes x times
the initial force. Find x.
27.
A sample of HCl gas is placed in a uniform electric
field of 3 × 104 NC−1 . The dipole moment of each
HCl molecule is 6 × 10−30 Cm. The maximum
torque that can act on a molecule is x × 10–26 Nm.
Find x.
Determine the electric dipole moment of the
system of three charges, placed on the vertices of
an equilateral triangle of length  , as shown in the
figure :
28.
A square surface of side L is in the plane of the

paper. A uniform electric field E , also in the plane
of the paper, is limited only to the lower half of the
square surface, (see figure). The electric flux
associated with the square surface is xEL2 . Find x.
(1) 2q ˆj
(3)
2 q ˆj
(2) −2q ˆj
Integer Type Questions (21-30)
21.
29.
A point charge q produces an electric field of
magnitude 2NC–1 at a point 0.25 m from it. The
x
× 10−11 C. Find x.
value of charge is
18
30.
A cylinder of length L and radius b has its axis
coincident with the x-axis (positive towards right).

The electric field in this region is E = 200iˆ . The
Three charges 1µC, 1µC and 2µC are kept at
vertices A, B and C of an equilateral triangle ABC
of side 10 cm respectively. The resultant force on
the charge at C is x 3 N. Find 10 x.
22.
E
(4) − 3 q ˆj
Three equal charges q1, q2, q3 are placed on the
three adjacent corners of a square taken in that
order. If the force between q1 and q2 is F12 and that
flux through the left end of cylinder is yπb2. Find
(y + 200). (Assume SI units)
[4]
SECTION-II (CHEMISTRY)
Single Correct Type Questions (31-50)
31.
If Raoult’s law is obeyed, the vapour pressure of
the solvent in a solution is directly proportional to
(1) Mole fraction of the solvent
(2) Mole fraction of the solute
(3) Mole fraction of the solvent and solute
(4) The volume of the solution
32.
What is the mole ratio of benzene (PB0 = 150 torr)
and toluene (PT0 = 50 torr) in vapour phase if the
given solution has a vapour pressure of 120 torr?
(1) 7 : 1
(2) 7 : 3
(3) 8 : 1
(4) 7 : 8
33.
At 323 K, the vapour pressure in millimeters of
mercury of a methanol-ethanol solution is
represented by the equation p = 120 XA + 140,
where XA is the mole fraction of methanol. Then
p
the value of lim A is (where PA is vapour
x A →1 X A
pressure of A)
(1) 250 mm
(3) 260 mm
34.
37.
The standard electrode potential for the reaction
Ag+ (aq) + e– → Ag(s)
Sn2+(aq) + 2e– → Sn(s)
at 25°C are 0.80 volt and – 0.14 volt, respectively.
The emf of the cell.
Sn | Sn2+(1M) | | Ag+(1M) | Ag is:
(1) 0.66 volt
(2) 0.80 volt
(3) 1.08 volt
(4) 0.94 volt
38.
The reduction electrode potential E(in V), of 0.1
M solution of M+ ions (E°RP = – 2.36 V) is:
(1) –2.41
(2) +2.41
(3) –4.82
(4) +4.82
39.
When two half-cells of electrode potential of E1
and E2 are combined to form a half cell of
electrode potential E3, then (when n1, n2 and n3 are
no. of electrons exchanged in first, second and
combined half-cells) (Consider E1, E2 and E3 are
reduction potentials and third half cell reaction is
attained by adding 1st and 2nd half cell reaction
directly).
(1) E3 = E2 – E1
(2) 140 mm
(4) 20 mm
An aqueous solution containing 28% by mass of a
liquid A (mol. mass = 140) has a vapour pressure
of 160 mm at 37°C. Find the vapour pressure of
the pure liquid A.
(The vapour pressure of water at 37°C is 150 mm).
(1) 360 mm
(2) 150 mm
(3) 160 mm
(4) 520 mm
(2) E3 =
(3) E3 =
36.
Azeotropic mixture are:
(1) Mixture of two solids
(2) Those which boil at different temperature
(3) Those which can be fractionally distilled
(4) Constant boiling mixtures
The oxidation potential of Zn, Cu, Ag, H2 and Ni
are 0.76, –0.34, –0.80, 0, 0.55 volt respectively.
Which of the following reaction will provide
maximum voltage?
(1) Zn + Cu2+ → Cu + Zn2+
(2) Zn + 2Ag+ → 2Ag + Zn2+
(3) H2 + Cu2+ → 2H+ + Cu
(4) H2 + Ni2+ → 2H+ + Ni
E1n1 − E2 n2
n32
(4) E3 = E1 + E2
40.
35.
E1n1 + E2 n2
n3
Which graph correctly correlates Ecell as a function
of concentration for the cell
Zn(s) + 2Ag+(aq) → Zn2+(aq) + 2Ag(s), Eºcell = 1.56V
Y-axis: Ecell, X-axis: log10
(1)
(2)
(3)
(4)
[ Zn 2+ ]
[ Ag + ]2
[5]
41.
42.
Among the following, that does not form an ideal
solution is(1) C6H6 and C6H5CH3
(2) C2H5Cl and C6H5OH
(3) C6H5Cl and C6H5Br
(4) C2H5Br and C2H5I
(1) –1.02 Volt
(3) + 1.02 Volt
47.
W g of copper deposited in a copper voltameter
when an electric current of 2 ampere is passed for
2 hours. If one ampere of electric current is passed
for 4 hours in the same voltameter, copper
deposited will be (in grams):
(1) W
(2) W/2
(3) W/4
(4) 2W
48.
The ratio of weights of hydrogen and magnesium
deposited by the same amount of electricity from
aqueous H2SO4 and fused MgSO4 are:
(1) 1 : 2
(2) 1 : 12
(3) 1 : 16
(4) None of these
49.
An electrolysis of a oxytungsten complex ion
using 1.10 A for 40 min produces 0.838 g of
tungsten. What is the charge of tungsten in the
material? (Atomic weight: W = 184)
(1) 6
(2) 2
(3) 4
(4) 1
50.
How many coulombs of electricity are consumed
when 100 mA current is passed through a solution
of AgNO3 for 30 minutes during an electrolysis
experiment:
(1) 108
(2) 18000
(3) 180
(4) 3000
List-I and List-II contains four entries each.
Entries of List-I are to be matched with entries of
List-II.
List- I
List- II
I
AlCl3, if α = 0.8
P
II
BaCl2, if α = 0.9
Q
i = 2.8
III
Na3PO4, if α = 0.9
R
i = 3.8
IV
K4[Fe(CN)6], if α = 0.7
S
i = 3.7
(1)
(2)
(3)
(4)
i = 3.4
I-P ; II-Q ; III-S ; IV-R
I-Q ; II-P ; III-S ; IV-R
I-Q ; II-R ; III-P ; IV-S
I-R ; II-S ; III-Q ; IV-P
43.
The substance A when dissolved in solvent B
shows the molecular mass corresponding to A3.
The vant Hoff’s factor will be(1) 1
(2) 2
(3) 3
(4) 1/3
44.
If P0 and P are the vapour pressures of a solvent
and its solution with non-volatile solute
respectively and N1 and N2 are the mole fractions
of the solvent and solute respectively, then correct
relation is:
(2) P = P0N1
(1) P = P0N2
(4) P = P0(N1/N2)
(3) P0 = PN1
45.
If relative decrease in vapour pressure is 0.4 for a
solution containing 1 mol NaCl in 3 mol H2O,
NaCl is .... % ionized.
(1) 60%
(2) 50%
(3) 100%
(4) 40%
46.
The standard electrode potentials of the two-half
cell are given below:
Ni2+ + 2e– → Ni ; E° = – 0.25 V
Zn2+ + 2e– → Zn ; E° = – 0.77 V
The emf of cell formed by combining the two half
cells would be: (consider cell reaction to be
spontaneous)
(2) +0.52 Volt
(4) –0.52 Volt
Integer Type Question (51-60)
51.
The ionization constant of a weak electrolyte is
25×10–6 while the equivalent conductance of its
0.01M solution is 19.6 S cm2 eq–1. The equivalent
conductance of the electrolyte at infinite dilution
(in S cm2 eq–1) will be
52.
Benzene and toluene form nearly ideal solutions.
At 20ºC, the vapour pressure of benzene is 75 torr
and that of toluene is 22 torr. The partial vapour
pressure of benzene at 20ºC for a solution
containing 78 g of benzene and 46 g of toluene in
torr is:
53.
Density of a 2.05 M solution of acetic acid in
water is 1.02 g/mL. The molality of the solution is
‘x’, then 10 x in nearest integer is:
54.
Resistance of 0.1 M KCl solution in a
conductance cell is 300 ohm and conductivity is
0.013 Scm–1. The value of cell constant is: (in cm–1)
(nearest integer)
[ 6]
55.
At infinite dilution, the eq. conductances of
CH3COONa, HCl and CH3COOH are 91, 426 and
391 mho cm2 eq–1 respectively at 25°C, The eq.
conductance of NaCl at infinite dilution will be:
56.
The weight of silver (in grams) (eq. wt = 108)
displaced by that quantity of current which
displaced 5600 ml. of hydrogen at STP is:
57.
Electro chemical equivalent of a substance is
0.0006735; its eq. wt. is: (in grams/eq) (nearest
integer) (1 F = 96500C)
58.
The % of phenol dimerized in benzene if 20 g of
phenol in 1 kg benzene exhibits a freezing point
depression of 0.69 K.
K – kg
(Kf benzene = 5.12
), (MW phenol = 94)
mol
(nearest integer)
59.
A solution of x moles of sucrose in 100 grams of
water freezes at −0.2ºC. As ice separates the
freezing point goes down to –0.25ºC. How many
grams of ice would have separated?
60.
A solution of glucose (C6H12O6) is isotonic with
4g of urea (NH2–CO–NH2) per liter of solution.
The mass of glucose in 1 litre of solution is (in grams)
SECTION-III (MATHEMATICS)
Single Correct Type Questions (61-80)
61.
1 2
3 2


 5 4 
1 2
(2)  1 1 
 0 3 
1 0 
(3)  3 −2 
 5 4 
1 0 
3 2 


5 4 
65.
Let A and B be two symmetric matrices of order 3.
Statement-1 : A(BA) and (AB)A are symmetric
matrices.
Statement-2 : AB is symmetric matrix if matrix
multiplication of A with B is commutative.
(1) Only statement-1 is true
(2) Both statements are true
(3) Only statement-2 is true
(4) Both statements are false
(4)
 x2 + x x 
−1
 0
0 −2 
= 

 + 

 then x
2 
− x + 1 x 
5 1 
 3
is equal to (1) – 1
(3) 1
63.
If A is a square matrix of order 3, then the true
statement is (where I is unit matrix).
(1) det (–A) = –det (A)
(2) det A = 0
(3) det (A + I) = 1 + det A
(4) det (2A) = 2 det A
A 3 × 2 matrix whose elements are given by
aij = 2i – j is
(1)
62.
64.
(2) 0
(4) No value of x
66.
 cos θ sin θ 
B= 
 , then B =
 − sin θ cos θ 
(1) I cos θ + J sin θ
(2) I cos θ − J sin θ
(3) I sin θ + J cos θ
(4) − I cos θ + J sin θ
Which one of the following is WRONG?
(1) The elements on the main diagonal of a
symmetric matrix are all zero
(2) The elements on the main diagonal of a
skew - symmetric matrix are all zero
(3) For any square matrix A,
1
(A + AT) is
2
symmetric matrix
(4) For any square matrix A,
-symmetric matrix
1
(A–AT) is skew
2
 0 1
1 0 
If I = 
,J= 
 and

 −1 0 
0 1 
67.
If A and B are square matrices of order 2, then
(A + B)2 =
(1) A2 + 2 AB + B2
(2) A2 + AB + BA + B2
(3) A2 + 2 BA + B2
(4) A2 + B2
[ 7]
68.
69.
70.
71.
 λ 1
 8 5
If A = 
and A2 = 

 then λ is
 −1 2 
 −5 3
equal to
(1) ±3
(2) 2
(3) 3
(4) –3
Let A = [aij]n × n where aij = i2 – j2 . Then A is :
(1) skew-symmetric matrix.
(2) symmetric matrix
(3) null matrix
(4) unit matrix
Let A be a 2 × 2 matrix.
Statement-1 : adj(adj (A)) = A.
Statement-2 : |adj A| = |A|
(1) Statement-1 is true, Statement-2 is true.
(2) Statement-1 is true, Statement-2 is false.
(3) Statement-1 is false, Statement-2 is true.
(4) Statement-1 is false, Statement-2 is false.
73.
74.
76.
77.
1 + ab + a 2b 2 1 + ac + a 2 c 2
1 + ab + a 2b 2
1 + b2 + b4
1 + bc + b 2 c 2 =
1 + ac + a 2 c 2
1 + bc + b 2 c 2
1 + c2 + c4
(a – b)2 (b – c)2 (c – a)2
2(a – b) (b – c) (c – a)
4(a – b) (b – c) (c – a)
(a + b + c)3
2cot x −1
0
1
cotx
−1
Let f(x) =
0
1
2cot x
Column-I
If A is a 3 × 3 matrix such that |5.adjA| = 5, then
|A| is equal to :
1
1
(2) ±
(1) ±
5
25
(3) ± 1
(4) ± 5
If A, B are two n × n non-singular matrices, then
(1) AB is non-singular matrix
(2) AB is singular matrix
(3) (AB)–1 = A–1 B–1
(4) (AB)–1 does not exist
then match
78.
Column-II
A
π
f'  
2
P
– 32
B
π
f 
4
Q
–4
C
π
f'  
4
R
8
D
π
f 
2
S
0
(1)
(2)
(3)
(4)
If A–1 =  0
(4) A is skew symmetric matrix
1 + a2 + a4
column-I with column-II
a + b – x is a factor of ∆
x2 + (a + b)x + a2 + b2 – ab is a factor of ∆
∆ = 0 has three real roots if a = b
all of these
 1 −1 0 
−2 1  , then

 0 0 −1 
(1) | A | = 2
(2) A is singular matrix
0 
 1 / 2 −1 / 2

1 / 2 
(3) Adj. A =  0
−1
 0
0
−1 / 2 
 −4 −1
If A = 
 , then the determinant of the
3 1
matrix (A2016 – 2A2015 – A2014) is
(1) 2014
(2) 2016
(3) –175
(4) –25
(1)
(2)
(3)
(4)
−x a
b
Let a, b > 0 and ∆ = b − x a , then
a
b −x
(1)
(2)
(3)
(4)
72.
75.
A
Q
Q
P
S
B
R
P
S
R
C
P
R
Q
Q
D
S
S
R
P
 2 −1
 1 4
For matrices A = 
and B = 


 −1 2 
 −1 1 
which relation is true
(1) (A + B)2 = A2 + 2AB + B2
(2) (A–B)2 = A2 – 2AB + B2
(3) AB = BA
(4) AB ≠ BA
[ 8]
79.
80.
 1 0
 , then P50 is:
If P =  1

1
2

85.
 1 0
(1) 

 25 1 
1 25
(2) 

0 1 
 1 0
(3) 

50 1 
1 50 
(4) 

0 1 
86.
Let I be an identity matrix of order 2 × 2 and
 2 −1
P=
 . Then the value of n ∈ N for which
 5 −3
P n = 5I – 8P is equal to
(1) 8
(2) 12
(3) 4
(4) 6
87.
82.
88.
The sum of the minors of all elements in the
1 −3 2
is –k
second row of determinant 4 −1 2
3 5 2
89.
If
x2 + x
x +1
x−2
2 x + 3x − 1
3x
3 x − 3 = ax – 12, then
and
1 2
(A + cA + dI ) then the value of (d – c)
6
x2 + 2 x + 3
2x −1 2x −1
1 1
b b 
and B =  1 2  . If
Let A = 

0 1
b3 b4 
10A10 + adj(A10) =B, then b1+ b2 + b3 + b4 is equal to
If α, β ≠ 0 and f (n) = α n + βn and
= K (1 − α) 2 (1 − β) 2 (α − β) 2 , then K is equal to
90.
‘a’ is equal to :
84.
1 0 0
0 1 0


 0 0 1 
3
1 + f (1) 1 + f (2)
1 + f (1) 1 + f (2) 1 + f (3)
1 + f (2) 1 + f (3) 1 + f (4)
then k is
83.
1 0 0
If A =  0 1 1  , I =
 0 −2 4 
is
The number of different possible orders of
matrices having 18 identical elements is
2
5 0 0 
If B is a non-singular matrix and A = 0 2 0 
0 0 3
then det (B–1 AB) is equal to
A–1 =
Integer Type Question (81-90)
81.
If for a matrix A, |A| = 6 and
 1 −2 4 
adj A =  4 1 1  , then k is equal to :
 −1 k 0 
If A and B are square matrices of order 3 such
that |A| = – 1, |B| = 3, then |3A2B| is equal to
Let P = [aij] be a 3 × 3 matrix and let Q = [bij],
where bij = 2i+jaij for 1 ≤ i, j ≤ 3. If the
determinant of P is 2, then the determinant of the
matrix Q is 2λ then λ is
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[ 9]
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