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JEE Main 2023 29 Jan Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202329 Jan, Evening shift

Physics 26Chemistry 25Mathematics 29

Physics

Q56An inductor of inductance 2 μ H is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance…Electromagnetic Induction and Alternating Currents
Q58A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time…Kinematics
Q61When two resistance R₁ and R₂ connected in series and introduced into the left gap of a meter bridge and a resistance of 10 Ω is introduced into the right…Current Electricity
Q63A null point is found at 200 cm in potentiometer when cell in secondary circuit is shunted by 5 Ω. When a resistance of 15 Ω is used for shunting, null point…Current Electricity
Q68For a charged spherical ball, electrostatic potential inside the ball varies with r as V=2ar²+b. Here, a and b are constant and r is the distance from the…Electrostatics
Q70In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass…Optics
Q78A particle of mass 250 g executes a simple harmonic motion under a periodic force F=(-25~x)N. The particle attains a maximum speed of 4 m/s during its…Oscillations and Waves
Q80Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium -1) and 6.8 (medium -2), respectively…Optics
Q6129Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half life of 1/2 day. If both A and B…Atoms and Nuclei
Q6282An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at x=+2~m, its velocity is - 4 j…Kinematics
Q6373The modulation index for an A.M. wave having maximum and minimum peak-to-peak voltages of 14 mV and 6 mV respectively is-Communication Systems
Q6504With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is (A) directly proportional to the…Current Electricity
Q6580The ratio of de-Broglie wavelength of an α particle and a proton accelerated from rest by the same potential is 1/(m), the value of m is -Dual Nature of Matter and Radiation
Q6710A square loop of area 25 cm ² has a resistance of 10 Ω. The loop is placed in uniform magnetic field of magnitude 40.0 T. The plane of loop is perpendicular…Electromagnetic Induction and Alternating Currents
Q6804Given below are two statements: Statement I: Electromagnetic waves are not deflected by electric and magnetic field. Statement II: The amplitude of electric…Electromagnetic Waves
Q6974A point charge 2×10⁻²~C is moved from P to S in a uniform electric field of 30~ NC⁻¹ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m…Electrostatics
Q7071A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)Optics
Q7276The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value…Gravitation
Q7414At 300 K, the rms speed of oxygen molecules is √((α + 5)/(α)) times to that of its average speed in the gas. Then, the value of α will be (used π = 22/7)Kinetic Theory of Gases
Q7465Heat energy of 184 kJ is given to ice of mass 600 g at -12° C. Specific heat of ice is 2222.3~J~kg^(-1°)~C⁻¹ and latent heat of ice in 336 kJ/kg⁻¹ A. Final…Properties of Solids and Liquids
Q7559The time taken by an object to slide down 45° rough inclined plane is n times as it takes to slide down a perfectly smooth 45° incline plane. The coefficient…Laws of Motion
Q7594A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of…Laws of Motion
Q7692The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular…Magnetic Effects of Current and Magnetism
Q7916A fully loaded boeing aircraft has a mass of 5.4×10⁵ kg. Its total wing area is 500 m ². It is in level flight with a speed of 1080 km/h. If the density of…Properties of Solids and Liquids
Q8266The equation of a circle is given by x²+y²=a², where a is the radius. If the equation is modified to change the origin other than (0, 0), then find out the…Units and Measurements
Q8623Identify the correct statements from the following: A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative…Work, Energy and Power

Chemistry

Q2The denticity of the ligand present in the Fehling's reagent is _ _ _ _ _ _.Organic Compounds Containing Oxygen
Q4At 298 K N₂~(g)+3H₂~(g) ~2NH₃~(g),~K₁=4×10⁵ N₂~(g)+O₂~(g) ~2NO~(g),~K₂=1.6×10¹² H₂~(g)+1/2O₂~(g) ~H₂O~(g),~K₃=1.0×10⁻¹³ Based on above equilibria, then…Equilibrium
Q5For conversion of compound A → B, the rate constant of the reaction was found to be 4.6×10⁻⁵~L~mol⁻¹~s⁻¹. The order of the reaction is _ _ _ _ _ _.Chemical Kinetics
Q11The equilibrium constant for the reaction Zn(s)+Sn²⁺(aq) Zn²⁺(aq)+Sn(s) is 1×10²⁰ at 298 K. The magnitude of standard electrode potential of Sn/Sn²⁺ if E_ Z…Redox Reactions and Electrochemistry
Q13A solution of Cr O₅ in amyl alcohol has a _ _ _ _ _ colour.Organic Compounds Containing Oxygen
Q16Total number of acidic oxides among N₂O₃,NO₂,N₂O,Cl₂O₇,SO₂,CO,CaO,Na₂O and NO is _ _ _ _ _ _.Classification of Elements and Periodicity in Properties
Q18On heating, LiNO₃ gives how many compounds among the following _ _ _ _ _ Li₂O,N₂,O₂,LiNO₂,NO₂S Block Elements
Q19A metal M forms hexagonal close-packed structure. The total number of voids in 0.02 mol of it is _ _ _ _ _ × 10²¹ (Nearest integer). (Given N A =6.02×10²³)Solid State
Q21The volume of HCl, containing 73 g L ⁻¹, required to completely neutralise NaOH obtained by reacting 0.69 g of metallic sodium with water, is _ _ _ _ _ mL…Some Basic Concepts in Chemistry
Q22When 0.01 mol of an organic compound containing 60% carbon was burnt completely, 4.4 g of CO ₂ was produced. The molar mass of compound is _ _ _ _ _ _ g mol…Some Basic Concepts in Chemistry
Q24Assume that the radius of the first Bohr orbit of hydrogen atom is 0.6 A^(o). The radius of the third Bohr orbit of He ⁺ is _ _ _ _ _ picometer. (Nearest…Atomic Structure
Q379According to MO theory the bond orders for O ₂²⁻, CO and NO⁺ respectively, areChemical Bonding and Molecular Structure
Q537Reaction of propanamide with Br₂/KOH(aq) produces:Organic Compounds Containing Nitrogen
Q637Correct order of spin only magnetic moment of the following complex ions is: (Given At.no. Fe: 26, Co: 27)Coordination Compounds
Q785An indicator 'X' is used for studying the effect of variation in concentration of iodide on the rate of reaction of iodide ion with H₂O₂ at room temp. The…d- and f-Block Elements
Q894Given below are two statements: Statement I: Nickel is being used as the catalyst for producing syn gas and edible fats. Statement II: Silicon forms both…d- and f-Block Elements
Q895The set of correct statements is: (i) Manganese exhibits +7 oxidation state in its oxide. (ii) Ruthenium and Osmium exhibit +8 oxidation in their oxides…d- and f-Block Elements
Q1102The concentration of dissolved Oxygen in water for growth of fish should be more than X ppm and Biochemical Oxygen Demand in clean water should be less than Y…Environmental Chemistry
Q1428The major component of which of the following ore is sulphide based mineral?Isolation of Elements
Q1617Given below are two statements: Statement I: The decrease in first ionization enthalpy from B to Al is much larger than that from Al to Ga. Statement II: The…Classification of Elements and Periodicity in Properties
Q1705Match List I with List II List I List II A. Elastomeric polymer I. Urea formaldehyde resin B. Fibre Polymer II. Polystyrene C. Thermosetting Polymer III…Polymers
Q1972Match List I with List II List I List II A. van't Hoff factor, i I. Cryoscopic constant B. k f II. Isotonic solutions C. Solutions with same osmotic pressure…Solutions
Q2104When a hydrocarbon A undergoes combustion in the presence of air, it requires 9.5 equivalents of oxygen and produces 3 equivalents of water. What is the…Some Basic Concepts in Chemistry
Q2278Match List I and List II List I List II A. Osmosis I. Solvent molecules pass through semi permeable membrane towards solvent side. B. Reverse osmosis II…Surface Chemistry
Q2330Which of the following relations are correct? (A) Δ U=q+pΔ V (B) Δ G=Δ H-TΔ S (C) Δ S=(q rev)/T (D) Δ H=Δ U-Δ nRT Choose the most appropriate answer from the…Chemical Thermodynamics

Mathematics

Q30If the equation of the normal to the curve y = (x - a)/((x + b)(x - 2)) at the point (1, - 3) is x - 4y = 13, then the value of a + b is equal to _ _ _ _ _ _.Limit, Continuity and Differentiability
Q33A circle with centre (2, 3) and radius 4 intersects the line x+y=3 at the points P and Q. If the tangents at P and Q intersect at the point S(α,β), then 4α-7β…Coordinate Geometry
Q34Let α = 8 - 14i,A = z c:(α z - α z)/(z² - (z)² - 112i)=1 and B = z c:| z + 3i | = 4. Then Σ z A B (Re z - Im z) is equal to _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q41Let A be a symmetric matrix such that |A|=2 and [ 2 1 3 3/2 ]A = [ 1 2 α β ]. If the sum of the diagonal elements of A is s, then (β s)/(α²) is equal to _ _ _…Matrices and Determinants
Q43A triangle is formed by the tangents at the point (2, 2) on the curves y²=2x and x²+y²=4x, and the line x+y+2=0. If r is the radius of its circumcircle, then…Coordinate Geometry
Q45The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is _ _ _ _ _.Permutations and Combinations
Q48Let α₁,α₂,....,α₇ be the roots of the equation x⁷ + 3x⁵ - 13x³ - 15x = 0 and |α ₁| ≥ |α ₂| ≥... ≥ |α ₇|. Then α₁α₂-α₃α₄+α₅α₆ is equal to _ _ _ _ _.Complex Numbers and Quadratic Equations
Q49Let a k and b k,k N, be two G.P.s with common ratios r₁ and r₂ respectively such that a₁ = b₁ = 4 and r₁ < r₂. Let c k = a k + b k,k N. If c₂ = 5 and c₃ =…Sequence and Series
Q50Let a₁=b₁=1 and a n = a n - 1 + (n - 1),b n = b n - 1 + a n - 1, n ≥ 2. If S = Σ n = 1 ¹⁰ b n /(2ⁿ) and T = Σ n = 1 ⁸ n/(2ⁿ⁻¹), then 2⁷(2S - T) is equal to _…Sequence and Series
Q52Let X=\11,12,13,....,40,41 and Y=\61,62,63,....,90,91 be the two sets of observations. If x and y are their respective means and σ² is the variance of all the…Statistics and Probability
Q2460The plane 2x-y+z=4 intersects the line segment joining the points A (a,-2,4) and B (2,b,-3) at the point C in the ratio 2: 1 and the distance of the point C…Three Dimensional Geometry
Q2461If the lines (x - 1)/1 = (y - 2)/2 = (z + 3)/1 and (x - a)/2 = (y + 2)/3 = (z - 3)/1 intersect at the point P, then the distance of the point P from the plane…Three Dimensional Geometry
Q2510The shortest distance between the lines (x - 1)/2 = (y + 8)/(-7) = (z - 4)/5 and (x - 1)/2 = (y - 2)/1 = (z - 6)/(- 3) is:Three Dimensional Geometry
Q2854The area of the region A = (x,y):| cos x - sin x | ≤ y ≤ sin x,0 ≤ x ≤ (π)/2 isIntegral Calculus
Q2956Let K be the sum of the coefficients of the odd powers of x in the expansion of (1+x)⁹⁹. Let a be the middle term in the expansion of (2 + 1/(2))²⁰⁰. If…Binomial Theorem and Its Simple Applications
Q3453The value of the integral ∫₁² ((t⁴ + 1)/(t⁶ + 1))dt isIntegral Calculus
Q3454The value of the integral ∫ 1/2 ² (tan ⁻¹x)/xdx is equal to:Integral Calculus
Q3555Let y=y(x) be the solution of the differential equation x log e xdy/dx + y = x² log e x,(x > 1). If y(2) = 2, then y(e) is equal toDifferential Equations
Q3709Let f and g be the twice differentiable functions on R such that f''(x)=g''(x)+6x f'(1)=4g'(1)-3=9 f(2)=3g(2)=12. Then which of the following is NOT true?Limit, Continuity and Differentiability
Q3874Consider a function f:N, satisfying f(1)+2f(2)+3f(3)+....+xf(x)=x(x+1)f(x);x≥2 with f(1)=1. Then 1/(f(2022))+1/(f(2028)) is equal toSets, Relations and Functions
Q4539The set of all values of t R, for which the matrix [ e^(t) e^(- t)(sin t - 2 cos t) e^(- t)(- 2 sin t - cos t) e^(t) e^(- t)(2 sin t + cos t) e^(- t)(sin t…Matrices and Determinants
Q4755If the tangent at a point P on the parabola y²=3x is parallel to the line x+2y=1 and the tangents at the points Q and R on the ellipse (x²)/4+(y²)/1=1 are…Coordinate Geometry
Q4779The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is:Permutations and Combinations
Q4849The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the…Permutations and Combinations
Q5003Let S = w₁,w₂,...... be the sample space associated to a random experiment. Let P(w n) = (P(w n - 1))/2,n ≥ 2. Let A = 2k + 3l:k,l N and B = w n:n A. Then…Statistics and Probability
Q5389Let R be a relation defined on N as aRb if 2a+3b is a multiple of 5,a,b N. Then R isSets, Relations and Functions
Q5661The set of all values of λ for which the equation cos ²2x - 2 sin ⁴x - 2 cos ²x = λ has a real solution x, is:Trigonometry
Q5834If a = i + 2 k, b = i + j + k, c = 7 i - 3 j + 4 k, r × b + b × c = 0 and r. a = 0. Then r. c is equal to:Vector Algebra
Q5835Let a = 4 i + 3 j and b = 3 i - 4 j + 5 k. If c is a vector such that c.(a × b) + 25 = 0, c.(i + j + k) = 4, and projection of c on a is 1, then the…Vector Algebra