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

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JEE Main 202329 Jan, Morning shift

Physics 25Chemistry 20Mathematics 30

Physics

Q52A radioactive element ₉₂²⁴² X emits two α -particles, one electron and two positrons. The product nucleus is represented by P ²³⁴ Y. The value of P is _ _ _ _…Atoms and Nuclei
Q56In a metre bridge experiment the balance point is obtained if the gaps are closed by 2 Ω and 3 Ω. A shunt of X Ω is added to 3 Ω resistor to shift the…Current Electricity
Q58A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0.8 T. When…Electromagnetic Induction and Alternating Currents
Q61A point charge q₁=4q₀ is placed at origin. Another point charge q₂=-q₀ is placed at x=12 cm. Charge of proton is q₀. The proton is placed on x axis so that…Electrostatics
Q66A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2s. The average…Kinematics
Q67A body cools from 60° C to 40° C in 6 minutes. If, temperature of surroundings is 10° C. Then, after the next 6 minutes, its temperature will be _ _ _ _ _ _° C.Properties of Solids and Liquids
Q70A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be _…Rotational Motion
Q73Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8…Oscillations and Waves
Q75A 0.4 kg mass takes 8s to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potential energy in the last second of fall…Work, Energy and Power
Q6130If a radioactive element having half-life of 30 ~min is undergoing beta decay, the fraction of radioactive element remains undecayed after 90 ~min. will beAtoms and Nuclei
Q6283A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34. [take…Kinematics
Q6324If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be: Given: Earth's radius =6.4×10⁶ mCommunication Systems
Q6438Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is:Current Electricity
Q6656The threshold wavelength for photoelectric emission from a material is 5500 A^(o). Photoelectrons will be emitted, when this material is illuminated with…Dual Nature of Matter and Radiation
Q6805Which of the following are true? A. Speed of light in vacuum is dependent on the direction of propagation. B. Speed of light in a medium is independent of the…Electromagnetic Waves
Q6883Which one of the following statement is not correct in the case of light emitting diodes? A. It is a heavily doped p-n junction. B. It emits light only when…Electronic Devices
Q6984In a cuboid of dimension 2 ~L × 2 ~L × L, a charge q is placed at the center of the surface ' S ' having area of 4 ~L². The flux through the opposite surface…Electrostatics
Q7277Two particles of equal mass ' m ' move in a circle of radius ' r ' under the action of their mutual gravitational attraction. The speed of each particle will…Gravitation
Q7535Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If d Q and d W represent the heat supplied…Thermodynamics
Q7560A block of mass m slides down the plane inclined at angle 30^(°) with an acceleration g/4. The value of coefficient of kinetic friction will be:Laws of Motion
Q7996A bicycle tyre is filled with air having pressure of 270 ~kPa at 27^(°) C. The approximate pressure of the air in the tyre when the temperature increases to…Properties of Solids and Liquids
Q8025Surface tension of a soap bubble is 2.0 × 10⁻² Nm⁻¹. Work done to increase the radius of soap bubble from 3.5 ~cm to 7 ~cm will be: Take [π=22/7]Properties of Solids and Liquids
Q8267Match List I with List II: List I (Physical Quantity) List II (Dimensional Formula) A. Pressure gradient I. [M^(°) L² ~T⁻²] B. Energy density II. [M¹ L⁻¹…Units and Measurements
Q8533A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of 30 ~m / s. If both trains emit sounds with…Oscillations and Waves
Q8590A stone is projected at angle 30^(°) to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest…Work, Energy and Power

Chemistry

Q4The number of molecules or ions from the following, which do not have odd number of electrons are _ _ _ _ _. (A) NO ₂ (B) ICl ₄^ - (C) BrF ₃ (D) ClO ₂ (E) NO…Chemical Bonding and Molecular Structure
Q6Water decomposes at 2300 K H₂O(g)→ H₂(g)+1/2O₂(g) The percent of water decomposing at 2300 K and 1 bar is _ _ _ _ _ _ (Nearest integer). Equilibrium constant…Equilibrium
Q7Consider the following reaction approaching equilibrium at 27° C and 1 atm pressure A+B 0pt k r = 10² ^(k f = 10³) C+D The standard Gibb's energy change (Δ r…Equilibrium
Q9The sum of bridging carbonyls in W(CO)₆ and Mn₂(CO)₁₀ is _ _ _ _ _ _.Coordination Compounds
Q14Millimoles of calcium hydroxide required to produce 100 mL of the aqueous solution of pH 12 is x×10⁻¹. The value of x is _ _ _ _ _ _ (Nearest integer). Assume…Equilibrium
Q18Solid Lead nitrate is dissolved in 1 litre of water. The solution was found to boil at 100.15° C. When 0.2 mol of NaCl is added to the resulting solution, it…Solutions
Q30The increasing order of pK a for the following phenols is (A) 2, 4 - Dinitrophenol (B) 4 - Nitrophenol (C) 2, 4, 5 - Trimethylphenol (D) Phenol (E)…Organic Compounds Containing Oxygen
Q214Number of cyclic tripeptides formed with 2 amino acids A and B is:Biomolecules
Q256The bond dissociation energy is highest forChemical Bonding and Molecular Structure
Q380The magnetic behaviour of Li₂O,Na₂O₂ and KO₂, respectively, are:Chemical Bonding and Molecular Structure
Q543Match List I with List II List I List II Reaction Reagents (A) Hoffmann Degradation (I) Conc. KOH, Δ (B) Clemenson reduction (II) CHCl₃,NaOH/H₃O ^ (C)…Organic Compounds Containing Nitrogen
Q691Chiral complex from the following is: Here en = ethylene diamineCoordination Compounds
Q1003The standard electrode potential (M³⁺/M²⁺) for V, Cr, Mn Co are - 0.26 V, - 0.41 V, + 1.57 V and + 1.97 V, respectively. The metal ions which can liberate H₂…Redox Reactions and Electrochemistry
Q1043Correct statement about smog is:Environmental Chemistry
Q1259Which of the given compounds can enhance the efficiency of hydrogen storage tank?Hydrogen
Q1446The reaction representing the Mond process for metal refining is _ _ _ _ _.Isolation of Elements
Q1757Compound that will give positive Lassaigne's test for both nitrogen and halogen is:Principles Related to Practical Chemistry
Q1900The correct order of hydration enthalpies is (A) K ⁺ (B) Rb ⁺ (C) Mg ²⁺ (D) Cs ⁺ (E) Ca ²⁺ Choose the correct answer from the options given below:S Block Elements
Q2168The shortest wavelength of hydrogen atom in Lyman series is λ. The longest wavelength is Balmer series of He ⁺ isAtomic Structure
Q2279Which of the following salt solutions would coagulate the colloid solution formed when FeCl₃ is added to NaOH solution, at the fastest rate?Surface Chemistry

Mathematics

Q21Let the equation of the plane P containing the line x+10=(8-y)/2=z be ax+by+3z=2(a+b) and the distance of the plane P from the point (1, 27, 7) be c. Then…Three Dimensional Geometry
Q22Let the co-ordinates of one vertex of Δ ABC be A(0,2,α) and the other two vertices lie on the line (x + α)/5 = (y - 1)/2 = (z + 4)/3. For α Z, if the area of…Three Dimensional Geometry
Q26Let the coefficients of three consecutive terms in the binomial expansion of (1+2x)ⁿ be in the ratio 2: 5: 8. Then the coefficient of the term, which is in…Binomial Theorem and Its Simple Applications
Q27If the co-efficient of x⁹ in (α x³ + 1/(β x))¹¹ and the co-efficient of x⁻⁹ in (α x - 1/(β x³))¹¹ are equal, then (αβ)² is equal to _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q32Let f:R be a differentiable function that satisfies the relation f(x+y)=f(x)+f(y)-1, x,y. If f'(0)=2, then |f(-2)| is equal to _ _ _ _ _ _.Limit, Continuity and Differentiability
Q35Suppose f is a function satisfying f(x + y) = f(x) + f(y) for all x,y N and f(1) = 1/5. If Σ n = 1 ^(m) (f(n))/(n(n + 1)(n + 2)) = 1/12, then m is equal to _…Sets, Relations and Functions
Q40If all the six digit numbers x₁ x₂ x₃ x₄ x₅ x₆ with 0< x₁ < x₂ < x₃ < x₄ < x₅ < x₆ are arranged in the increasing order, then the sum of the digits in the…Permutations and Combinations
Q41Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number…Permutations and Combinations
Q44Let a₁,a₂,a₃,... be a GP of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24, then…Sequence and Series
Q49Let a, b and c be three non-zero non-coplanar vectors. Let the position vectors of four points A,B,C and D be a - b + c,λ a - 3 b + 4 c, - a + 2 b - 3 c and 2…Vector Algebra
Q2855Let Δ be the area of the region (x,y) R²:x² + y² ≤ 21,y² ≤ 4x,x ≥ 1. Then 1/2(Δ - 21 sin ⁻¹2/(7)) is equal toIntegral Calculus
Q2856Let [x] denote the greatest integer ≤ x. Consider the function f(x) = max x²,1 + [x]. Then the value of the integral ∫₀² f(x)dx isIntegral Calculus
Q2857Let A=\(x, y) R²: y ≥ 0,2 x ≤ y ≤ √(4-(x-1)²) and B=\(x, y) R × R: 0 ≤ y ≤ min \2 x, √(4-(x-1)²).. Then the ratio of the area of A to the area of B isIntegral Calculus
Q3033Let the tangents at the points A(4,-11) and B(8,-5) on the circle x²+y²-3 x+10 y-15=0, intersect at the point C. Then the radius of the circle, whose centre…Coordinate Geometry
Q3160For two non-zero complex numbers z₁ and z₂, if Re(z₁ z₂)=0 and Re(z₁+z₂)=0, then which of the following are possible? A. Im(z₁)>0 and Im(z₂) > 0 B. Im(z₁) < 0…Complex Numbers and Quadratic Equations
Q3455Let f(x) = x + a/(π ² - 4) sin x + b/(π ² - 4) cos x,x R be a function which satisfies f(x) = x + ∫₀^(π /2) sin (x + y)f(y)dy. then (a+b) is equal toIntegral Calculus
Q3635Let y=f(x) be the solution of the differential equation y(x+1)dx-x²dy=0,y(1)=e. Then lim x → 0⁺ f(x) is equal toDifferential Equations
Q3808Let f:R → R be a function such that f(x) = (x² + 2x + 1)/(x² + 1). ThenSets, Relations and Functions
Q3845The domain of f(x) = (log (x + 1) (x - 2))/(e^(2 log e x) - (2x + 3)),x R isSets, Relations and Functions
Q4297Let x=2 be a root of the equation x²+px+q=0 and f(x) = \ (1 - cos (x² - 4px + q² + 8q + 16))/((x - 2p)⁴), x ≠ 2p 0, x = 2p. Then lim x → 2p⁺ [f(x)], where […Limit, Continuity and Differentiability
Q4383If p,q and r are three propositions, then which of the following combination of truth values of p,q and r makes the logical expression (p q) ((p) r) → ((q) r)…Mathematical Reasoning
Q4508Let α and β be real numbers. Consider a 3 × 3 matrix A such that A²=3A+α I. If A⁴=21A+β I, thenMatrices and Determinants
Q4621Consider the following system of equations α x+2y+z=1 2α x+3y+z=1 3x+α y+2z=β for some α,β R. Then which of the following is NOT correct.Matrices and Determinants
Q4990Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the…Statistics and Probability
Q5161Let λ ≠ 0 be a real number. Let α,β be the roots of the equation 14x² - 31x + 3λ = 0 and α,γ be the roots of the equation 35x² - 53x + 4λ = 0. Then (3α)/(β)…Complex Numbers and Quadratic Equations
Q5480Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the…Statistics and Probability
Q5525Let B and C be the two points on the line y+x=0 such that B and C are symmetric with respect to the origin. Suppose A is a point on y-2 x=2 such that A B C is…Coordinate Geometry
Q5620A light ray emits from the origin making an angle 30° with the positive x -axis. After getting reflected by the line x+y=1, if this ray intersects x -axis at…Coordinate Geometry
Q5656Let f(θ) = 3(sin ⁴((3π)/2 - θ) + sin ⁴(3π + θ)) - 2(1 - sin ²2θ) and S = θ [0,π ]:f'(θ) = - (3)/2. If 4β = Σ θ S θ, then f(β) is equal toTrigonometry
Q5782If the vectors a = λ i + μ j + 4 k, b = - 2 i + 4 j - 2 k and c = 2 i + 3 j + k are coplanar and the projection of a on the vector b is √(54) units, then the…Vector Algebra