JEE Main 24 January 2023 Shift 1 Question Paper with Answers
24 January 2023 · January session · 90 questions
The complete JEE Main 24 January 2023 Shift 1 paper — all 90 questions with the correct answer for each, tagged to the chapter it tests. Free to read, no account needed.
Physics
30
Chemistry
30
Mathematics
30
Physics — JEE Main 24 January 2023 Shift 1
Q1·PhysicsSingle correct
A circular loop of radius r is carrying current I A. The ratio of magnetic field at the centre of the circular loop and at a distance r from the centre of the loop on its axis is:
(A)22:1
(B)1:32
(C)1:2
(D)32:2
Q2·PhysicsSingle correct
The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth Re=6400 km):
(A)8 N
(B)4.9 N
(C)9.8 N
(D)19.6 N
Q3·PhysicsSingle correct
Two long straight wires P and Q carrying equal current 10 A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is F1. If distance between wires is halved and currents on them are doubled, force F2 on 10 cm length of wire P will be:
(A)8F1
(B)8F1
(C)10F1
(D)10F1
Q4·PhysicsSingle correct
Given below are two statements:
Statement I: The temperature of a gas is −73∘C. When the gas is heated to 527∘C, the root mean square speed of the molecules is doubled.
Statement II: The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.
In the light of the above statements, choose the correct answer from the options given below:
(A)Statement I is false but Statement II is true
(B)Both Statement I and Statement II are false
(C)Statement I is true but Statement II is false
(D)Both Statement I and Statement II are true
Q5·PhysicsSingle correct
The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is:
(A)272 m
(B)68 m
(C)192 m
(D)136 m
Q6·PhysicsSingle correct
Given below are two statements:
Statement I: If the Brewster's angle for the light propagating from air to glass is θB, then the Brewster's angle for the light propagating from glass to air is 2π−θB.
Statement II: The Brewster's angle for the light propagating from glass to air is tan−1(μg) where μg is the refractive index of glass.
In the light of the above statements, choose the correct answer from the options given below:
(A)Both Statement I and Statement II are false
(B)Statement I is true but Statement II is false
(C)Statement I is false but Statement II is true
(D)Both Statement I and Statement II are true
Q7·PhysicsSingle correct
A 100 m long wire having cross-sectional area 6.25×10−4 m2 and Young's modulus is 1010 Nm−2 is subjected to a load of 250 N, then the elongation in the wire will be:
(A)4×10−3 m
(B)6.25×10−3 m
(C)6.25×10−6 m
(D)4×10−4 m
Q8·PhysicsSingle correct
If two charges q1 and q2 are separated with distance ′d′ and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?
(A)2dK
(B)1.5dK
(C)dK
(D)Kd
Q9·PhysicsSingle correct
Consider the following radioactive decay process: 84218AαA1β−A2γA3αA4β+A5γA6. The mass number and the atomic number of A6 are given by:
(A)210 and 84
(B)210 and 82
(C)211 and 80
(D)210 and 80
Q10·PhysicsSingle correct
From the photoelectric effect experiment, following observations are made. Identify which of these are correct. A. The stopping potential depends only on the work function of the metal. B. The saturation current increases as the intensity of incident light increases. C. The maximum kinetic energy of a photo electron depends on the intensity of the incident light. D. Photoelectric effect can be explained using wave theory of light. Choose the correct answer from the options given below:
(A)A, C, D only
(B)B, C only
(C)B only
(D)A, B, D only
Q11·PhysicsSingle correct
Given below are two statements:
Statement I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.
Statement II: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed.
In the light of the above statements, choose the correct answer from the options given below:
(A)Both Statement I and Statement II are true
(B)Statement I is false but Statement II is true
(C)Statement I is true but Statement II is false
(D)Both Statement I and Statement II are false
Q12·PhysicsSingle correct
1 g of a liquid is converted to vapour at 3×105 Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm3 during this phase change, then the increase in internal energy in the process will be:
(A)432000 J
(B)4320 J
(C)4800 J
(D)4.32×108 J
Q13·PhysicsSingle correct
As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal resistance of 3Ω. The currents through the resistors R4 and R5 are I4 and I5 respectively. The values of I4 and I5 are:
(A)I4=52 A and I5=58 A
(B)I4=524 A and I5=56 A
(C)I4=58 A and I5=52 A
(D)I4=56 A and I5=524 A
Q14·PhysicsSingle correct
A modulating signal is a square wave, as shown in the figure. If the carrier wave is given as c(t)=2sin(8πt) volts, the modulation index is:
(A)41
(B)21
(C)1
(D)31
Q15·PhysicsSingle correct
A conducting circular loop of radius π10 cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is:
(A)emf = 1 mV
(B)emf = 5 mV
(C)emf = 100 mV
(D)emf = 10 mV
Q16·PhysicsSingle correct
If E and K represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by (ω - angular frequency):
(A)ω(E×K)
(B)ω(K×E)
(C)K×E
(D)ω1(K×E)
Q17·PhysicsSingle correct
Match List I (physical quantities) with List II (their dimensional formulae). Choose the correct answer from the options given below:
List I
List II
A.Planck's constant (h)
I.[M1L2T−2]
B.Stopping potential (Vs)
II.[M1L1T−1]
C.Work function (ϕ)
III.[M1L2T−1]
D.Momentum (p)
IV.[M1L2T−3A−1]
(A)A-I, B-III, C-IV, D-II
(B)A-III, B-I, C-II, D-IV
(C)A-II, B-IV, C-III, D-I
(D)A-III, B-IV, C-I, D-II
Q18·PhysicsSingle correct
A travelling wave is described by the equation y(x,t)=[0.05sin(8x−4t)] m. The velocity of the wave is: [all the quantities are in SI unit]
(A)8 ms−1
(B)4 ms−1
(C)0.5 ms−1
(D)2 ms−1
Q19·PhysicsSingle correct
As shown in the figure, a weightless pulley P is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if g=10 m/s2):
(A)(43+1) N
(B)4(3+1) N
(C)(43−1) N
(D)4(3−1) N
Q20·PhysicsAssertion & Reason
Assertion A: Photodiodes are preferably operated in reverse bias condition for light intensity measurement.
Reason R: The current in the forward bias is more than the current in the reverse bias for a p−n junction diode.
In the light of the above statements, choose the correct answer from the options given below:
(A)A is true but R is false
(B)A is false but R is true
(C)Both A and R are true and R is the correct explanation of A
(D)Both A and R are true but R is NOT the correct explanation of A
Q21·PhysicsNumerical
Vectors ai^+bj^+k^ and 2i^−3j^+4k^ are perpendicular to each other when 3a+2b=7, the ratio of a to b is 2x. The value of x is _______ .
Q22·PhysicsNumerical
Assume that protons and neutrons have equal masses. Mass of a nucleon is 1.6×10−27 kg and radius of nucleus is 1.5×10−15A1/3 m. The approximate ratio of the nuclear density and water density is n×1013. The value of n is _______ .
Q23·PhysicsNumerical
A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is n×10−3Ω. If the resistivity of the material is 2.4×10−8Ωm. The value of n is _______ .
Q24·PhysicsNumerical
A stream of positively charged particles having mq=2×1011kgC and velocity v0=3×107i^ m/s is deflected by an electric field 1.8j^ kV/m. The electric field exists in a region of 10 cm along x direction. Due to the electric field, the deflection of the charge particles in the y direction is _______ mm.
Q25·PhysicsNumerical
As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both the lenses is 1.75. Both the lenses are placed at distance of 40 cm from each other. Due to the combination, the image of the object is formed at distance = _______ cm, from concave lens.
Q26·PhysicsNumerical
Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be x cm. The value of x is _______ .
Q27·PhysicsNumerical
A block of mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is xπ in SI unit. The value of x is _______ .
Q28·PhysicsNumerical
A hole is drilled in a metal sheet. At 27∘C, the diameter of hole is 5 cm. When the sheet is heated to 177∘C, the change in the diameter of hole is d×10−3 cm. The value of d will be _______ if coefficient of linear expansion of the metal is 1.6×10−5/∘C.
Q29·PhysicsNumerical
In the circuit shown in the figure, the ratio of the quality factor and the band width is _______ S.
Q30·PhysicsNumerical
A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of 5th second. The force acted on the body is _______ N.
Chemistry — JEE Main 24 January 2023 Shift 1
Q31·ChemistrySingle correct
'A' and 'B' formed in the following set of reactions are:
(A)(1)
(B)(2)
(C)(3)
(D)(4)
Q32·ChemistrySingle correct
Decreasing order of the hydrogen bonding in following forms of water is correctly represented by: A. Liquid water B. Ice C. Impure water. Choose the correct answer from the options given below:
It is observed that characteristic X-ray spectra of elements show regularity. When frequency to the power 'n' i.e. vn of X-rays emitted is plotted against atomic number 'Z', the following graph is obtained. The value of 'n' is:
(A)3
(B)2
(C)1
(D)21
Q42·ChemistrySingle correct
Given below are two statements:
Statement I: Noradrenaline is a neurotransmitter.
Statement II: Low level of noradrenaline is not the cause of depression in human.
In the light of the above statements, choose the correct answer from the options given below:
(A)Statement I is correct but Statement II is incorrect
(B)Both Statement I and Statement II are correct
(C)Both Statement I and Statement II are incorrect
(D)Statement I is incorrect but Statement II is correct
Q43·ChemistrySingle correct
Which of the Phosphorus oxoacid can create silver mirror from AgNO3 solution?
(A)(HPO3)n
(B)H4P2O6
(C)H4P2O5
(D)H4P2O7
Q44·ChemistrySingle correct
Compound (X) undergoes the following sequence of reactions to give the Lactone (Y). Compound (X) is:
(A)(1)
(B)(2)
(C)(3)
(D)(4)
Q45·ChemistrySingle correct
Order of Covalent bond: A. KF > KI; LiF > KF. B. KF < KI; LiF > KF. C. SnCl4 > SnCl2; CuCl > NaCl. D. LiF > KF; CuCl < NaCl. E. KF < KI; CuCl > NaCl. Choose the correct answer from the options given below:
(A)C, E only
(B)B, C, E only
(C)A, B only
(D)B, C only
Q46·ChemistrySingle correct
Which of the following is true about freons?
(A)These are radicals of chlorine and chlorine monoxide
(B)These are chemicals causing skin cancer
(C)These are chlorofluorocarbon compounds
(D)All radicals are called freons
Q47·ChemistrySingle correct
In the depression of freezing point experiment: A. Vapour pressure of the solution is less than that of pure solvent. B. Vapour pressure of the solution is more than that of pure solvent. C. Only solute molecules solidify at the freezing point. D. Only solvent molecules solidify at the freezing point. Choose the most appropriate answer from the options given below:
(A)A and C only
(B)A only
(C)A and D only
(D)B and C only
Q48·ChemistrySingle correct
Statement I: For colloidal particles, the values of colligative properties are of small order as compared to values shown by true solutions at same concentration.
Statement II: For colloidal particles, the potential difference between the fixed layer and the diffused layer of same charges is called the electrokinetic potential or zeta potential.
In the light of the above statements, choose the correct answer from the options given below:
(A)Statement I is false but Statement II is true
(B)Statement I is true but Statement II is false
(C)Both Statement I and Statement II are true
(D)Both Statement I and Statement II are false
Q49·ChemistryAssertion & Reason
Assertion A: Hydrolysis of an alkyl chloride is a slow reaction but in the presence of NaI, the rate of the hydrolysis increases.
Reason R: I− is a good nucleophile as well as a good leaving group.
In the light of the above statements, choose the correct answer from the options given below:
(A)A is false but R is true
(B)A is true but R is false
(C)Both A and R are true but R is NOT the correct explanation of A
(D)Both A and R are true and R is the correct explanation of A
Q50·ChemistrySingle correct
The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is:
(A)Cr2+
(B)Ti2+
(C)V2+
(D)Mn2+
Q51·ChemistryNumerical
When Fe0.93O is heated in presence of oxygen, it converts to Fe2O3. The number of correct statement/s from the following is: A. The equivalent weight of Fe0.93O is 0.79Molecular weight. B. The number of moles of Fe2+ and Fe3+ in 1 mole of Fe0.93O is 0.79 and 0.14 respectively. C. Fe0.93O is metal deficient with lattice comprising of cubic closed packed arrangement of O2− ions. D. The % composition of Fe2+ and Fe3+ in Fe0.93O is 85% and 15% respectively.
Q52·ChemistryNumerical
The number of correct statement/s from the following is: A. Larger the activation energy, smaller is the value of the rate constant. B. The higher is the activation energy, higher is the value of the temperature coefficient. C. At lower temperatures, increase in temperature causes more change in the value of k than at higher temperature. D. A plot of lnk vs T1 is a straight line with slope equal to −REa.
Q53·ChemistryNumerical
For independent processes at 300 K: Process A (ΔH=−25 kJ mol−1, ΔS=−80 J K−1); Process B (ΔH=−22 kJ mol−1, ΔS=40 J K−1); Process C (ΔH=25 kJ mol−1, ΔS=−50 J K−1); Process D (ΔH=22 kJ mol−1, ΔS=20 J K−1). The number of non-spontaneous processes from these is _______ .
Q54·ChemistryNumerical
5 g of NaOH was dissolved in deionized water to prepare a 450 mL stock solution. What volume (in mL) of this solution would be required to prepare 500 mL of 0.1 M solution? Given: Molar Mass of Na, O and H is 23, 16 and 1 g mol−1 respectively.
Q55·ChemistryNumerical
If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of the second line of this series is _______ nm. (Nearest integer)
Q56·ChemistryNumerical
Uracil is a base present in RNA. The percentage of nitrogen (by mass) in uracil is _______ .
Q57·ChemistryNumerical
The dissociation constant of acetic acid is x×10−5. When 25 mL of 0.2 M CH3COONa solution is mixed with 25 mL of 0.02 M CH3COOH solution, the pH of the resultant solution is found to be equal to 5. The value of x is _______ .
Q58·ChemistryNumerical
Number of moles of AgCl formed in the following reaction is _______ .
Q59·ChemistryNumerical
The d-electronic configuration of [CoCl4]2− in tetrahedral crystal field is emt2n. Sum of 'm' and 'number of unpaired electrons' is _______ .
Q60·ChemistryNumerical
At 298 K, a 1 litre solution containing 10 mmol of Cr2O72− and 100 mmol of Cr3+ shows a pH of 3.0. Given: Cr2O72−→Cr3+; E∘=1.330 V and F2.303RT=0.059 V. The potential for the half cell reaction is x×10−3 V. The value of x is _______ .
Mathematics — JEE Main 24 January 2023 Shift 1
Q61·MathematicsSingle correct
Let u=i^−j^−2k^, v=2i^+j^−k^, v⋅w=2 and v×w=u+λv. Then u⋅w is equal to
(A)2
(B)23
(C)1
(D)−32
Q62·MathematicsSingle correct
t→0lim(1sin2t1+2sin2t1+⋯+nsin2t1)sin2t is equal to
(A)n2
(B)2n(n+1)
(C)n
(D)n2+n
Q63·MathematicsSingle correct
Let α be a root of the equation (a−c)x2+(b−a)x+(c−b)=0 where a,b,c are distinct real numbers such that the matrix α21aα1b11c is singular. Then, the value of (b−a)(c−b)(a−c)2+(a−c)(c−b)(b−a)2+(a−c)(b−a)(c−b)2 is
(A)12
(B)9
(C)3
(D)6
Q64·MathematicsSingle correct
The area enclosed by the curves y2+4x=4 and y−2x=2 is:
(A)9
(B)322
(C)323
(D)325
Q65·MathematicsSingle correct
Let p,q∈R and (1−3i)200=2199(p+iq), i=−1. Then p+q+q2 and p−q+q2 are roots of the equation
(A)x2−4x−1=0
(B)x2−4x+1=0
(C)x2+4x−1=0
(D)x2+4x+1=0
Q66·MathematicsSingle correct
Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations x+y+z=1, 2x+Ny+2z=2, 3x+3y+Nz=3 has unique solution is 6k, then the sum of value of k and all possible values of N is
(A)21
(B)18
(C)20
(D)19
Q67·MathematicsSingle correct
For three positive integers p,q,r, xpq2=yqr=zp2r and r=pq+1 such that 3,3logyx,3logzy,7logxz are in A.P. with common difference 21. Then r−p−q is equal to
(A)−6
(B)12
(C)6
(D)2
Q68·MathematicsSingle correct
The relation R={(a,b):gcd(a,b)=1,2a=b,a,b∈Z} is:
(A)reflexive but not symmetric
(B)transitive but not reflexive
(C)symmetric but not transitive
(D)neither symmetric nor transitive
Q69·MathematicsSingle correct
Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively such that ARQA=BPRB=CQPC=21. Then Area(△ABC)Area(△PQR) is equal to
(A)4
(B)3
(C)25
(D)2
Q70·MathematicsSingle correct
Let y=y(x) be the solution of the differential equation x3dy+(xy−1)dx=0, x>0, y(21)=3−e. Then y(1) is equal to
(A)1
(B)e
(C)3
(D)2−e
Q71·MathematicsSingle correct
If A and B are two non-zero n×n matrices such that A2+B=A2B, then
(A)A2=I or B=I
(B)A2B=I
(C)AB=I
(D)A2B=BA2
Q72·MathematicsSingle correct
The equation x2−4x+[x]+3=x[x], where [x] denotes the greatest integer function, has:
(A)a unique solution in (−∞,1)
(B)no solution
(C)exactly two solutions in (−∞,∞)
(D)a unique solution in (−∞,∞)
Q73·MathematicsSingle correct
Let a tangent to the curve y2=24x meet the curve xy=2 at the points A and B. Then the mid points of such line segments AB lie on a parabola with the
(A)Length of latus rectum 23
(B)directrix 4x=−3
(C)length of latus rectum 2
(D)directrix 4x=3
Q74·MathematicsSingle correct
Let Ω be the sample space and A⊆Ω be an event. Given below are two statements: (S1): If P(A)=0, then A=∅. (S2): If P(A)=1, then A=Ω. Then
(A)both (S1) and (S2) are true
(B)only (S1) is true
(C)only (S2) is true
(D)both (S1) and (S2) are false
Q75·MathematicsSingle correct
The value of r=0∑2222Cr23Cr is
(A)44C23
(B)45C23
(C)44C22
(D)45C24
Q76·MathematicsSingle correct
The distance of the point (−1,9,−16) from the plane 2x+3y−z=5 measured parallel to the line 3x+4=42−y=12z−3 is
The compound statement (∼(P∧Q))∨((∼P)∧Q)⇒((∼P)∧(∼Q)) is equivalent to
(A)(∼Q)∨P
(B)((∼P)∨Q)∧(∼Q)
(C)(∼P)∨Q
(D)((∼P)∨Q)∧((∼Q)∨P)
Q80·MathematicsSingle correct
The distance of the point (7,−3,−4) from the plane passing through the points (2,−3,1), (−1,1,−2) and (3,−4,2) is:
(A)5
(B)4
(C)52
(D)42
Q81·MathematicsNumerical
Let λ∈R and let the equation E be ∣x∣2−2∣x∣+∣λ−3∣=0. Then the largest element in the set S={x+λ:x is an integer solution of E} is _______ .
Q82·MathematicsNumerical
Let a tangent to the curve 9x2+16y2=144 intersect the coordinate axes at the points A and B. Then, the minimum length of the line segment AB is _______ .
Q83·MathematicsNumerical
The shortest distance between the lines 3x−2=2y+1=2z−6 and 3x−6=21−y=0z+8 is equal to _______ .
Q84·MathematicsNumerical
Suppose r=0∑2023r22023Cr=2023×α×22022. Then the value of α is _______ .
Q85·MathematicsNumerical
The value of π8∫0π/2(sinx)2023+(cosx)2023(cosx)2023dx is _______ .
Q86·MathematicsNumerical
The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is _______ .
Q87·MathematicsNumerical
A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is _______ .
Q88·MathematicsNumerical
The 4th term of GP is 500 and its common ratio is m1, m∈N. Let Sn denote the sum of the first n terms of this GP. If S6>S5+1 and S7<S6+21, then the number of possible values of m is _______ .
Q89·MathematicsNumerical
Let C be the largest circle centred at (2,0) and inscribed in the ellipse 36x2+16y2=1. If (1,α) lies on C, then 10α2 is equal to _______ .
Q90·MathematicsNumerical
The value of 12∫03∣x2−3x+2∣dx is _______ .
Chapters tested in this paper
Open any chapter to practise every past-year question on that topic across all papers, and see how often it has actually appeared.
Take the 24 January 2023 Shift 1 paper as a timed mock and Jarvis marks it, then tells you which errors were conceptual gaps, which were silly mistakes, and which pattern you have now repeated. Step-by-step solutions for every question included.