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JEE Main 2023 31 Jan Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202331 Jan, Morning shift

Physics 24Chemistry 18Mathematics 30

Physics

Q53An inductor of 0.5 ~mH, a capacitor of 20 ~μ F and resistance of 20 ~Ω are connected in series with a 220 ~V ac source. If the current is in phase with the…Electromagnetic Induction and Alternating Currents
Q57Two identical cells, when connected either in parallel or in series gives same current in an external resistance 5 ~Ω. The internal resistance of each cell…Current Electricity
Q62In a medium the speed of light wave decreases to 0.2 times to its speed in free space The ratio of relative permittivity to the refractive index of the medium…Electromagnetic Waves
Q69The speed of a swimmer is 4 ~km ~h⁻¹ in still water. If the swimmer makes his strokes normal to the flow of river of width 1 ~km, he reaches a point 750 ~m…Kinematics
Q70A thin rod having a length of 1 ~m and area of cross-section 3 × 10⁻⁶ ~m² is suspended vertically from one end. The rod is cooled from 210^(°) C to 160^(°) C…Properties of Solids and Liquids
Q72A solid sphere of mass 1 ~kg rolls without slipping on a plane surface. Its kinetic energy is 7 × 10⁻³ ~J. The speed of the centre of mass of the sphere is _…Rotational Motion
Q75A lift of mass M=500 ~kg is descending with speed of 2 ~ms⁻¹. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of 2…Work, Energy and Power
Q5915If R, X L, and X C represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:Electromagnetic Induction and Alternating Currents
Q6127A free neutron decays into a proton but a free proton does not decay into neutron. This is becauseAtoms and Nuclei
Q6248100 balls each of mass m moving with speed v simultaneously strike a wall normally and reflected back with same speed, in time t ~s. The total force exerted…Rotational Motion
Q6370The amplitude of 15 sin (1000 π t) is modulated by 10 sin (4 π t) signal. The amplitude modulated signal contains frequency (ies) of A. 500 ~Hz B. 2 ~Hz C…Communication Systems
Q6403The drift velocity of electrons for a conductor connected in an electrical circuit is V d. The conductor in now replaced by another conductor with same…Current Electricity
Q6531Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R Assertion A: The beam of electrons show wave nature and…Dual Nature of Matter and Radiation
Q6605If a source of electromagnetic radiation having power 15 ~kW produces 10¹⁶ photons per second, the radiation belongs to a part of spectrum is. (Take Planck…Dual Nature of Matter and Radiation
Q6723Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the…Electromagnetic Induction and Alternating Currents
Q6882The effect of increase in temperature on the number of electrons in conduction band (n e) and resistance of a semiconductor will be as:Electronic Devices
Q7157At a certain depth "d " below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3 R above earth surface…Gravitation
Q7411The correct relation between γ = c p /c v and temperature T is:Thermodynamics
Q7615A bar magnet with a magnetic moment 5.0 Am² is placed in parallel position relative to a magnetic field of 0.4 ~T. The amount of required work done in turning…Magnetic Effects of Current and Magnetism
Q7728A rod with circular cross-section area 2 ~cm² and length 40 ~cm is wound uniformly with 400 turns of an insulated wire. If a current of 0.4 ~A flows in the…Magnetic Effects of Current and Magnetism
Q7798The initial speed of a projectile fired from ground is u. At the highest point during its motion, the speed of projectile is (√(3))/2 u. The time of flight of…Kinematics
Q8023If 1000 droplets of water of surface tension 0.07 ~N / m, having same radius 1 ~mm each, combine to from a single drop. In the process the released surface…Properties of Solids and Liquids
Q8169The maximum potential energy of a block executing simple harmonic motion is 25 ~J. A is amplitude of oscillation. At A / 2, the kinetic energy of the block isOscillations and Waves
Q8467Two polaroide A and B are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid C is placed between A…Optics

Chemistry

Q2For reaction: SO₂(~g)+1/2 O₂(~g) SO₃(~g) K p =2 × 10¹² at 27^(°) C and 1 ~atm pressure. The K c for the same reaction is _ _ _ _ _ _ × 10¹³. (Nearest integer)…Equilibrium
Q3A → B The rate constants of the above reaction at 200 K and 300 K are 0.03 min ⁻¹ and 0.05 min ⁻¹ respectively. The activation energy for the reaction is _ _…Chemical Kinetics
Q10The logarithm of equilibrium constant for the reaction Pd²⁺+4 Cl⁻ PdCl₄²⁻ is _ _ _ _ _ _ (Nearest integer) Given: (2.303 R ~T)/(~F)=0.06 ~V Pd (aq) ²⁺+2 e⁻…Redox Reactions and Electrochemistry
Q11The total pressure of a mixture of non-reacting gases X(0.6 ~g) and Y(0.45 ~g) in a vessel is 740 ~mm of Hg. The partial pressure of the gas X is _ _ _ m m of…Gaseous State
Q16The oxidation state of phosphorus in hypophosphoric acid is + _ _ _ _ _ _ _.Redox Reactions and Electrochemistry
Q17At 27^(°) C, a solution containing 2.5 ~g of solute in 250.0 ~mL of solution exerts an osmotic pressure of 400 ~Pa. The molar mass of the solute is _ _ _ _ _…Solutions
Q18Zinc reacts with hydrochloric acid to give hydrogen and zinc chloride. The volume of hydrogen gas produced at STP from the reaction of 11.5 ~g of zinc with…Some Basic Concepts in Chemistry
Q19On complete combustion, 0.492 ~g of an organic compound gave 0.792 ~g of CO₂. The% of carbon in the organic compound is _ _ _ _ _ _ (Nearest integer)Some Basic Concepts in Chemistry
Q21The enthalpy change for the conversion of 1/2 Cl₂(~g) to Cl⁻ (aq) is (-) _ _ _ _ _ k J mol⁻¹ (Nearest integer) Given: Δ dis H C l 2(~g) ^(θ)^()=240 ~kJ…Chemical Thermodynamics
Q516Which of the following artificial sweeteners has the highest sweetness value in comparison to cane sugar ?Chemistry in Everyday Life
Q781When Cu²⁺ ion is treated with KI, a white precipitate, X appears in solution. The solution is titrated with sodium thiosulphate, the compound Y is formed. X…d- and f-Block Elements
Q892Nd²⁺ = _ _ _ _ _d- and f-Block Elements
Q893The correct order of basicity of oxides of vanadium is:d- and f-Block Elements
Q950Which one of the following statements is correct for electrolysis of brine solution?Redox Reactions and Electrochemistry
Q1234H₂ O₂ acts as a reducing agent in:Hydrogen
Q1361The methods NOT involved in concentration of ore are A. Liquation B. Leaching C. Electrolysis D. Hydraulic washing E. Froth floatation Choose the correct…Isolation of Elements
Q1564The correct increasing order of the ionic radii isClassification of Elements and Periodicity in Properties
Q2167Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from n=4 to n=2 of He⁺ spectrumAtomic Structure

Mathematics

Q22Let the line L: (x-1)/2=(y+1)/(-1)=(z-3)/1 intersect the plane 2 x+y+3 z=16 at the point P. Let the point Q be the foot of perpendicular from the point…Three Dimensional Geometry
Q23Let θ be the angle between the planes P₁: r ·(i+j+2 k)=9 and P₂: r ·(2 i-j+k)=15. Let L be the line that meets P₂ at the point (4,-2,5) and makes an angle θ…Three Dimensional Geometry
Q26Let for x R, f(x)=(x+|x|)/2 and g(x)=\ cc x, x<0 x², x ≥ 0.. Then area bounded by the curve y=(f° g)(x) and the lines y=0,2 y-x=15 is equal to _ _ _ _ _.Integral Calculus
Q27The remainder on dividing 5⁹⁹ by 11 is _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q28Let α>0, be the smallest number such that the expansion of (x^(2/3)+2/(x³))³⁰ has a term β x^(-α), β N. Then α is equal to _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q42Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11, is equal to _ _ _ _ _ _.Permutations and Combinations
Q43Let 5 digit numbers be constructed using the digits 0,2,3,4,7,9 with repetition allowed, and are arranged in ascending order with serial numbers. Then the…Permutations and Combinations
Q46Let a₁, a₂,, a n be in A.P. If a₅=2 a₇ and a₁₁=18, then 12(1/(√(a₁₀)+√(a₁₁))+1/(√(a₁₁)+√(a₁₂))+ +1/(√(a₁₇)+√(a₁₈))) is equal to _ _ _ _ _ _.Sequence and Series
Q49If the variance of the frequency distribution x i | 2 | 3 | 4 | 5 | 6 | 7 | 8 Frequency f i | 3 | 6 | 16 | α | 9 | 5 | 6 is 3, then α is equal to _ _ _ _ _ _ _.Statistics and Probability
Q51Let a and b be two vectors such that |a|=√(14),|b|=√(6) and |a × b|=√(48). Then (a · b)² is equal to _ _ _ _ _ _.Vector Algebra
Q2509Let the shortest distance between the lines L: (x-5)/(-2)=(y-λ)/0=(z+λ)/1, λ ≥ 0 and L₁: x+1=y-1=4-z be 2 √(6). If (α, β, γ) lies on L, then which of the…Three Dimensional Geometry
Q2674A wire of length 20 ~m is to be cut into two pieces. A piece of length l₁ is bent to make a square of area A₁ and the other piece of length l₂ is made into a…Limit, Continuity and Differentiability
Q3075Let a circle C₁ be obtained on rolling the circle x²+y²-4 x-6 y+11=0 upwards 4 units on the tangent T to it at the point (3,2). Let C₂ be the image of C₁ in…Coordinate Geometry
Q3198For all z C on the curve C₁:|z|=4, let the locus of the point z+1/z be the curve C₂. Then:Complex Numbers and Quadratic Equations
Q3450Let α (0,1) and β = log e (1 - α). Let P n (x) = x + (x²)/2 + (x³)/3 +... + (xⁿ)/n,x (0,1). Then the integral ∫₀^α (t⁵⁰)/(1 - t)dt is equal toIntegral Calculus
Q3451The value of ∫ (π)/3 ^((π)/2) ((2+3 sin x))/(sin x(1+ cos x)) d x is equal to:Integral Calculus
Q3502Let a differentiable function f satisfy f(x)+∫₃ˣ (f(t))/t d t=√(x+1), x ≥ 3. Then 12 f(8) is equal to:Differential Equations
Q3673Let y=f(x)= sin ³((π)/3(cos ((π)/(3 √(2))(-4 x³+5 x²+1)^(3/2)))). Then, at x = 1,Limit, Continuity and Differentiability
Q3733If the maximum distance of normal to the ellipse (x²)/4+(y²)/(b²)=1, b < 2, from the origin is 1, then the eccentricity of the ellipse is:Coordinate Geometry
Q3893If the domain of the function f(x)=([x])/(1+x²), where [x] is greatest integer ≤ x, is [2,6), then its range isSets, Relations and Functions
Q4117If sin ⁻¹(α)/17 + cos ⁻¹4/5 - tan ⁻¹77/36 = 0,0 < α < 13, then sin ⁻¹(sin α) + cos ⁻¹(cos α) is equal to:Trigonometry
Q4381(S 1)~(p ⇒ q) (p (q)) is a tautology (S 2)~((p) ⇒(q)) ((p) q) is a contradiction. ThenMathematical Reasoning
Q4618For the system of linear equations x+y+z=6 α x+β y+7 z=3 x+2 y+3 z=14 which of the following is NOT true ?Matrices and Determinants
Q4655Let A = (1 0 0 0 4 - 1 0 12 - 3). Then the sum of the diagonal elements of the matrix (A + I)¹¹ is equal to:Matrices and Determinants
Q4754Let y=f(x) represent a parabola with focus (-1/2, 0) and directrix y=-1/2. Then S= R: tan ⁻¹(√(f(x)))+ sin ⁻¹(√(f(x)+1))=(π)/2:Coordinate Geometry
Q4862A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is:Statistics and Probability
Q5104The number of real roots of the equation √(x²-4 x+3)+√(x²-9)=√(4 x²-14 x+6), is:Complex Numbers and Quadratic Equations
Q5266If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296, respectively, then the sum of common ratios of all such GPs isSequence and Series
Q5387Let R be a relation on N × N defined by (a, b) ~R~(c, d) if and only if a d(b-c)=b c(a-d). Then R isSets, Relations and Functions
Q5781Let a=2 i+j+k, and b and c be two nonzero vectors such that |a+b+c|=|a+b-c| and b · c=0. Consider the following two statements: (A) |a+λ c| ≥|a| for all λ R…Vector Algebra