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JEE Main 2023 12 Apr Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202312 Apr, Morning shift

Physics 29Chemistry 20Mathematics 29

Physics

Q52A common example of alpha decay is ₉₂²³⁸ U ₉₀²³⁴ Th+ ₂ He⁴+Q Given: ₉₂²³⁸ U=238.05060 ~u, ₉₀²³⁴ Th=234.04360 ~u, ₂⁴ He=4.00260 ~u and 1 u=931.5 MeV/(c²) The…Atoms and Nuclei
Q54The current flowing through a conductor connected across a source is 2 ~A and 1.2 A at 0^(°) C and 100^(°) C respectively. The current flowing through the…Current Electricity
Q57A conducting circular loop is placed in a uniform magnetic field of 0.4 ~T with its plane perpendicular to the field. Somehow, the radius of the loop starts…Electromagnetic Induction and Alternating Currents
Q6164 identical drops each charged upto potential of 10 ~mV are combined to form a bigger drop. The potential of the bigger drop will be _ _ _ _ _ mV.Electrostatics
Q62Two convex lenses of focal length 20 ~cm each are placed coaxially with a separation of 60 ~cm between them. The image of the distant object formed by the…Optics
Q68A compass needle oscillates 20 times per minute at a place where the dip is 30^(°) and 30 times per minute where the dip is 60^(°). The ratio of total…Magnetic Effects of Current and Magnetism
Q72Glycerin of density 1.25 × 10³ ~kg ~m⁻³ is flowing through the conical section of pipe The area of cross-section of the pipe at its ends are 10 ~cm² and 5…Properties of Solids and Liquids
Q73For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is x/5. The value of x is _ _ _ _ _ _.Rotational Motion
Q76For a certain organ pipe, the first three resonance frequencies are in the ratio of 1:3:5 respectively. If the frequency of fifth harmonic is 405 ~Hz and the…Oscillations and Waves
Q78To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be _ _ _ _ _ _ KJ…Work, Energy and Power
Q5919Given below are two statements: Statement I: When the frequency of an a.c source in a series LCR circuit increases, the current in the circuit first…Electromagnetic Induction and Alternating Currents
Q6019A 12.5 ~eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:Atoms and Nuclei
Q6375The amplitude of 15 sin (1000 π t) is modulated by 10 sin (4 π t) signal. The amplitude modulated signal contains frequencies of A. 500 ~Hz B. 2 ~Hz C. 250…Communication Systems
Q6523A wire of resistance 160 ~Ω is melted and drawn in a wire of one-fourth of its length. The new resistance of the wire will beCurrent Electricity
Q6584A proton and an α -particle are accelerated from rest by 2 ~V and 4 ~V potentials, respectively. The ratio of their de-Broglie wavelength is:Dual Nature of Matter and Radiation
Q6845Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: EM waves used for optical communication have…Electromagnetic Waves
Q6913In an n-p-n common emitter (CE) transistor the collector current changes from 5 mA to 16 ~mA for the change in base current from 100~ μ A and 200 ~μ A…Electronic Devices
Q6949Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: If an electric dipole of dipole moment 30 ×…Electrostatics
Q7122An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12 ~cm. When viewed from the opposite side, the apparent…Optics
Q7209The ratio of escape velocity of a planet to the escape velocity of earth will be:- Given: Mass of the planet is 16 times mass of earth and radius of the…Gravitation
Q7210Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will beGravitation
Q7419If the r. m.s speed of chlorine molecule is 490 ~m / s at 27^(°) C, the r. m. s speed of argon molecules at the same temperature will be (Atomic mass of argon…Thermodynamics
Q7543Three forces F₁=10 ~N, F₂=8 ~N, ~F₃=6 ~N are acting on a particle of mass 5 ~kg. The forces F₂ and F₃ are applied perpendicularly so that particle remains at…Laws of Motion
Q7651Given below are two statements: Statement I: The diamagnetic property depends on temperature. Statement II: The induced magnetic dipole moment in a…Magnetic Effects of Current and Magnetism
Q7870A ball is thrown vertically upward with an initial velocity of 150 ~m / s. The ratio of velocity after 3 ~s and 5 ~s is (x+1)/x. The value of x is _ _ _ _ _…Kinematics
Q7975A body cools from 80^(°) C to 60^(°) C in 5 minutes. The temperature of the surrounding is 20^(°) C. The time it takes to cool from 60^(°) C to 40^(°) C is:Properties of Solids and Liquids
Q8173A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its…Oscillations and Waves
Q8347Match List I with List II LIST I LIST II A. Spring constant I. [T⁻¹] B. Angular speed II. [MT⁻²] C. Angular momentum III. [ML²] D. Moment of inertia IV…Units and Measurements
Q8592Given below are two statements: Statement I: A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal…Work, Energy and Power

Chemistry

Q1The mass of NH ₃ produced when 131.8 kg of cyclohexanecarbaldehyde undergoes Tollen's test is _ _ _ _ kg. (Nearest Integer) Molar Mass of C = 12g/mol N =…Organic Compounds Containing Oxygen
Q2In an oligopeptide named Alanylglycylphenyl alanyl isoleucine, the number of sp² hybridised carbons is _ _ _ _ _.Biomolecules
Q4The reaction 2 NO+Br₂ → 2 NOBr takes places through the mechanism given below: NO+Br₂ NOBr₂ (fast) NOBr₂+NO → 2 NOBr (slow) The overall order of the reaction…Chemical Kinetics
Q9At 600 ~K, the root mean square (rms) speed of gas X (molar mass =40) is equal to the most probable speed of gas Y at 90 ~K. The molar mass of the gas Y is _…Gaseous State
Q11An analyst wants to convert 1 ~L ~HCl of pH=1 to a solution of HCl of pH ~2. The volume of water needed to do this dilution is _ _ _ _ _ mL. (Nearest integer)Equilibrium
Q1780 mole percent of MgCl₂ is dissociated in aqueous solution. The vapour pressure of 1.0 ~molal aqueous solution of MgCl₂ at 38^(°) C is _ _ _ _ _ _ mm ~Hg…Solutions
Q19Values of work function (W ₀) for a few metals are given below Metal | Li | Na | K | Mg | Cu | Ag W ₀ /eV | 2.42 | 2.3 | 2.25 | 3.7 | 4.8 | 4.3 The number of…Atomic Structure
Q20One mole of an ideal gas at 350 ~K is in a 2.0 ~L vessel of thermally conducting walls, which are in contact with the surroundings. It undergoes isothermal…Chemical Thermodynamics
Q383The bond order and magnetic property of acetylide ion are same as that ofChemical Bonding and Molecular Structure
Q641Match List I with List II LIST I Complex LIST II CFSE (Δ₀) A. [Cu(NH₃)₆]²⁺ I. -0.6 B. [Ti(H₂O)₆]³⁺ II. -2.0 C. [Fe(CN)₆]³⁻ III. -1.2 D. [NiF₆]⁴⁻ IV. -0.4…Coordination Compounds
Q833Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: 5 f electrons can participate in bonding to a…d- and f-Block Elements
Q918For lead storage battery pick the correct statements A. During charging of battery, PbSO₄ on anode is converted into PbO₂ B. During charging of battery, PbSO₄…Redox Reactions and Electrochemistry
Q1075Match List I with List II LIST I LIST II A. Nitrogen oxides in air I. Eutrophication B. Methane in air II. pH of rain water becomes 5.6 C. Carbon dioxide III…Environmental Chemistry
Q1208Match List I with List II LIST I Type of Hydride LIST II Example A. Electron deficient hydride I. MgH₂ B. Electron rich hydride II. HF C. Electron precise…Hydrogen
Q1374Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: In the Ellingham diagram, a sharp change in…Isolation of Elements
Q1458Given below are two statements: Statement I: Boron is extremely hard indicating its high lattice energy. Statement II: Boron has highest melting and boiling…p-Block Elements
Q1496Given below are two statements: Statement I: SbCl₅ is more covalent than SbCl₃ Statement II: The higher oxides of halogens also tend to be more stable than…p-Block Elements
Q1709Match List I with List II LIST I (Examples) LIST II (Type) A. 2-chloro-1,3- butadiene I. Biodegradable polymer B. Nylon 2-nylon 6 II. Synthetic Rubber C…Polymers
Q1865The density of alkali metals is in the order:S Block Elements
Q2080A metal chloride contains 55.0% of chlorine by weight. 100 ~mL vapours of the metal chloride at STP weigh 0.57 ~g. The molecular formula of the metal chloride…Some Basic Concepts in Chemistry

Mathematics

Q23Let the plane x+3 y-2 z+6=0 meet the co-ordinate axes at the points A, B, C. If the orthocenter of the triangle ABC is (α, β, 6/7), then 98(α+β)² is equal to…Three Dimensional Geometry
Q28Two circles in the first quadrant of radii r₁ and r₂ touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line x+y=2. Then…Coordinate Geometry
Q30If ∫ -0.15 ^(0.15)|100 x²-1| d x=k/3000, then k is equal to _ _ _ _ _ _.Integral Calculus
Q34Let I(x)=∫ √((x+7)/x) ~d x and I(9)=12+7 log e 7. If I(1)=α+7 log e (1+2 √(2)), then α⁴ is equal to _ _ _ _ _.Integral Calculus
Q35Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x)=|[x]|+√(x-[x]) is discontinuous, is _ _ _ _ _ _.Limit, Continuity and Differentiability
Q37Let D k =| ccc1 2 k 2 k-1 n n²+n+2 n² n n²+n n²+n+2 |. If Σ k=1 ⁿ D k =96, then n is equal to _ _ _ _ _ _ _.Matrices and Determinants
Q40Let the digits a, b, c be in A. P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P…Permutations and Combinations
Q42A fair n(n > 1) faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is n/9, then n is equal to _ _…Statistics and Probability
Q45The number of relations, on the set \1,2,3 containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is _ _ _ _ _.Sets, Relations and Functions
Q46Let the positive numbers a₁, a₂, a₃, a₄ and a₅ be in a G.P. Let their mean and variance be 31/10 and m/n respectively, where m and n are co-prime. If the mean…Statistics and Probability
Q2467Let the plane P: 4 x-y+z=10 be rotated by an angle (π)/2 about its line of intersection with the plane x+y-z=4. If α is the distance of the point (2,3,-4)…Three Dimensional Geometry
Q2517Let the lines l₁: (x+5)/3=(y+4)/1=(z-α)/(-2) and l₂: 3 x+2 y+z-2=0=x-3 y+2 z-13 be coplanar. If the point P(a, b, c) on l₁ is nearest to the point Q(-4,-3,2)…Three Dimensional Geometry
Q2679If the local maximum value of the function f(x)=((√(3 e))/(2 sin x))^ sin ² x, x (0, (π)/2), is k/e, then (k/e)⁸+(k⁸)/(e⁵)+k⁸ is equal toLimit, Continuity and Differentiability
Q2861The area of the region enclosed by the curve y=x³ and its tangent at the point (-1,-1) is:Integral Calculus
Q3008If 1/(n+1) ⁿ C n +1/n ⁿ C n-1 + +1/2 ⁿ C₁+ ⁿ C₀=1023/10 then n is equal to:Binomial Theorem and Its Simple Applications
Q3009The sum, of the coefficients of the first 50 terms in the binomial expansion of (1-x)¹⁰⁰, is equal toBinomial Theorem and Its Simple Applications
Q3200Let C be the circle in the complex plane with centre z₀=1/2(1+3 i) and radius r=1. Let z₁=1+i and the complex number z₂ be outside the circle C such that…Complex Numbers and Quadratic Equations
Q3560Let y=y(x), y > 0, be a solution curve of the differential equation (1+x²) d y=y(x-y) d x. If y(0)=1 and y(2 √(2))=β, thenDifferential Equations
Q3738Let P((2 √(3))/(√(7)), 6/(√(7))), Q, R and S be four points on the ellipse 9 x²+4 y²=36. Let PQ and RS be mutually perpendicular and pass through the origin…Coordinate Geometry
Q3846Let D be the domain of the function f(x)= sin ⁻¹(log 3 x ((6+2 log ₃ x)/(-5 x))). If the range of the function g: D → R defined by g(x)=x-[x],([x] is the…Sets, Relations and Functions
Q4391Among the two statements (S 1):(p ⇒ q) (p (q)) is a contradiction and (S 2):(p q) ((p) q) (p (q)) ((p) (q)) is a tautologyMathematical Reasoning
Q4495Let A=[ cc1 1/51 0 1 ]. If B=[ cc1 2 -1 -1 ] A[ cc-1 -2 1 1 ], then the sum of all the elements of the matrix Σ n=1 ⁵⁰ Bⁿ is equal toMatrices and Determinants
Q4800The number of five digit numbers, greater than 40000 and divisible by 5, which can be formed using the digits 0,1,3,5,7 and 9 without repetition, is equal to:Permutations and Combinations
Q5005Two dice A and B are rolled. Let the numbers obtained on A and B be α and β respectively. If the variance of α-β is p/q, where p and q are co-prime, then the…Statistics and Probability
Q5163Let α, β be the roots of the quadratic equation x²+√(6) x+3=0. Then (α²³+β²³+α¹⁴+β¹⁴)/(α¹⁵+β¹⁵+α¹⁰+β¹⁰) is equal to:Complex Numbers and Quadratic Equations
Q5342Let < a n > be a sequence such that a₁+a₂+ +a n =(n²+3 n)/((n+1)(n+2)). If 28 Σ k=1 ¹⁰ 1/(a k)=p₁ p₂ p₃ p m, where p₁, p₂,., p m are the first m prime…Sequence and Series
Q5571If the point (α, (7 √(3))/3) lies on the curve traced by the mid-points of the line segments of the lines x cos θ+y sin θ=7, θ (0, (π)/2) between the…Coordinate Geometry
Q5748Let a, b, c be three distinct real numbers, none equal to one. If the vectors a i+j+k, i+b j+k and i+j+c k are coplanar, then 1/(1-a)+1/(1-b)+1/(1-c) is equal…Vector Algebra
Q5749Let λ Z, a=λ i+j-k and b=3 i-j+2 k. Let c be a vector such that (a+b+c) × c=0, a · c=-17 and b · c=-20. Then |c ×(λ i+j+k)|² is equal to:Vector Algebra