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JEE Main 2023 1 Feb Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 20231 Feb, Morning shift

Physics 25Chemistry 19Mathematics 29

Physics

Q49A series LCR circuit is connected to an ac source of 220 ~V, 50 ~Hz. The circuit contain a resistance R=100 ~Ω and an inductor of inductive reactance X L…Electromagnetic Induction and Alternating Currents
Q51A light of energy 12.75 ~eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The…Atoms and Nuclei
Q54In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf 1.5 ~V is found to be 60 ~cm. If this cell is replaced…Current Electricity
Q58Two equal positive point charges are separated by a distance 2 a. The distance of a point from the centre of the line joining two charges on the equatorial…Electrostatics
Q59A thin cylindrical rod of length 10 ~cm is placed horizontally on the principle axis of a concave mirror of focal length 20 ~cm. The rod is placed in a such a…Optics
Q66A charge particle of 2 ~μ C accelerated by a potential difference of 100 ~V enters a region of uniform magnetic field of magnitude 4 ~mT at right angle to the…Magnetic Effects of Current and Magnetism
Q68A certain pressure ' P ' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0.01% whereas the liquid gets compressed…Properties of Solids and Liquids
Q70The amplitude of a particle executing SHM is 3 ~cm. The displacement at which its kinetic energy will be 25% more than the potential energy is: _ _ _ _ _ cmOscillations and Waves
Q73A small particle moves to position 5 i-2 j+k from its initial position 2 i+3 j-4 k under the action of force 5 i+2 j+7 k ~N. The value of work done will be _…Work, Energy and Power
Q5943Match List - I with List - II: List I List II A. AC generator I. Presence of both L and C B. Transformer II. Electromagnetic Induction C. Resonance phenomenon…Electromagnetic Induction and Alternating Currents
Q6055The mass of proton, neutron and helium nucleus are respectively 1.0073~u,1.0087~u and 4.0015~u. The binding energy of helium nucleus is:Atoms and Nuclei
Q6323Which of the following frequencies does not belong to FM broadcast ?Communication Systems
Q6578A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ. An alpha particle having certain kinetic energy has the same…Dual Nature of Matter and Radiation
Q6843Match List I with List II: List I List II A. Microwaves I. Radio active decay of the nucleus B. Gamma rays II. Rapid acceleration and deceleration of electron…Electromagnetic Waves
Q6881Match List I with List II: List I List II A. Intrinsic semiconductor I. Fermi-level near the valence bond B. n-type semiconductor II. Fermi-level in the…Electronic Devices
Q7156Given below are two statements: Statement I: Acceleration due to gravity is different at different places on the surface of earth. Statement II: Acceleration…Gravitation
Q7206If earth has a mass nine times and radius twice to that of a planet P. Then (v e)/3 √(x) ~ms⁻¹ will be the minimum velocity required by a rocket to pull out…Gravitation
Q7409(P+a/(V²))(V-b)=R T represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the…Thermodynamics
Q7410The average kinetic energy of a molecule of the gas isKinetic Theory of Gases
Q7494A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is (given, γ=3/2):Thermodynamics
Q7558A block of mass 5 ~kg is placed at rest on a table of rough surface. Now, if a force of 30 ~N is applied in the direction parallel to surface of the table…Laws of Motion
Q7797A child stands on the edge of the cliff 10 ~m above the ground and throws a stone horizontally with an initial speed of 5 ~ms⁻¹. Neglecting the air…Kinematics
Q8022A mercury drop of radius 10⁻³~m is broken into 125 equal size droplets. Surface tension of mercury is 0.45~Nm⁻¹. The gain in surface energy is:Properties of Solids and Liquids
Q8466' n ' polarizing sheets are arranged such that each makes an angle 45^(°) with the preceeding sheet. An unpolarized light of intensity I is incident into this…Optics
Q8509A steel wire with mass per unit length 7.0 × 10⁻³ ~kg ~m⁻¹ is under tension of 70 ~N. The speed of transverse waves in the wire will be:Oscillations and Waves

Chemistry

Q1Number of isomeric compounds with molecular formula C₉ H₁₀ O which (i) do not dissolve in NaOH (ii) do not dissolve in HCl. (iii) do not give orange…Organic Compounds Containing Oxygen
Q3(i) X(g) Y(g)+Z(g) K p 1 =3 (ii) A(g) 2 ~B(g) K p 2 =1 If the degree of dissociation and initial concentration of both the reactants X(g) and A(g) are equal…Equilibrium
Q4A and B are two substances undergoing radioactive decay in a container. The half life of A is 15 min and that of B is 5 min. If the initial concentration of B…Chemical Kinetics
Q9At what pH, given half cell MnO₄⁻(0.1~M)~|~Mn²⁺(0.001~M) will have electrode potential of 1.282 V? _ _ _ _ _ _ (Nearest Integer) Given E_ MnO₄^ - |M n²⁺ ^(o)…Redox Reactions and Electrochemistry
Q13Sum of oxidation states of bromine in bromic acid and perbromic acid is _ _ _ _ _ _.Redox Reactions and Electrochemistry
Q1625 mL of an aqueous solution of KCl was found to require 20 mL of 1 M AgNO₃ solution when titrated using K₂CrO₄ as an indicator. What is the depression in…Solutions
Q17The density of 3 M solution of NaCl is 1.0 ~g ~mL⁻¹. Molality of the solution is _ _ _ _ _ _ × 10⁻² ~m. (Nearest integer). Given: Molar mass of Na and Cl is…Some Basic Concepts in Chemistry
Q18Electrons in a cathode ray tube have been emitted with a velocity of 1000 m s ⁻¹. The number of following statements which is/are true about the emitted…Atomic Structure
Q19At 25^(°) C, the enthalpy of the following processes are given: H₂(g)+O₂(g) | → | 2OH(g) | Δ H°=78~kJ~mol⁻¹ H₂(g)+1/2O₂(g) | → | H₂O(g) | Δ H°=-242~kJ~mol⁻¹…Chemical Thermodynamics
Q181Match List I with List II List I List II Test Functional group / Class of Compound A. Molisch's Test I. Peptide B. Biuret Test II. Carbohydrate C. Carbylamine…Biomolecules
Q566A solution of FeCl₃ when treated with K₄[Fe(CN)₆] gives a prussium blue precipitate due to the formation of:Coordination Compounds
Q597Which of the following are the example of double salt? A. FeSO₄ ·(NH₄)₂ SO₄ · 6 H₂ O B. CuSO₄· 4 NH₃ · H₂ O C. K₂ SO₄ · Al₂(SO₄)₃ · 24 H₂ O D. Fe(CN)₂·4 KCN…Coordination Compounds
Q635Which of the following complex will show largest splitting of d-orbitals?Coordination Compounds
Q891Highest oxidation state of Mn is exhibited in Mn₂O₇. The correct statements about Mn₂O₇ are (A) Mn is tetrahedrally surrounded by oxygen atoms. (B) Mn is…d- and f-Block Elements
Q1041How can photochemical smog be controlled?Environmental Chemistry
Q1258Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: Hydrogen is an environment friendly fuel…Hydrogen
Q1372Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: In an Ellingham diagram, the oxidation of…Isolation of Elements
Q1834Match List I with List II: List I List II A. Slaked lime I. NaOH B. Dead burnt plaster II. Ca(OH)₂ C. Caustic soda III. Na₂CO₃· 10H₂O D. Washing soda IV…S Block Elements
Q1897Choose the correct statement(s): A. Beryllium oxide is purely acidic in nature. B. Beryllium carbonate is kept in the atmosphere of CO₂. C. Beryllium sulphate…S Block Elements

Mathematics

Q22Let A be the area bounded by the curve y=x|x-3|, the x -axis and the ordinates x=-1 and x=2. Then 12 A is equal to _ _ _ _ _ _.Integral Calculus
Q23The remainder, when 19²⁰⁰+23²⁰⁰ is divided by 49, is _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q26If ∫₀¹(x²¹+x¹⁴+x⁷)(2 x¹⁴+3 x⁷+6)^(1 / 7) d x=1/l(11)^(m / n) where l, m, n N, m and n are coprime then l+m+n is equal to _ _ _ _ _ _.Integral Calculus
Q27Let f: R → R be a differentiable function such that f^()(x)+f(x)=∫₀² f(t) d t. If f(0)=e⁻², then 2 f(0)-f(2) is equal to _ _ _ _ _ _.Integral Calculus
Q31If f(x)=x²+g^()(1) x+g^()(2) and g(x)=f(1) x²+x f^()(x)+f^()(x), then the value of f(4)-g(4) is equal to _ _ _ _ _ _.Limit, Continuity and Differentiability
Q36The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is _ _ _ _…Permutations and Combinations
Q38The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7, is _ _ _ _ _ _.Permutations and Combinations
Q41Let a₁=8, a₂, a₃,, a n be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170, then the product of its middle two terms…Sequence and Series
Q47Let v=α i+2 j-3 k, w=2 α i+j-k and u be a vector such that |u|=α>0. If the minimum value of the scalar triple product [ u v w ] is -α √(3401), and |u ·…Vector Algebra
Q48A(2,6,2), B(-4,0, λ), C(2,3,-1) and D(4,5,0),|λ| ≤ 5 are the vertices of a quadrilateral A B C D. If its area is 18 square units, then 5-6 λ is equal to _ _ _…Vector Algebra
Q2508The shortest distance between the lines (x - 5)/1 = (y - 2)/2 = (z - 4)/(- 3) and (x + 3)/1 = (y + 5)/4 = (z - 1)/(- 5) is:Three Dimensional Geometry
Q2603Let the image of the point P(2,-1,3) in the plane x+2 y-z=0 be Q. Then the distance of the plane 3 x+2 y+z+29=0 from the point Q is:Three Dimensional Geometry
Q3197If the center and radius of the circle | (z - 2)/(z - 3) | = 2 are respectively (α,β) and γ, then 3(α+β+γ) is equal to:Complex Numbers and Quadratic Equations
Q3295lim n → ∞ [ 1/(1 + n) + 1/(2 + n) + 1/(3 + n) +... + 1/2n ] is equal toIntegral Calculus
Q3553If y=y(x) is the solution curve of the differential equation (d y)/(d x)+y tan x=x sec x, 0 ≤ x ≤ (π)/3, y(0)=1, then y((π)/6) is equal toDifferential Equations
Q3633The area enclosed by the closed curve C given by the differential equation (d y)/(d x)+(x+a)/(y-2)=0, y(1)=0 is 4 π. Let P and Q be the points of intersection…Differential Equations
Q3708Let f(x) = 2x + tan ⁻¹x and g(x) = log e (√(1 + x²) + x),x [0,3]. ThenLimit, Continuity and Differentiability
Q3873Let f(x) = | 1 + sin ²x cos ²x sin 2x sin ²x 1 + cos ²x sin 2x sin ²x cos ²x 1 + sin 2x |, x [ (π)/6,(π)/3 ]. If α and β respectively are the maximum and the…Sets, Relations and Functions
Q4116Let S be the set of all solutions of the equation cos ⁻¹(2 x)-2 cos ⁻¹(√(1-x²))=π, x [-1/2, 1/2]. Then Σ x S 2 sin ⁻¹(x²-1) is equal to:Trigonometry
Q4380The negation of the expression q ((q) p) is equivalent toMathematical Reasoning
Q4617Let S denote the set of all real values of λ such that the system of equations λ x+y+z=1 x+λ y+z=1 x+y+λ z=1 is inconsistent, then Σ λ S (|λ|²+|λ|) is equal toMatrices and Determinants
Q4848The value of 1/(1 ! 50 !)+1/(3 ! 48 !)+1/(5 ! 46 !)+.+1/(49 ! 2 !)+1/(51 ! 1 !) is:Permutations and Combinations
Q4895In a binomial distribution B(n,p), the sum and the product of the mean and the variance are 5 and 6 respectively, then 6(n+p-q) is equal to:Statistics and Probability
Q5160Let S = x:x R and (3 + 2)^(x² - 4) + (3 - 2)^(x² - 4) = 10. Then n(S) is equal toComplex Numbers and Quadratic Equations
Q5340The sum of 10 terms of the series 1/(1 + 1² + 1⁴) + 2/(1 + 2² + 2⁴) + 3/(1 + 3² + 3⁴) +.... isSequence and Series
Q5386Let R be a relation on R, given by R=\(a, b): 3 a-3 b+√(7) is an irrational number. Then R isSets, Relations and Functions
Q5478The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observations is:Statistics and Probability
Q5511The combined equation of the two lines ax+by+c=0 and a'x+b'y+c'=0 can be written as (ax+by+c)(a'x+b'y+c')=0. The equation of the angle bisectors of the lines…Coordinate Geometry
Q5543If the orthocentre of the triangle, whose vertices are (1, 2), (2, 3) and (3, 1) is (α,β), then the quadratic equation whose roots are α+4β and 4α+β, is:Coordinate Geometry