BEST JEE PYQ EUSTIONS ULL EER FIND

1. Q1. A body is moving with constant speed, in a circle of radius . The body completes one revolution in . At
the end of second, the displacement of body (in ) from its starting point is:
(1) (2)
(3) (4)
Q2. Match List I with List II
List I List II
A Angular momentum I
B Torque II
C Stress III
D Pressure gradient IV
Choose the correct answer from the options given below :
(1) A-I, B-IV, C-III, D-II (2) A-III, B-I, C-IV, D-II
(3) A-II, B-III, C-IV, D-I (4) A-IV, B-II, C-I, D-III
Q3. A stone of mass is tied to end of a massless string of length . If the breaking tension of the string is
, then maximum linear velocity, the stone can have without breaking the string, while rotating in
horizontal plane, is:
(1) (2)
(3) (4)
Q4. Two bodies are projected from ground with same speeds at two different angles with respect to
horizontal. The bodies were found to have same range. If one of the body was projected at an angle of , with
horizontal then sum of the maximum heights, attained by the two projectiles, is _____ . (Given )
Q5. A body of mass is moving with an initial speed of . The body stops after due to friction
between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity
)
(1) (2)
(3) (4)
Q6. A ball is dropped from a height of . If the coefficient of restitution for the collision between ball and floor
is , after hitting the floor, the ball rebounds to a height of ______ .
Q7. Two discs of same mass and different radii are made of different materials such that their thicknesses are
and respectively. The densities of materials are in the ratio . The moment of inertia of these discs
respectively about their diameters will be in the ratio of . The value of is ______.
Q8. A body weight , is projected vertically upwards from earth's surface to reach a height above the earth which is
equal to nine times the radius of earth. The weight of the body at that height will be:
(1) (2)
(3) (4)
Q9. Under the same load, wire A having length and cross section stretches uniformly by the
same amount as another wire of length and a cross section of stretches. The ratio of the
JEE Main 2023 (31 Jan Shift 2)
Question Paper
JEE Main Previous Year Paper
MathonGo
10 m 4 s
3rd m
30 15 π
5 π 10√2
[ML
2
T
−2
]
[ML
−2
T
−2
]
[ML
2
T
−1
]
[ML
−1
T
−2
]
1 kg 1 m
400 N
20 m s
−1
40 m s
−1
400 m s
−1
10 m s
−1
40 m s
−1
60°
m g = 10 m s
−2
10 kg 20 m s
−1
5 s
g = 10 m s
−2
0. 2 0. 3
0. 5 0. 4
20 m
0. 5 m
1 cm
0. 5 cm 3 : 5
x
6
x
W
W
91
W
100
W
9
W
3
5. 0 m 2. 5 × 10
−5
m
2
B 6. 0 m 3. 0 × 10
−5
m
2
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2. Young's modulus of wire to that of wire will be:
(1) (2)
(3) (4)
Q10.A water heater of power is used to heat water. The specific heat capacity of water is
. The efficiency of heater is . Time required to heat of water from to is _____ .
(Assume that the specific heat capacity of water remains constant over the temperature range of the water).
Q11.Heat energy of is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas
molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will
be:
(1) (2)
(3) (4)
Q12.A hypothetical gas expands adiabatically such that its volume changes from litres to litres. If the ratio of
final pressure of the gas to initial pressure of the gas is . Then the ratio of will be.
(1) (2)
(3) (4)
Q13.For a solid rod, the Young's modulus of elasticity is and density is . The
velocity of longitudinal wave in the rod will be
(1) (2)
(3) (4)
Q14.The displacement equations of two interfering waves are given by ,
respectively. The amplitude of the resultant wave is _____ .
Q15.Considering a group of positive charges, which of the following statements is correct?
(1) Net potential of the system cannot be zero at a
point but net electric field can be zero at that
point
(2) Net potential of the system at a point can be zero
but net electric field can't be zero at that point
(3) Both the net potential and the net field can be
zero at a point
(4) Both the net potential and the net electric field
cannot be zero at a point
Q16.Two parallel plate capacitors and each having capacitance of are individually charged by a
D.C. source. Capacitor is kept connected to the source and a dielectric slab is inserted between it plates.
Capacitor is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the
capacitor is also disconnected from the source and the two capacitors are finally connected in parallel
combination. The common potential of the combination will be _____ .
(Assuming Dielectric constant )
Q17.The number of turns of the coil of a moving coil galvanometer is increased in order to increase current
sensitivity by . The percentage change in voltage sensitivity of the galvanometer will be :
(1) (2)
(3) (4)
JEE Main 2023 (31 Jan Shift 2)
Question Paper
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MathonGo
A B
1 : 4 1 : 1
1 : 10 1 : 2
2000 W 4200 J kg
−1
K
−1
70% 2 kg 10°C 60°C s
735 J
525 J 441 J
572 J 735 J
08 27
16
81
Cp
Cv
4
3
3
1
1
2
3
2
3. 2 × 10
11
N m
−2
8 × 10
3
kg m
−3
145. 75 × 10
3
m s
−1
3. 65 × 10
3
m s
−1
18. 96 × 10
3
m s
−1
6. 32 × 10
3
m s
−1
y1 = 10 sin (ωt +
π
3
) cm
y2 = 5[sin (ωt) + √3 cos ωt] cm cm
C1
C2
10 μF 100 V
C1
C2
C1
V
= 10
50%
100% 50%
75% 0%
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3. Q18.The amount of thermal energy is developed by a resistor in when a current of is passed through it.
If the current is increased to , the thermal energy developed by the resistor in will be
(1) (2)
(3) (4)
Q19.For the given circuit, in the steady state, _____ .
Q20.A long conducting wire having a current flowing through it, is bent into a circular coil of turns. Then it is
bent into a circular coil of turns. The magnetic field is calculated at the centre of coils in both the cases. The
ratio of the magnetic field in first case to that of second case is:
(1) (2)
(3) (4)
Q21.An alternating voltage source is connected across a pure inductor of . Inductive
reactance in the circuit is:
(1) (2)
(3) (4)
Q22.A series LCR circuit consists of . , and . The input voltage is
. The amplitude of current, in the circuit, is _____ .
Q23.Match List I and List II
List I List II
A Microwaves I Physiotherapy
B UV rays II Treatment of cancer
JEE Main 2023 (31 Jan Shift 2)
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MathonGo
H 10 s 4 A
16 A 10 s
H 16H
H
4
4H
|VB − VD| = V
I N
n
N : n n
2
: N
2
N
2
: n
2
n : N
V = 260 sin(628t) 5 mH
3. 14Ω 6. 28Ω
0. 5Ω 0. 318Ω
R = 80 Ω XL = 100 Ω XC = 40 Ω
2500 cos(100πt) V A
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4. C Infra-red rays III Lasik eye surgery
D X-rays IV Aircraft navigation
Choose the correct answer from the option given below:
(1) A-II, B-IV, C-III, D-I (2) A-IV, B-I, C-II, D-III
(3) A-IV, B-III, C-I, D-II (4) A-III, B-II, C-I, D-IV
Q24.A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index is poured
inside the bucket, then microscope have to be raised by to focus the object again. The height of the
liquid in the bucket is :
(1) (2)
(3) (4)
Q25.Two light waves of wavelengths and are used in Young's double slit experiment to obtain
interference fringes on a screen placed away from plane of slits. If the two slits are separated by
, then shortest distance from the central bright maximum to the point where the bright fringes of the two
wavelength coincide will be ______ .
Q26.If the two metals and are exposed to radiation of wavelength . The work functions of metals
and are . Then choose the correct option
(1) Metal will not emit photo-electrons (2) Both metals and will emit photo-electrons
(3) Both metals and will not emit
photoelectrons
(4) Metal will not emit photo-electrons
Q27.The radius of electron's second stationary orbit in Bohr's atom is . The radius of orbit will be
(1) (2)
(3) (4)
Q28.If the binding energy of ground state electron in a hydrogen atom is , then, the energy required to
remove the electron from the second excited state of will be: . The value of is _____.
Q29.Given below are two statements:
Statement I : In a typical transistor, all three regions emitter, base and collector have same doping level.
Statement II : in a transistor, collector is the thickest and base is the thinnest segment.
In the light of the above statements, choose the most appropriate answer from the options given below.
(1) Both Statement I and Statement II are correct (2) Both Statement I and Statement II are incorrect
(3) Statement I is incorrect but Statement II is
correct
(4) Statement I is correct but Statement II is
incorrect
Q30.Given below are two statements
Statement I : For transmitting a signal, size of antenna should be comparable to wavelength of signal (at
least in dimension).
Statement II : In amplitude modulation, amplitude of carrier wave remains constant (unchanged).
In the light of the above statements, choose the most appropriate answer from the options given below
JEE Main 2023 (31 Jan Shift 2)
Question Paper
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MathonGo
5
3
30 cm
75 cm 50 cm
18 cm 12 cm
800 600 nm
7 m 0. 35 mm
mm
A B 350 nm A
B 4. 8 eV and 2. 2 eV
B A B
A B A
R 3
rd
R
3
2. 25 R
3R 9R
13. 6 eV
Li
2+
x × 10
−1
eV x
(l)
l =
λ
4
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5. (1) Both Statement I and Statement II are correct (2) Both Statement I and Statement II are incorrect
(3) Statement I is incorrect but Statement II is
correct
(4) Statement I is correct but Statement II is
incorrect
Q31.When a hydrocarbon undergoes complete combustion it requires equivalents of oxygen and produces
equivalents of water. What is the molecular formula of ?
(1) (2)
(3) (4)
Q32.Assume carbon burns according to following equation :
when carbon is burnt in of oxygen, the volume of carbon monoxide produced is at
STP [nearest integer]
[Given : Assume as ideal gas, Mass of is , mass of is and molar volume of an
idal gas at STP is ]
Q33.Arrange the following orbitals in decreasing order of energy.
A.
B.
C.
D.
The correct option for the order is:
(1) D > B > C > A (2) B > D > C > A
(3) A > C > B > D (4) D > B > A > C
Q34.Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The first ionization enthalpy of series elements is more than that of group metals
Reason (R): In series of elements successive filling of -orbitals takes place.
In the light of the above statements, choose the correct answer from the options given below:
(1) Both (A) and (R) are true and (R) is the correct
explanation of (A)
(2) (A) is true but (R) is false
(3) (A) is false but (R) is true (4) Both (A) and (R) are true but (R) is not the
correct explanation of (A)
Q35.Amongst the following, the number of species having the linear shape is
and
Q36.Enthalpies of formation of and are and
respectively. The magnitude of enthalpy of the reaction given below is . (nearest integer)
Q37.Incorrect statement for the use of indicator in acid-base titration is:
JEE Main 2023 (31 Jan Shift 2)
Question Paper
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MathonGo
A 11 4
A
C11H8 C11H4
C5H8 C9H8
2C(s) + O2( g) → 2 CO (s)
12 g 48 g ______ × 10
−1
L
CO C 12 g mol
−1
O 16 g mol
−1
22. 7 L mol
−1
n = 3, l = 0, m = 0
n = 4, l = 0, m = 0
n = 3, l = 1, m = 0
n = 3, l = 2, m = 1
3d 2
3d d
XeF2, I
+
3
, C3O2, I
−
3
, CO2, SO2, BeCl2 BCl
⊖
2
CCl4( g), H2O(g), CO2( g) HCl −105, −242, −394 −92 kJ mol
−1
kJmol
−1
CCl4( g) + 2H2O(g) → CO2( g) + 4 HCl(g)
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6. (1) Methyl orange may be used for a weak acid vs
weak bas titration.
(2) Phenolphthalein may be used for a strong acid vs
strong base titration.
(3) Methyl orange is a suitable indicator for a strong
acid vs weak base titration.
(4) Phenolphthalein is a suitable indicator for a weak
acid vs strong base titration.
Q38.At , the solubility of silver chloride in water is . The value of for silver
chloride is
(Given mass of Ag is , and mass of is )
Q39.Given below are two statements :
Statement I : is used in the synthesis of Cephalosporin
Statement II : is used for the restoration of aerobic conditions to sewage wastes.
In the light of the above statements, choose the most appropriate answer from the options given below :
(1) Statement I is correct but Statement II is
incorrect
(2) Both Statement I and Statement II are correct
(3) Statement I is incorrect but Statement II is
correct
(4) Both Statement I and Statement II are incorrect
Q40.The element playing significant role in neuromuscular function and interneuronal transmission is :
(1) (2)
(3) (4)
Q41.The number of alkali metal(s), from having ionization enthalpy greater than
and forming stable super oxide is
Q42.The Lewis acid character of boron tri halides follows the order:
(1) (2)
(3) (4)
Q43.In Dumas method for the estimation of , the sample is heated with copper oxide and the gas evolved is
passed over:
(1) Copper gauze (2)
(3) (4) Copper oxide
Q44.A hydrocarbon 'X' with formula uses two moles of on catalystic hydrogenation of its one mole. On
ozonolysis, 'X' yields two moles of methane dicarbaldehyde. The hydrocarbon 'X' is :
(1) hexa- -triene (2) -methylcyclopenta- , diene
(3) cyclohexa , diene (4) cyclohexa , diene
Q45.The normal rain water is slightly acidic and its value is because of which one of the following ?
(1) (2)
(3) (4)
Q46.A sample of a metal oxide has formula . The metal can exist in two oxidation states and .
In the sample of , the percentage of metal ions existing in oxidation state is . (nearest integer)
JEE Main 2023 (31 Jan Shift 2)
Question Paper
JEE Main Previous Year Paper
MathonGo
298 K 1. 434 × 10
−3
g L
−1
− logK
sp
107. 9 g mol
−1
Cl 35. 5 g mol
−1
H2O2
H2O2
Be Mg
Ca Li
Li, K, Cs, Rb 400 kJ mol
−1
BCl3 > BF3 > BBr3 > Bl3 Bl3 > BBr3 > BCl3 > BF3
BBr3 > Bl3 > BCl3 > BF3 BF3 > BCl3 > BBr3 > Bl3
N2
Pd
Ni
C6H8 H2
1, 3, 5 1 1 4−
−1 3− −1 4−
pH 5. 6
CO2 + H2O → H2 CO3 N2O5 + H2O → 2 HNO3
2 SO2 + O2 + 2H2O → 2H2 SO4 4 NO2 + O2 + 2H2O → 4 HNO3
M0.83O1.00 M +2 +3
M0.83O1.00 +2 %
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7. Q47.Evaluate the following statements for their correctness.
A. The elevation in boiling point temperature of water will be same for and urea.
B. Azeotropic mixture boil without change in their composition.
C. Osmosis always takes place from hypertonic to hypotonic solution.
D. The density of solution having molarity is approximately .
E. A negatively charged sol is obtained when solution is added to silver nitrate solution.
Choose the correct answer from the options given below:
(1) B and D only (2) B, D and E only
(3) A and C only (4) A, B and C only
Q48.The resistivity of a solution of an electrolyte is . Its molar conductivity is
. (Nearest integer)
Q49.The rate constant for a first order reaction is . The time required for the initial concentration of the
reactant to reduce to its level is . (Nearest integer)
Q50.Match List I with List II
List I List II
A Physisorption I Single Layer Adsorption
B Chemisorption II
C III Chromatography
D Analytical Application or Adsorption IV Heterogeneous catalysis
Choose the correct answer from the options given below:
(1) A-III, B-IV, C-I, D-II (2) A-II, B-III, C-I, D-IV
(3) A-II, B-I, C-IV, D-III (4) A-IV, B-II, C-III, D-I
Q51.Which one of the following statements is incorrect ?
(1) van Arkel method is used to purify tungsten. (2) The malleable iron is prepared from cast iron by
oxidising impurities in a reverberatory furnace.
(3) Cast iron is obtained by melting pig iron with
scrap iron and coke using hot air blast.
(4) Boron and Indium can be purified by zone
refining method.
Q52.Which of the following elements have half-filled f-orbitals in their ground state ?
(Given : atomic number )
Choose the correct answer from the options given below :
(1) A and B only (2) C and D only
(3) B and D only (4) A and E only
Q53.If the CFSE of is , this complex will absorb maximum at wavelength .
(nearest integer)
Assume Planck' constant , Speed of light and Avogadro's constant
.
JEE Main 2023 (31 Jan Shift 2)
Question Paper
JEE Main Previous Year Paper
MathonGo
0. 1 M NaCl 0. 1 M
32% H2 SO4 4. 09 M 1. 26 g mL
–1
KI
0. 8M 5 × 10
−3
Ωcm
10
4
Ω
−1
cm
2
mol
−1
20 min
−1
1
32
______ × 10
−2
min
20 − 40 kJ mol
−1
N2
(g) + 3H2
(g)
Fe(s)
2 NH3
(g)
−
→
Sm − 62; Eu = 63; Tb = 65; Gd = 64, Pm = 61
[Ti (H2
O)
6
]
3+
−96. 0 kJ / mol nm
(h) = 6. 4 × 10
−34
Js (c) = 3. 0 × 10
8
m/s
(NA) = 6 × 10
23
/ mol
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8. Q54.In the following halogenated organic compounds the one with maximum number of chlorine atoms in its
structure is:
(1) Chloral (2) Gammaxene
(3) Chloropicrin (4) Freon-
Q55.Cyclohexylamine when treated with nitrous acid yields (P). On treating (P) with PCC results in (Q). When (Q)
is heated with dil. we get (R) The final product (R) is:
(1) (2)
(3) (4)
Q56. The number of molecules which gives haloform test among the following molecules is :
Q57.An organic compound , shows optical activity and gives gas on treatment with . The
compound reacts with producing a compound which is soluble in . The structure of is :
JEE Main 2023 (31 Jan Shift 2)
Question Paper
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MathonGo
12
NaOH
[A](C4H11 N) N2 HNO2
[A] PhSO2 Cl KOH A
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9. (1) (2)
(3) (4)
Q58.Which of the following compounds are not used as disinfectants?
A. Chloroxylenol
B. Bithional
C. Veronal
D. Prontosil
E. Terpineol
Choose the correct answer from the options given below:
(1) A, B, E (2) C, D
(3) A, B (4) B, D, E
Q59.Given below are two statements :
Statement I : Upon heating a borax bead dipped in cupric sulphate in a luminous flame, the colour of the bead
becomes green.
Statement II : The green colour observed is due to the formation of copper(I) metaborate In the light of the
above statements, choose the most appropriate answer from the options given below:
(1) Both Statement I and Statement II are false (2) Both Statement I and Statement II are true
(3) Statement I is false but Statement II is true (4) Statement I is true but Statement II is false
Q60.Compound , given a tetraacetate with and oxidation of with gives an acid,
. Reduction of with gives isopentane. The possible structure of is :
JEE Main 2023 (31 Jan Shift 2)
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MathonGo
A, C5H10O5 AC2 O A Br2 − H2O
C5H10O6 A HI A
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10. (1) (2)
(3) (4)
Q61.The equation has :
(1) four solutions two of which are negative (2) two solutions and both are negative
(3) no solution (4) two solutions and only one of them is negative
Q62.The complex number is equal to:
(1) (2)
(3) (4)
Q63.Let . be an A.P. If , the product is minimum and the sum of its first terms is
zero then is equal to
(1) (2)
(3) (4)
Q64.The sum is _____ .
Q65.The coefficient of , in the expansion of , is
Q66.
If the constant term in the binomial expansion of is and the coefficient of is where
is an odd number, then is equal to _____ .
Q67.If , then is equal to :
Q68.The set of all values of for which the line bisects two distinct chords drawn from a point
on the circle , is equal to :
(1) (2)
(3) (4)
JEE Main 2023 (31 Jan Shift 2)
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MathonGo
e
4x
+ 8e
3x
+ 13e
2x
− 8e
x
+ 1 = 0, x ∈ R
z =
i−1
cos
π
3
+i sin
π
3
√2i(cos
5π
12
− i sin
5π
12
) cos
π
12
− i sin
π
12
√2(cos
π
12
+ i sin
π
12
) √2(cos
5π
12
+ i sin
5π
12
)
a1, a2, a3, … … a7 = 3 (a1a4) n
n! − 4an(n+2)
381
4
9
33
4
24
1
2
− 2. 3
2
+ 3. 5
2
− 4. 7
2
+ 5. 9
2
− … . . +15. 29
2
x
−6
(
4x
5
+
5
2x
2
)
9
(
x
5
2
2
−
4
x
l
)
9
−84 x
−3l
2
α
β
β < 0 |αl − β|
2n+1
P
n−1
:
2n−1
P
n
= 11 : 21 n
2
+ n + 15
a
2
x + y = 0
P(
1+a
2
,
1−a
2
) 2x
2
+ 2y
2
− (1 + a)x − (1 − a)y = 0
(8, ∞) (0, 4]
(4, ∞) (2, 12]
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11. Q69.Let be the set of all such that the area of the triangle formed by the tangent at the point
, on the parabola and the lines is , then is equal to
_____ .
Q70.Let be the hyperbola, whose foci are and eccentricity is . Then the length of its latus rectum
is:
(1) (2)
(3) (4)
Q71.
(1) is equal to (2) is equal to
(3) does not exist (4) is equal to
Q72.The number of values of for which is a tautology, is :
(1) (2)
(3) (4)
Q73.Let the mean and standard deviation of marks of class A of students be respectively and , and
the mean and standard deviation of marks of class of students be respectively and . If the mean
and variance of the marks of the combined class of students are respectively and , then the
sum of variances of classes and is
(1) (2)
(3) (4)
Q74.Among the relations
and ,
(1) is transitive but is not (2) both and are symmetric
(3) neither not is transitive (4) is symmetric but is not
Q75.Let . The number of matrices such that the sum of all entries is
prime number is _____ .
Q76.Let be a matrix such that . If the determinant of the matrix is , then
is equal to _____ .
Q77.
If a point satisfying lies on the plane , then
is equal to
(1) (2)
(3) (4)
Q78.Let be the largest interval for which , holds . If
and , then is equal to;
JEE Main 2023 (31 Jan Shift 2)
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MathonGo
S a ∈ N
P (b, c), b, c ∈ N y
2
= 2ax x = b, y = 0 16 unit
2
∑
a∈S
a
H (1 ± √2, 0) √2
3
5
2
2
3
2
lim
x→∞
(√3x+1+√3x−1)
6
+(√3x+1−√3x−1)
6
(x+√x
2
−1)
6
+(x−√x
2
−1)
6
x
3
27
2
9
27
r ∈ {p, q, ~p, ~q} ((p ∧ q) ⇒ (r ∨ q) ∧ ((p ∧ r) ⇒ q)
1 2
4 3
100 40 α(> 0)
B n 55 30 − α
100 + n 50 350
A B
500 450
650 900
S = {(a, b) : a, b ∈ R − {0}, 2 +
a
b
> 0} T = {(a, b) : a, b ∈ R, a
2
− b
2
∈ Z}
S T S T
S T T S
A = ⌊a
îĵ
⌋ ⋅ aij ∈ Z ∩ [0, 4], 1 ≤ i, j ≤ 2 A a
p ∈ (2, 13)
A n × n |A| = 2 Adj (2. Adj (2 A
−1
)) 2
84
n
P (α, β, γ) ( ) = ( )
α β γ
⎛
⎝
2 10 8
9 3 8
8 4 8
⎞
⎠
0 0 0 2x + 4y + 3z = 5
6α + 9β + 7γ
5
4
−1
11
11
5
(a, b) ⊂ (0, 2π) sin
−1
(sin θ) − cos
−1
(sin θ) > 0, θ ∈ (0, 2π)
αx
2
+ βx + sin
−1
(x
2
− 6x + 10) + cos
−1
(x
2
− 6x + 10) = 0 α − β = b − a α
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12. (1) (2)
(3) (4)
Q79.Let be real valued function defined as . Then range of is
(1) (2)
(3) (4)
Q80.The absolute minimum value, of the function , where denotes the
greatest integer function, in the interval , is
(1) (2)
(3) (4)
Q81.Let . If then is equal to :
(1) (2)
(3) (4)
Q82.If then is equal to
(1) (2)
(3) (4)
Q83.Let the area of the region be . Then is equal to
_____ .
Q84.Let be the solution of the differential equation such that
. Then is equal to :
(1) (2)
(3) (4)
Q85.Let and , be there(three) vector. If is a vector such that,
and , then is equal to
(1) (2)
(3) (4)
Q86.Let be three vectors such that and . If the angle
between and is , then is equal to _____ .
Q87.Let the plane be parallel to the line . If the intercept of
on the -axis is , then the distance between and is
(1) (2)
(3) (4)
JEE Main 2023 (31 Jan Shift 2)
Question Paper
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π
8
π
48
π
16
π
12
f : R − {2, 6} → R f(x) =
x+2x+1
x
2
−8x+12
f
(−∞, −
21
4
] ∪ [
21
4
, ∞) (−∞, −
21
4
] ∪ [0, ∞)
(−∞, −
21
4
) ∪ (0, ∞) (−∞, −
21
4
] ∪ [1, ∞)
f(x) = x
2
− x + 1 + [x
2
− x + 1]
∣∣[t]
[−1, 2]
3
2
1
4
5
4
3
4
α > 0 ∫
α
0
x
√x+α−√x
dx =
16+20√2
15
α
2 2√2
4 √2
ϕ(x) =
1
√x
∫
x
π
4
(4√2 sin t − 3ϕ
′
(t))dt, x > 0 ϕ
′
(
π
4
)
4
6+√π
8
6+√π
8
√π
4
6−√π
{(x, y) : |2x − 1| ≤ y ≤ x
2
− x , 0 ≤ x ≤ 1}
∣∣A (6A + 11)
2
y = y(x) (3y
2
− 5x
2
)ydx + 2x(x
2
− y
2
)dy = 0
y(1) = 1 (y(2))
3
− 12y(2)
64 32√2
32 16√2
→
a = î + 2ĵ + 3k̂,
→
b = î − ĵ + 2k̂
→
c = 5î − 3ĵ + 3k̂
→
r
→
r ×
→
b =
→
c ×
→
b
→
r ⋅
→
a = 0 25
→
r
2
560 339
449 336
→
a,
→
b,
→
c
→
a = √31, 4
→
b =
→
c = 2 2(
→
a ×
→
b) = 3(
→
c ×
→
a)
→
b
→
c
2π
3
(
→
a×
→
c
→
a⋅
→
b
)
2
P : 8x + α1y + α2z + 12 = 0 L :
x+2
2
=
y−3
3
=
z+4
5
P
y 1 P L
√
2
7
6
√14
√
7
2
√14
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13. Q88.Let be the plane, passing through the point and perpendicular to the line joining the points
and . Then the distance of from the point is
(1) (2)
(3) (4)
Q89.The foot of perpendicular from the origin to a plane which meets the co-ordinate axes at the point ,
is . If the volume of the tetrahedron is , then which of the following points is
NOT on ?
(1) (2)
(3) (4)
Q90.Let be the event that the absolute difference between two randomly chosen real numbers in the sample space
is less than or equal to . If , then a is equal to _____ .
JEE Main 2023 (31 Jan Shift 2)
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MathonGo
P (1, −1, −5)
(4, 1, −3) (2, 4, 3) P (3, −2, 2)
6 4
5 7
O P A B, C
(2, a, 4), a ∈ N OABC 144 unit
3
P
(0, 4, 4) (3, 0, 4)
(0, 6, 3) (2, 2, 4)
A
[0, 60] a P (A) =
11
36
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14. ANSWER KEYS
1. (4) 2. (2) 3. (1) 4. (4) 5. (2) 6. (2) 7. (1) 8. (1)
9. (4) 10. (1) 11. (4) 12. (2) 13. (3) 14. (1) 15. (3) 16. (1)
17. (4) 18. (2) 19. (3) 20. (4) 21. (80) 22. (5) 23. (5) 24. (300)
25. (20) 26. (55) 27. (1) 28. (25) 29. (48) 30. (136) 31. (4) 32. (1)
33. (1) 34. (1) 35. (2) 36. (3) 37. (2) 38. (1) 39. (4) 40. (1)
41. (1) 42. (3) 43. (1) 44. (3) 45. (2) 46. (2) 47. (4) 48. (2)
49. (1) 50. (3) 51. (227) 52. (5) 53. (173) 54. (10) 55. (2) 56. (59)
57. (25) 58. (17) 59. (480) 60. (3) 61. (2) 62. (4) 63. (4) 64. (1)
65. (3) 66. (4) 67. (2) 68. (1) 69. (4) 70. (3) 71. (4) 72. (2)
73. (4) 74. (1) 75. (2) 76. (2) 77. (2) 78. (4) 79. (3) 80. (2)
81. (6952) 82. (5040) 83. (98) 84. (45) 85. (146) 86. (204) 87. (5) 88. (125)
89. (3) 90. (10)
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