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

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JEE Main 202330 Jan, Morning shift

Physics 22Chemistry 24Mathematics 30

Physics

Q57A capacitor of capacitance 900 μ F is charged by a 100 ~V battery. The capacitor is disconnected from the battery and connected to another uncharged identical…Electrostatics
Q62A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of 24 ~W. The radius of curvature of…Electromagnetic Waves
Q66In an experiment for estimating the value of focal length of converging mirror, image of an object placed at 40 ~cm from the pole of the mirror is formed at…Optics
Q71A horse rider covers half the distance with 5 ~m / s speed. The remaining part of the distance was travelled with speed 10 ~m / s for half the time and with…Kinematics
Q74A thin uniform rod of length 2 ~m, cross sectional area ' A ' and density ' d ' is rotated about an axis passing through the centre and perpendicular to its…Rotational Motion
Q75The general displacement of a simple harmonic oscillator is x = A sin ω t. Let T be its time period. The slope of its potential energy (U) - time (t) curve…Oscillations and Waves
Q76In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by 0.5 ~mm on a complete rotation of the circular scale. The zero of…Units and Measurements
Q5916In a series LR circuit with X L =R, power factor P₁. If a capacitor of capacitance C with X C =X L is added to the circuit the power factor becomes P₂. The…Electromagnetic Induction and Alternating Currents
Q6017Speed of an electron in Bohr's 7^(th) orbit for Hydrogen atom is 3.6 × 10⁶ ~m / s. The corresponding speed of the electron in 3^(rd) orbit, in m / s is:Atoms and Nuclei
Q6250A ball of mass 200 ~g rests on a vertical post of height 20 ~m. A bullet of mass 10 ~g, travelling in horizontal direction, hits the centre of the ball. After…Rotational Motion
Q6372A sinusoidal carrier voltage is amplitude modulated. The resultant amplitude modulated wave has maximum and minimum amplitude of 120 ~V and 80 ~V…Communication Systems
Q6404The charge flowing in a conductor changes with time as Q(t)=α t-β t²+γ t³. Where α, β and γ are constants. Minimum value of current is:Current Electricity
Q6606A small object at rest, absorbs a light pulse of power 20 ~mW and duration 300 ~ns. Assuming speed of light as 3 × 10⁸ ~m / s, the momentum of the object…Dual Nature of Matter and Radiation
Q6931Two isolated metallic solid spheres of radii R and 2 R are charged such that both have same charge density σ. The spheres are then connected by a thin…Electrostatics
Q6973Electric field in a certain region is given by E=(A/(x²) i+B/(y³) j). The SI unit of A and B are:Electrostatics
Q7051A person has been using spectacles of power -1.0 dioptre for distant vision and a separate reading glass of power 2.0 dioptres. What is the least distance of…Optics
Q7236If the gravitational field in the space is given as (-K/(r²)). Taking the reference point to be at r=2 ~cm with gravitational potential V=10 ~J / kg. Find the…Gravitation
Q7413The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation PT²= constant. The volume expansion coefficient of the gas will be:Thermodynamics
Q7495Heat is given to an ideal gas in an isothermal process. A. Internal energy of the gas will decrease. B. Internal energy of the gas will increase. C. Internal…Thermodynamics
Q7729The magnetic moments associated with two closely wound circular coils A and B of radius r A =10 cm and r B =20 ~cm respectively are equal if: (Where N A, I A…Magnetic Effects of Current and Magnetism
Q7957Choose the correct relationship between Poisson ratio (σ), bulk modulus (K) and modulus of rigidity (η) of a given solid object:Properties of Solids and Liquids
Q8024The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, 5 ~cm. If the tube is dipped in a similar…Properties of Solids and Liquids

Chemistry

Q1A trisubstituted compound ' A ', C₁₀ H₁₂ O₂ gives neutral FeCl₃ test positive. Treatment of compound 'A' with NaOH and CH₃ Br gives C₁₁ H₁₄ O₂, with…Organic Compounds Containing Oxygen
Q5If compound A reacts with B following first order kinetics with rate constant 2.011 × 10⁻³ ~s⁻¹. The time taken by A (in seconds) to reduce from 7 ~g to 2 ~g…Chemical Kinetics
Q9The number of electrons involved in the reduction of permanganate to manganese dioxide in acidic medium is _ _ _ _ _ _ _.d- and f-Block Elements
Q10Consider the cell Pt (s) |H₂(~g, 1 ~atm)| H⁺(aq, 1 M)|| Fe³⁺(aq), Fe²⁺(aq) Pt(s) When the potential of the cell is 0.712 ~V at 298 ~K, the ratio [Fe²⁺]…Redox Reactions and Electrochemistry
Q12A 300 ~mL bottle of soft drink has 0.2 ~M~ CO₂ dissolved in it. Assuming CO₂ behaves as an ideal gas, the volume of the dissolved CO₂ at STP is _ _ _ _ _ _…Gaseous State
Q13600 ~mL of 0.01~M ~HCl is mixed with 400 ~mL of 0.01~M ~H₂ SO₄. The pH of the mixture is _ _ _ _ _ _ × 10⁻². (Nearest integer) [Given log 2=0.30 log 3=0.48…Equilibrium
Q20A solution containing 2 ~g of a non-volatile solute in 20 ~g of water boils at 373.52 ~K. The molecular mass of the solute is _ _ _ _ _ g ~mol⁻¹. (Nearest…Solutions
Q21Some amount of dichloromethane (CH₂ Cl₂) is added to 671.141 ~mL of chloroform (CHCl₃) to prepare 2.6 × 10⁻³ M solution of CH₂ Cl₂(DCM). The concentration of…Some Basic Concepts in Chemistry
Q22The energy of one mole of photons of radiation of frequency 2 × 10¹² ~Hz in J ~mol⁻¹ is _ _ _ _ _ _. (Nearest integer) [Given: h=6.626 × 10⁻³⁴ ~Js N A =6.022…Atomic Structure
Q24When 2 litre of ideal gas expands isothermally into vacuum to a total volume of 6 litre, the change in internal energy is _ _ _ _ _ _ J. (Nearest integer)Chemical Thermodynamics
Q182Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Ketoses give Seliwanoff's test faster…Biomolecules
Q255For OF₂ molecule consider the following: A. Number of lone pairs on oxygen is 2. B. FOF angle is less than 104.5^(°). C. Oxidation state of O is -2. D…Chemical Bonding and Molecular Structure
Q315Match List I with List II List I (molecules/ions) List II (No. of lone pairs of e ^(- o)n central atom) A. IF₇ I. Three B. ICl ₄^(- I)I. One C. XeF₆ III. Two…Chemical Bonding and Molecular Structure
Q567To inhibit the growth of tumours, identify the compounds used from the following: A. EDTA B. Coordination Compounds of Pt C. D - Penicillamine D. Cis - Platin…Coordination Compounds
Q636Which of the following is correct order of ligand field strength?Coordination Compounds
Q784During the qualitative analysis of SO₃²⁻ using dilute H₂ SO₄, SO₂ gas is evolved which turns K₂ Cr₂ O₇ solution (acidified with dilute H₂ SO₄):d- and f-Block Elements
Q1042Formation of photochemical smog involves the following reaction in which A, B and C are respectively. i. NO₂ h v A+B ii. B+O₂ → C iii. A+C → NO₂+O₂ Choose the…Environmental Chemistry
Q1403In the extraction of copper, its sulphide ore is heated in a reverberatory furnace after mixing with silica to:Isolation of Elements
Q1659Match List I with List II List I (Atomic number) List II (Block of periodic table) A. 37 I. p-block B. 78 II. d-block C. 52 III. f-block D. 65 IV. s-block…Classification of Elements and Periodicity in Properties
Q1704Caprolactam when heated at high temperature in presence of water, givesPolymers
Q1777In the wet tests for identification of various cations by precipitation, which transition element cation doesn't belong to group IV in qualitative inorganic…Principles Related to Practical Chemistry
Q1836Lithium aluminium hydride can be prepared from the reaction of:S Block Elements
Q1899The alkaline earth metal sulphate(s) which are readily soluble in water is/are: A. BeSO₄ B. MgSO₄ C. CaSO₄ D. SrSO₄ E. BaSO₄ Choose the correct answer from…S Block Elements
Q2277Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In expensive scientific instruments…Surface Chemistry

Mathematics

Q26If the equation of the plane passing through the point (1,1,2) and perpendicular to the line x-3 y+ 2 z-1=0=4 x-y+z is A x+B y+C z=1, then 140(C-B+A) is equal…Three Dimensional Geometry
Q27If λ₁ < λ₂ are two values of λ such that the angle between the planes P₁: r(3 i-5 j+k)=7 and P₂: r ·(λ i+j-3 k)=9 is sin ⁻¹((2 √(6))/5), then the square of…Three Dimensional Geometry
Q29Let α be the area of the larger region bounded by the curve y²=8 x and the lines y=x and x=2, which lies in the first quadrant. Then the value of 3 α is equal…Integral Calculus
Q33Let z=1+i and z₁=(1+i z)/(z(1-z)+1/z). Then 12/(π) arg (z₁) is equal to _ _ _ _ _.Complex Numbers and Quadratic Equations
Q34lim x → 0 48/(x⁴) ∫₀ˣ (t³)/(t⁶+1) ~d t is equal to _ _ _ _ _ _.Integral Calculus
Q37Let f¹(x)=(3 x+2)/(2 x+3), x R-\(-3)/2 For n ≥ 2, define fⁿ(x)=f¹ o fⁿ⁻¹(x). If f⁵(x)=(a x+b)/(b x+a), gcd(a, b)=1, then a+b is equal to _ _ _ _ _ _.Limit, Continuity and Differentiability
Q38Let S=\1,2,3,4,5,6. Then the number of one-one functions f: S → P(S), where P(S) denote the power set of S, such that f(n) f(~m) where n < m is _ _ _ _ _ _.Sets, Relations and Functions
Q45Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1, 2, 3 and 5, and are divisible by 15, is equal to _ _ _ _ _ _.Permutations and Combinations
Q49Let Σ n=0 ^(∞) (n³((2 n) !)+(2 n-1)(n !))/((n !)((2 n) !))=ae+b/e+c, where a, b, c Z and e=Σ n=0 ^(∞) 1/(n !) Then a²-b+c is equal to _ _ _ _ _ _.Sequence and Series
Q51The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and a and b are respectively mean and variance of…Statistics and Probability
Q2459The line l₁ passes through the point (2, 6, 2) and is perpendicular to the plane 2x+y-2z=10. Then the shortest distance between the line l₁ and the line…Three Dimensional Geometry
Q2790The number of points on the curve y=54 x⁵-135 x⁴-70 x³+180 x²+210 x at which the normal lines are parallel to x+90 y+2=0 is:Limit, Continuity and Differentiability
Q2939If the coefficient of x¹⁵ in the expansion of (a x³+1/(~b x^(1 / 3)))¹⁵ is equal to the coefficient of x⁻¹⁵ in the expansion of (a x^(1 / 3)-1/(b x³))¹⁵…Binomial Theorem and Its Simple Applications
Q3004The coefficient of x³⁰¹ in (1 + x)⁵⁰⁰ + x (1 + x)⁴⁹⁹ + x²(1 + x)⁴⁹⁸ +... + x⁵⁰⁰ is:Binomial Theorem and Its Simple Applications
Q3139Let y=x+2,4y=3x+6 and 3y=4x+1 be three tangent lines to the circle (x-h)²+(y-k)²=r². Then h+k is equal to:Coordinate Geometry
Q3452If [t] denotes the greatest integer ≤ t, then the value of (3(e - 1))/e∫₁² x²e^([x] + [x³])dx is:Integral Calculus
Q3554Let the solution curve y=y(x) of the differential equation (d y)/(~d x)-(3 x⁵ tan ⁻¹(x³))/((1+x⁶)^(3 / 2)) y=2 x exp \(x³- tan ⁻¹ x³)/(√((1+x⁶))) pass through…Differential Equations
Q4211Suppose f: R →(0, ∞) be a differentiable function such that 5 f(x+y)=f(x) · f(y), x, y R. If f(3)=320, then Σ n=0 ⁵ f(n) is equal to:Limit, Continuity and Differentiability
Q4304If the solution of the equation log cos x cot x+4 log sin x tan x=1, x (0, (π)/2), is sin ⁻¹((α+√(β))/2), where α, β are integers, then α+β is equal to:Limit, Continuity and Differentiability
Q4382Among the statements: (S 1)~((p q) ⇒ r) (p ⇒ r) (S 2)~((p q) ⇒ r) ((p ⇒ r) (q ⇒ r))Mathematical Reasoning
Q4538Let A=(ccm n p q), d=|A| ≠ 0 and |A-d(A d j A)|=0. ThenMatrices and Determinants
Q4620Let the system of linear equations x+y+kz=2 2x+3y-z=1 3x+4y+2z=k have infinitely many solutions. Then the system (k+1)x+(2k-1)y=7 (2k+1)x+(k+5)y=10 has:Matrices and Determinants
Q4714If P(h, k) be a point on the parabola x=4 y², which is nearest to the point Q(0,33), then the distance of P from the directrix of the parabola y²=4(x+y) is…Coordinate Geometry
Q4922If an unbiased die, marked with -2,-1,0,1,2,3 on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is:Statistics and Probability
Q5030A straight line cuts off the intercepts OA=a and OB=b on the positive directions of x -axis and y axis respectively. If the perpendicular from origin O to…Properties of Triangle
Q5341If a n = (- 2)/(4n² - 16n + 15), then a₁ + a₂ +.... + a₂₅ is equal to:Sequence and Series
Q5388The minimum number of elements that must be added to the relation R=\(a, b),(b, c) on the set, b, c so that it becomes symmetric and transitive is:Sets, Relations and Functions
Q5673If tan 15° + 1/(tan 75°) + 1/(tan 105°) + tan 195° = 2a, then the value of (a + 1/a) is:Trigonometry
Q5742If a, b, c are three non-zero vectors and n is a unit vector perpendicular to c such that a = α b - n,(α ≠ 0) and b. c = 12, then | c × (a × b) | is equal to:Vector Algebra
Q5833Let a unit vector O P make angles α, β, γ with the positive directions of the co-ordinate axes OX, OY, OZ respectively, where β (0, (π)/2). If OP is…Vector Algebra