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JEE Main 2023 30 Jan Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202330 Jan, Evening shift

Physics 18Chemistry 21Mathematics 29

Physics

Q51In an ac generator, a rectangular coil of 100 turns each having area 14 × 10⁻² ~m² is rotated at 360 ~rev / min about an axis perpendicular to a uniform…Electromagnetic Induction and Alternating Currents
Q53A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is 30 ~s. The effective…Atoms and Nuclei
Q55A stone tied to 180 ~cm long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is 1936/x…Kinematics
Q62A faulty thermometer reads 5^(°) C in melting ice and 95^(°) C in stream. The correct temperature on absolute scale will be _ _ _ _ _ K when the faulty…Thermodynamics
Q65The velocity of a particle executing SHM varies with displacement (x) as 4 v²=50-x². The time period of oscillations is x/7 s. The value of x is _ _ _ _ _ _…Oscillations and Waves
Q67In a Young's double slit experiment, the intensities at two points, for the path differences (λ)/4 and (λ)/3 (λ being the wavelength of light used) are I₁ and…Optics
Q68A body of mass 2 ~kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in 4 ~s is…Work, Energy and Power
Q6128Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: The nuclear density of nuclides ₅¹⁰ ~B, ₃⁶…Atoms and Nuclei
Q6249A machine gun of mass 10 ~kg fires 20 ~g bullets at the rate of 180 bullets per minute with a speed of 100 ~m ~s⁻¹ each. The recoil velocity of the gun isRotational Motion
Q6371Match List I with List II: List I List II A. Attenuation I. Combination of a receiver and transmitter. B. Transducer II. process of retrieval of information…Communication Systems
Q6579An electron accelerated through a potential difference V₁ has a de-Broglie wavelength of λ. When the potential is changed to V₂, its de-Broglie wavelength…Dual Nature of Matter and Radiation
Q6803A point source of 100 ~W emits light with 5% efficiency. At a distance of 5 ~m from the source, the intensity produced by the electric field component is:Electromagnetic Waves
Q7119A thin prism P₁ with an angle 6^(°) and made of glass of refractive index 1.54 is combined with another prism P₂ made from glass of refractive index 1.72 to…Optics
Q7235An object is allowed to fall from a height R above the earth, where R is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air…Gravitation
Q7412A flask contains hydrogen and oxygen in the ratio of 2: 1 by mass at temperature 27^(°) C. The ratio of average kinetic energy per molecule of hydrogen and…Kinetic Theory of Gases
Q7827A vehicle travels 4 ~km with speed of 3 ~km / h and another 4 ~km with speed of 5 ~km / h, then its average speed isKinematics
Q7956A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is 0.2 ~mm. If same force is applied to another steel…Properties of Solids and Liquids
Q8346Match List I with List II: List I List II A. Torque I. kg m⁻¹ ~s⁻² B. Energy density II. kg ms⁻¹ C. Pressure gradient III. kg m⁻² ~s⁻² D. Impulse IV. kg m²…Units and Measurements

Chemistry

Q2A short peptide on complete hydrolysis produces 3 moles of glycine (G), two moles of leucine (L) and two moles of valine (V) per mole of peptide. The number…Biomolecules
Q3Consider the following equation: 2 SO₂(g)+O₂(g) 2 SO₃(g), Δ H=-190 ~kJ The number of factors which will increase the yield of SO₃ at equilibrium from the…Equilibrium
Q4An organic compound undergoes first-order decomposition. If the time taken for the 60% decomposition is 540 ~s, then the time required for 90% decomposition…Chemical Kinetics
Q9The electrode potential of the following half cell at 298 ~K X|X²⁺(0.001 M) \| Y²⁺(0.01 M)| Y is _ _ _ _ × 10⁻² ~V (Nearest integer) Given: E⁰ X²⁺ X =-2.36 ~V…Redox Reactions and Electrochemistry
Q15Iron oxide FeO, crystallises in a cubic lattice with a unit cell edge length of 5.0 Å. If density of the FeO in the crystal is 4.0 ~g ~cm⁻³, then the number…Solid State
Q16Lead storage battery contains 38% by weight solution of H₂ SO₄. The van't Hoff factor is 2.67 at this concentration. The temperature in Kelvin at which the…Solutions
Q18The strength of 50 volume solution of hydrogen peroxide is _ _ _ g / L (Nearest integer). Given: Molar mass of H₂ O₂ is 34 ~g ~mol⁻¹ Molar volume of gas at…Some Basic Concepts in Chemistry
Q211 mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of 27^(°) C. The work done is 3 ~kJ ~mol⁻¹. The final temperature of…Chemical Thermodynamics
Q137Match List I with List II: List I (Mixture) List II (Separation Technique) A. CHCl₃+C₆ H₅ NH₂ I. Steam distillation B. C₆ H₁₄+C₅ H₁₂ II. Differential…Some Basic Principles of Organic Chemistry
Q690The Cl-Co-Cl bond angle values in a fac- [Co(NH₃)₃ Cl₃] complex is/are:Coordination Compounds
Q743Match List I with List II: List I (Complexes) List II (Hybridisation) A. [Ni(CO)₄] I. sp³ B. [Cu(NH₃)₄]²⁺ II. dsp ² C. [Fe(NH₃)₆]²⁺ III. sp³d² D. [Fe(H₂…Coordination Compounds
Q782Formulae for Nessler's reagent is:d- and f-Block Elements
Q783KMnO₄ oxidises I⁻ in acidic and neutral/faintly alkaline solutions, respectively, to:d- and f-Block Elements
Q1101The water quality of a pond was analyzed and its BOD was found to be 4. The pond has:Environmental Chemistry
Q1445Given below are two statements: Statement I: During Electrolytic refining, the pure metal is made to act as anode and its impure metallic form is used as…Isolation of Elements
Q1658Bond dissociation energy of "E-H" bond of the " H₂ E " hydrides of group 16 elements (given below), follows order. A. O B. S C. Se D. Te Choose the correct…Classification of Elements and Periodicity in Properties
Q1835Which of the following reaction is correct?S Block Elements
Q1898Chlorides of which metal are soluble in organic solvents:S Block Elements
Q20441 ~L, 0.02 M solution of [Co(NH₃)₅ SO₄] Br is mixed with 1 ~L, 0.02 M solution of [Co(NH₃)₅ Br] SO₄. The resulting solution is divided into two equal parts…Some Basic Concepts in Chemistry
Q2185The wave function (Ψ) of 2 ~s is given by Ψ 2 ~s =1/(2 √(2 π))(1/a₀)^(1 / 2)(2-r/a₀) e^(-r / 2 a₀) At r=r₀, radial node is formed. Thus, r₀ in terms of a₀Atomic Structure
Q2211Maximum number of electrons that can be accommodated in shell with n=4 are:Atomic Structure

Mathematics

Q24Let a line L pass through the point P(2,3,1) and be parallel to the line x+3 y-2 z-2=0=x-y+2 z. If the distance of L from the point (5,3,8) is α, then 3 α² is…Three Dimensional Geometry
Q27Let A be the area of the region \(x, y): y ≥ x², y ≥(1-x)², y ≤ 2 x(1-x). Then 540 ~A is equal to:Integral Calculus
Q2850^(th) root of a number x is 12 and 50^(th) root of another number y is 18. Then the remainder obtained on dividing (x+y) by 25 is _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q30Let P(a₁, b₁) and Q(a₂, b₂) be two distinct points on a circle with center C(√(2), √(3)). Let O be the origin and OC be perpendicular to both CP and CQ. If…Coordinate Geometry
Q33Let A=\1,2,3,5,8,9. Then the number of possible functions f: A → A such that f(m · n)=f(m) · f(n) for every m, n A with m · n A is equal to _ _ _ _ _ _.Sets, Relations and Functions
Q35If ∫ √(sec 2 x-1) d x=α log e | cos 2 x+β+√(cos 2 x(1+ cos 1/(β) x))|+ constant, then β-α is equal to _ _ _ _ _ _.Integral Calculus
Q43The number of seven digits odd numbers, that can be formed using all the seven digits 1, 2, 2, 2, 3, 3, 5 is _ _ _ _ _ _.Permutations and Combinations
Q44A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour…Statistics and Probability
Q45If the value of real number a>0 for which x²-5 a x+1=0 and x²-a x-5=0 have a common real root is 3/(√(2 β)) then β is equal to _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q47The 8^(th) common term of the series S₁=3+7+11+15+19+.. S₂=1+6+11+16+21+.. is:Sequence and Series
Q2457A vector v in the first octant is inclined to the x -axis at 60^(°), to the y -axis at 45 and to the z -axis at an acute angle. If a plane passing through the…Three Dimensional Geometry
Q2458If a plane passes through the points (-1, k, 0),(2, k,-1),(1,1,2) and is parallel to the line (x-1)/1=(2 y+1)/2=(z+1)/(-1), then the value of…Three Dimensional Geometry
Q2675If the functions f(x)=(x³)/3+2 b x+(a x²)/2 and g(x)=(x³)/3+a x+b x², a ≠ 2 b have a common extreme point, then a+2 b+7 is equal to:Limit, Continuity and Differentiability
Q2853Let q be the maximum integral value of p in [0,10] for which the roots of the equation x²-p x+5/4 p=0 are rational. Then the area of the region \(x, y): 0 ≤ y…Integral Calculus
Q2953Let x=(8 √(3)+13)¹³ and y=(7 √(2)+9)⁹. If [t] denotes the greatest integer ≤ t, then:Binomial Theorem and Its Simple Applications
Q3296lim n → ∞ 3/n\4+(2+1/n)²+(2+2/n)²+ +(3-1/n)² is equal to:Integral Calculus
Q3634The solution of the differential equation (d y)/(d x)=-((x²+3 y²)/(3 x²+y²)), y(1)=0 is:Differential Equations
Q3894The range of the function f(x)=√(3-x)+√(2+x) is:Sets, Relations and Functions
Q4296Let f, g and h be the real valued functions defined on R as f(x)=\ ccx/(|x|), x ≠ 0 1, x=0. g(x)=\ cc(sin (x+1))/((x+1)), x ≠-1 1, x=-1. and h(x)=2[x]-f(x)…Limit, Continuity and Differentiability
Q4422Consider the following statements: P: I have fever Q: I will not take medicine R: I will take rest. The statement "If I have fever, then I will take medicine…Mathematical Reasoning
Q4537If P is a 3 × 3 real matrix such that P^(T)=a P+(a-1) I, where a>1, then:Matrices and Determinants
Q4619For α, β R, suppose the system of linear equations x-y+z=5 2 x+2 y+α z=8 3 x-y+4 z=β has infinitely many solutions. Then α and β are the roots of:Matrices and Determinants
Q4690Let A be a point on the x -axis. Common tangents are drawn from A to the curves x²+y²=8 and y²=16 x. If one of these tangents touches the two curves at Q and…Coordinate Geometry
Q4700The parabolas: a x²+2 b x+c y=0 and d x²+2 e x+f y=0 intersect on the line y=1. If a, b, c, d, e, f are positive real numbers and a, b, c are in G.P., then:Coordinate Geometry
Q4778The number of ways of selecting two numbers a and b, a \2,4,6,., 100 and b \1,3,5,.., 99 such that 2 is the remainder when a+b is divided by 23 is:Permutations and Combinations
Q5267Let a, b, c>1, a³, b³ and c³ be in A.P., and log a b, log c a and log b c be in G.P. If the sum of first 20 terms of an A.P., whose first term is (a+4 b+c)/3…Sequence and Series
Q5479Let S be the set of all values of a₁ for which the mean deviation about the mean of 100 consecutive positive integers a₁, a₂, a₃,., a₁₀₀ is 25. Then S is:Statistics and Probability
Q5741Let λ R, a=λ i+2 j-3 k, b=i-λ j+2 k. If ((a+b) ×(a × b)) ×(a-b)=8 i-40 j-24 k, then |λ(a+b) ×(a-b)|² is equal to:Vector Algebra
Q5832Let a and b be two vectors, Let |a|=1,|b|=4 and a · b=2. If c=(2 a × b)-3 b, then the value of b · c is:Vector Algebra