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JEE Main 2023 25 Jan Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202325 Jan, Morning shift

Physics 22Chemistry 18Mathematics 30

Physics

Q50An LCR series circuit of capacitance 62.5 nF and resistance of 50 Ω, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of…Electromagnetic Induction and Alternating Currents
Q51The wavelength of the radiation emitted is λ₀ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the…Atoms and Nuclei
Q60A ray of light is incident from air on a glass plate having thickness 3 cm and refractive index 2. The angle of incidence of a ray is equal to the critical…Optics
Q68If P = 3 i + 3 j + 2 k and Q = 4 i + 3 j + 2.5 k then, the unit vector in the direction of P × Q is 1/x(3 i + j - 2 3 k). The value of x is _ _ _ _ _.Kinematics
Q70The distance between two consecutive points with phase difference of 60° in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is travelling is…Oscillations and Waves
Q5917In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes x…Electromagnetic Induction and Alternating Currents
Q6131The ratio of the density of oxygen nucleus (₈¹⁶O) and helium nucleus (₂⁴He) isAtoms and Nuclei
Q6161A parallel plate capacitor has plate area 40 cm ² and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1…Electrostatics
Q6284A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless…Kinematics
Q6374A message signal of frequency 5 kHz is used to modulate a carrier signal of frequency 2 MHz. The bandwidth for amplitude modulation is:Communication Systems
Q6498A uniform metallic wire carries a current 2 A, when 3.4 V battery is connected across it. The mass of uniform metallic wire is 8.92 × 10 ⁻³ kg, density is…Current Electricity
Q6581Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of λ₀. IF the voltage is increased to 40 kV…Dual Nature of Matter and Radiation
Q6807An electromagnetic wave is transporting energy in the negative z direction. At a certain point and certain time the direction of electric field of the wave is…Electromagnetic Waves
Q6885Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: Photodiodes are used in forward bias usually…Electronic Devices
Q7158Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is…Gravitation
Q7415The root mean square velocity of molecules of gas isKinetic Theory of Gases
Q7650A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the…Magnetic Effects of Current and Magnetism
Q7828A car travels a distance of ' x ' with speed v₁ and then same distance ' x ' with speed v₂ in the same direction. The average speed of the car is:Kinematics
Q7974A bowl filled with very hot soup cools from 98° C to 86° C in 2 minutes when the room temperature is 22° C. How long it will take to cool from 75° C to 69° C?Properties of Solids and Liquids
Q8026Match List I with List II List I List II A. Surface tension I. kg~m⁻¹~s⁻¹ B. Pressure II. kg~ms⁻¹ C. Viscosity III. kg~m⁻¹~s⁻² D. Impulse IV. kg~s⁻² Choose…Properties of Solids and Liquids
Q8212T is the time period of simple pendulum on the earth's surface. Its time period becomes x T when taken to a height R (equal to earth's radius) above the…Oscillations and Waves
Q8449In Young's double slits experiment, the position of 5 ^(th) bright fringe from the central maximum is 5 cm. The distance between slits and screen is 1 m and…Optics

Chemistry

Q3The total number of lone pairs of electrons on oxygen atoms of ozone is _ _ _ _ _.Chemical Bonding and Molecular Structure
Q4For the first order reaction A → B, the half life is 30 min. The time taken for 75% completion of the reaction is _ _ _ _ m in. (Nearest integer) Given: log 2…Chemical Kinetics
Q5The number of paramagnetic species from the following is _ _ _ _ _ _ _. [Ni (CN)₄ ]²⁻,[Ni (CO)₄ ], [NiC l₄ ]²⁻ [Fe (CN)₆ ]⁴⁻, [Cu (N H₃)₄ ]²⁺ [Fe (CN)₆ ]³⁻…Coordination Compounds
Q6How many of the following metal ions have similar value of spin only magnetic moment in gaseous state? _ _ _ _ _ _ _ (Given: Atomic number V, 23; Cr, 24; Fe…d- and f-Block Elements
Q7Consider the cell Pt(s)|H₂(g) (1 atm)|H⁺ (aq,[H⁺ ] = 1)||F e³⁺ (aq),F e²⁺ (aq)|Pt(s) Given E_ F e³⁺ /F e²⁺ ^(o) = 0.771 V and E H⁺ /1/2 H₂ ^(o) = 0 V, T = 298…Redox Reactions and Electrochemistry
Q8A litre of buffer solution contains 0.1 mole of each of NH ₃ and NH ₄ Cl. On the addition of 0.02 mole of HCl by dissolving gaseous HCl, the pH of the…Equilibrium
Q13The density of a monobasic strong acid (Molar mass 24.2 g/mol) is 1.21 kg/L. The volume of its solution required for the complete neutralization of 25 mL of…Redox Reactions and Electrochemistry
Q16In sulphur estimation, 0.471 g of an organic compound gave 1.4439 g of barium sulphate. The percentage of sulphur in the compound is _ _ _ _ _ _ (Nearest…Some Basic Concepts in Chemistry
Q18An athlete is given 100 g of glucose (C ₆ H ₁₂ O ₆) for energy. This is equivalent to 1800kJ of energy. The 50% of this energy gained is utilized by the…Chemical Thermodynamics
Q32Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R: Assertion A: Acetal / Ketal is stable in basic medium…Organic Compounds Containing Oxygen
Q74The correct order in aqueous medium of basic strength in case of methyl substituted amines is:Some Basic Principles of Organic Chemistry
Q1404Which one of the following reactions does not occur during extraction of copper?Isolation of Elements
Q1580Inert gases have positive electron gain enthalpy. Its correct order is:Classification of Elements and Periodicity in Properties
Q1778Match List I with List II List I Elements List II Colour imparted to the flame A. K I. Brick Red B. Ca II. Violet C. Sr III. Apple Green D. Ba IV. Crimson Red…Principles Related to Practical Chemistry
Q1779Match the List-I with List-II: List-I Cations List-II Group reagents A. Pb²⁺,Cu²⁺ i) H₂S gas in presence of dilute HCl B. Al³⁺,Fe³⁺ ii) (NH₄)₂CO₃ in presence…Principles Related to Practical Chemistry
Q1931A cubic solid is made up of two elements X and Y. Atoms of X are present on every alternate corner and one at the center of cube. Y is at 1/3^(rd) of the…Solid State
Q2046'25 volume' hydrogen peroxide meansSome Basic Concepts in Chemistry
Q2125The radius of the 2^(nd) orbit of Li²⁺ is x. The expected radius of the 3^(rd) orbit of Be³⁺ isAtomic Structure

Mathematics

Q19Let the equation of the plane passing through the line x - 2y - z - 5 = 0 = x + y + 3z - 5 and parallel to the line x + y + 2z - 7 = 0 = 2x + 3y + z - 2 be ax…Three Dimensional Geometry
Q24If the area enclosed by the parabolas P₁:2y=5x² and P₂:x²-y+6=0 is equal to the area enclosed by P₁ and y=α x,α > 0, then α³ is equal to _ _ _ _ _ _.Integral Calculus
Q25The constant term in the expansion of (2x + 1/(x⁷) + 3x²)⁵ is _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q32For some a, b, c, let f(x) = ax - 3 and g(x)=x^(b)+c,x. If (fog)⁻¹(x) = ((x - 7)/2)^(1/3), then (fog)(ac) + (gof)(b) is equal to _ _ _ _ _ _.Sets, Relations and Functions
Q33The vertices of a hyperbola H are (± 6, 0) and its eccentricity is (5)/2. Let N be the normal to H at a point in the first quadrant and parallel to the line 2…Coordinate Geometry
Q35If the sum of all the solutions of tan ⁻¹(2x/(1 - x²)) + cot ⁻¹((1 - x²)/2x) = (π)/3, - 1 < x < 1,x ≠ 0, is α - 4/(3), then α is equal to _ _ _ _ _ _ _.Trigonometry
Q37Let S = α: log ₂(9^(2α - 4) + 13) - log ₂(5/2. 3^(2α - 4) + 1) = 2. Then the maximum value of β for which the equation x² - 2(Σ α s α)²x + Σ α s (α + 1)²β = 0…Limit, Continuity and Differentiability
Q39Let A₁,A₂,A₃ be the three A.P. with the same common difference d and having their first terms as A,A+1,A+2, respectively. Let a, b, c be the…Matrices and Determinants
Q43Let x and y be distinct integers where 1 ≤ x ≤ 25 and 1 ≤ y ≤ 25. Then, the number of ways of choosing x and y, such that x+y is divisible by 5, is _ _ _ _ _ _.Permutations and Combinations
Q45Let S = 1, 2, 3, 5, 7, 10, 11. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _ _ _ _ _ _ _.Sets, Relations and Functions
Q2513The distance of the point P(4, 6, - 2) from the line passing through the point (- 3, 2, 3) and parallel to a line with direction ratios 3, 3, - 1 is equal to:Three Dimensional Geometry
Q2514Consider the lines L₁ and L₂ given by L₁:(x - 1)/2 = (y - 3)/1 = (z - 2)/2 L₂:(x - 2)/1 = (y - 2)/2 = (z - 3)/3. A line L₃ having direction ratios 1, - 1…Three Dimensional Geometry
Q2677Let x=2 be a local minima of the function f(x)=2x⁴-18x²+8x+12,x (-4,4). If M is local maximum value of the function f in (-4,4), then M =Limit, Continuity and Differentiability
Q2728Let f:(0,1) be a function defined f(x) = 1/(1 - e⁻ˣ), and g(x) = (f(- x) - f(x)). Consider two statements (I) g is an increasing function in (0, 1) (II) g is…Limit, Continuity and Differentiability
Q3005If a r is the coefficient of x^(10-r) in the Binomial expansion of (1 + x)¹⁰, then Σ r = 1 ¹⁰ r³(a r /(a r - 1))² is equal toBinomial Theorem and Its Simple Applications
Q3027The points of intersection of the line ax + by = 0,(a ≠ b) and the circle x² + y² - 2x = 0 are A(α,0) and B(1,β). The image of the circle with AB as a…Coordinate Geometry
Q3199Let z₁=2+3i and z₂=3+4i. The set S = z C:| z - z₁ |² - | z - z₂ |² = | z₁ - z₂ |² \ represents aComplex Numbers and Quadratic Equations
Q3457The minimum value of the function f(x) = ∫₀² e^(|x - t|)dt is:Integral Calculus
Q3557Let y = y(x) be the solution curve of the differential equation dy/dx = y/x(1 + x y² (1 + log e x)),x > 0,y(1) = 3. Then (y²(x))/9 is equal to:Differential Equations
Q3710Let y(x) = (1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)(1 + x¹⁶). Then y' - y'' at x = - 1 is equal toLimit, Continuity and Differentiability
Q4034Let f(x) = ∫ 2x/((x² + 1)(x² + 3))dx. If f(3) = 1/2(log e 5 - log e 6), then f(4) is equal toIntegral Calculus
Q4243The value of lim n → ∞ (1 + 2 - 3 + 4 + 5 - 6 +..... + (3n - 2) + (3n - 1) - 3n)/(√(2n⁴ + 4n + 3) - √(n⁴ + 5n + 4)) is:Limit, Continuity and Differentiability
Q4385The statement (p (q)) ⇒ (p ⇒ (q)) isMathematical Reasoning
Q4540Let x,y,z > 1 and A = [ 1 log x y log x z log y x 2 log y z log z x log z y 3 ]. Then |adj~(adj~A²)| is equal toMatrices and Determinants
Q4622Let S ₁ and S ₂ be respectively the sets of all a R - 0 for which the system of linear equations ax + 2ay - 3az = 1 (2a + 1)x + (2a + 3)y + (a + 1)z = 2 (3a +…Matrices and Determinants
Q4691The distance of the point (6,-2 2) from the common tangent y=mx+c,m > 0, of the curves x=2y² and x=1+y² is:Coordinate Geometry
Q4924Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space S = x Z:x(66 - x) ≥ 5/9M and the event A = x S:x…Statistics and Probability
Q5481The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8…Statistics and Probability
Q5745Let a, b and c be three non zero vectors such that b. c = 0 and a × (b × c) = (b - c)/2. If d be a vector such that b. d = a. b, then (a × b). (c × d) is…Vector Algebra
Q5783The vector a = - i + 2 j + k is rotated through a right angle, passing through the y-axis in its way and the resulting vector is b. Then the projection of 3 a…Vector Algebra