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JEE Main 2024 8 Apr Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 20248 Apr, Evening shift

Physics 23Chemistry 25Mathematics 29

Physics

Q57An alternating emf E=110 √(2) sin 100 t volt is applied to a capacitor of 2 μ F, the rms value of current in the circuit is _ _ _ _ mA.Electromagnetic Induction and Alternating Currents
Q67The coercivity of a magnet is 5 × 10³ ~A / m. The amount of current required to be passed in a solenoid of length 30 ~cm and the number of turns 150, so that…Magnetic Effects of Current and Magnetism
Q70A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of 100 ~m from the foot of the…Kinematics
Q71Small water droplets of radius 0.01 ~mm are formed in the upper atmosphere and falling with a terminal velocity of 10 ~cm / s. Due to condensation, if 8 such…Properties of Solids and Liquids
Q73An object of mass 0.2 ~kg executes simple harmonic motion along x axis with frequency of (25/(π)) Hz. At the position x=0.04 ~m the object has kinetic energy…Oscillations and Waves
Q77Two slits are 1 ~mm apart and the screen is located 1 ~m away from the slits. A light of wavelength 500 ~nm is used. The width of each slit to obtain 10…Optics
Q5930A coil of negligible resistance is connected in series with 90 Ω resistor across 120 ~V, 60 ~Hz supply. A voltmeter reads 36 ~V across resistance. Inductance…Electromagnetic Induction and Alternating Currents
Q6065If M₀ is the mass of isotope ₅¹² B, M p and M n are the masses of proton and neutron, then nuclear binding energy of isotope is:Atoms and Nuclei
Q6066In a hypothetical fission reaction ₉₂ X²³⁶ → ₅₆ Y¹⁴¹+ ₃₆ Z⁹²+3 R The identity of emitted particles (R) is:Atoms and Nuclei
Q6163A capacitor has air as dielectric medium and two conducting plates of area 12 ~cm² and they are 0.6 ~cm apart. When a slab of dielectric having area 12 ~cm²…Electrostatics
Q6444Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be _ _ _ _ t o _…Current Electricity
Q6592A proton and an electron have the same de Broglie wavelength. If K p and K e be the kinetic energies of proton and electron respectively, then choose the…Dual Nature of Matter and Radiation
Q7286Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A is 3 v, the speed of B will be:Gravitation
Q7436Given below are two statements: Statement (I): The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement (II)…Kinetic Theory of Gases
Q7506A diatomic gas (γ=1.4) does 100 ~J of work in an isobaric expansion. The heat given to the gas is:Thermodynamics
Q7563A given object takes n times the time to slide down 45^(°) rough inclined plane as it takes the time to slide down an identical perfectly smooth 45^(°)…Laws of Motion
Q7662A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at…Magnetic Effects of Current and Magnetism
Q7808The angle of projection for a projectile to have same horizontal range and maximum height is:Kinematics
Q8062A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with…Rotational Motion
Q8284If ε o is the permittivity of free space and E is the electric field, then ε o E² has the dimensions:Units and Measurements
Q8339There are 100 divisions on the circular scale of a screw gauge of pitch 1 ~mm. With no measuring quantity in between the jaws, the zero of the circular scale…Experimental Skills
Q8365Least count of a vernier caliper is 1/(20 ~N) ~cm. The value of one division on the main scale is 1 ~mm. Then the number of divisions of main scale that…Experimental Skills
Q8513A plane progressive wave is given by y=2 cos 2 π(330 t-x) m. The frequency of the wave is:Oscillations and Waves

Chemistry

Q2Two moles of benzaldehyde and one mole of acetone under alkaline conditions using aqueous NaOH after heating gives x as the major product. The number of π…Organic Compounds Containing Oxygen
Q4The total number of carbon atoms present in tyrosine, an amino acid, is _ _ _ _.Biomolecules
Q7Number of molecules having bond order 2 from the following molecules is _ _ _ _ _. C₂, O₂, Be₂, Li₂, Ne₂, ~N₂, He₂Chemical Bonding and Molecular Structure
Q12Total number of unpaired electrons in the complex ions [Co(NH₃)₆]³⁺ and [NiCl₄]²⁻ is _ _ _ _.Coordination Compounds
Q23A solution is prepared by adding 1 mole ethyl alcohol in 9 mole water. The mass percent of solute in the solution is _ _ _ _ (Integer answer) (Given: Molar…Some Basic Concepts in Chemistry
Q24Molality of an aqueous solution of urea is 4.44 ~m. Mole fraction of urea in solution is x × 10⁻³, Value of x is _ _ _ _. (Integer answer)Some Basic Concepts in Chemistry
Q25Wavenumber for a radiation having 5800 A^(o) wavelength is x × 10 ~cm⁻¹ The value of x is _ _ _ _. (Integer answer)Atomic Structure
Q26Δ vap H^() for water is +40.79 ~kJ ~mol⁻¹ at 1 bar and 100^(°) C. Change in internal energy for this vapourisation under same condition is _ _ _ _ kJ ~mol⁻¹…Chemical Thermodynamics
Q40Which one the following compounds will readily react with dilute NaOH ?Organic Compounds Containing Oxygen
Q77The correct sequence of acidic strength of the following aliphatic acids in their decreasing order is: CH₃ CH₂ COOH, CH₃ COOH, CH₃ CH₂ CH₂ COOH, HCOOHSome Basic Principles of Organic Chemistry
Q326The shape of carbocation is:Chemical Bonding and Molecular Structure
Q386When ψ A and ψ B are the wave functions of atomic orbitals, then σ^ is represented by:Chemical Bonding and Molecular Structure
Q502For a reaction A K₁ ~B K₂ C If the rate of formation of B is set to be zero then the concentration of B is given by:Chemical Kinetics
Q549Given below are two statements: Statement (I): All the following compounds react with p-toluenesulfonyl chloride. C₆ H₅ NH₂ (C₆ H₅)₂ NH (C₆ H₅)₃ N Statement…Organic Compounds Containing Nitrogen
Q554Given below are two statements: Statement (I): Kjeldahl method is applicable to estimate nitrogen in pyridine. Statement (II): The nitrogen present in…Organic Compounds Containing Nitrogen
Q955Given below are two statements: Statement (I): Fusion of MnO₂ with KOH and an oxidising agent gives dark green K₂ MnO₄. Statement (II): Manganate ion on…Redox Reactions and Electrochemistry
Q1009The emf of cell Tl| (0.001 M) Tl⁺ | (0.01 M) Cu²⁺ Cu is 0.83 ~V at 298 ~K. It could be increased by:Redox Reactions and Electrochemistry
Q1010The reaction; 1/2 H 2(~g) +AgCl (s) → H (aq) ⁺+Cl (aq) ⁻+Ag (s) occurs in which of the following galvanic cell:Redox Reactions and Electrochemistry
Q1182Given below are two statements: Statement (I): S N 2 reactions are 'stereospecific', indicating that they result in the formation of only one stereo-isomer as…Hydrocarbons
Q1316Given below are two statements: Statement (I): A Buffer solution is the mixture of a salt and an acid or a base mixed in any particular quantities Statement…Equilibrium
Q1317The equilibrium Cr₂ O₇²⁻ 2 CrO₄²⁻ is shifted to the right in:Equilibrium
Q1500Identify the incorrect statements about group 15 elements: (A) Dinitrogen is a diatomic gas which acts like an inert gas at room temperature. (B) The common…p-Block Elements
Q1501In qualitative test for identification of presence of phosphorous, the compound is heated with an oxidising agent. Which is further treated with nitric acid…p-Block Elements
Q1524Identify the correct statements about p-block elements and their compounds. (A) Non metals have higher electronegativity than metals. (B) Non metals have…p-Block Elements
Q1763Match List I with List II LIST I (Test) LIST II (Identification) A. Bayer's test I. Phenol B. Ceric ammonium nitrate test II. Aldehyde C. Phthalein dye test…Principles Related to Practical Chemistry

Mathematics

Q28Let P(α, β, γ) be the image of the point Q(1,6,4) in the line x/1=(y-1)/2=(z-2)/3. Then 2 α+β+γ is equal to _ _ _ _Three Dimensional Geometry
Q30Let A be the region enclosed by the parabola y²=2 x and the line x=24. Then the maximum area of the rectangle inscribed in the region A is _ _ _ _.Limit, Continuity and Differentiability
Q37Let α|x|=|y| e^(x y-β), α, β N be the solution of the differential equation x ~d y-y ~d x+x y(x ~d y+y ~d x)=0,y(1)=2. Then α+β is equal to _ _ _ _Differential Equations
Q39Let S be the focus of the hyperbola (x²)/3-(y²)/5=1, on the positive x -axis. Let C be the circle with its centre at A(√(6), √(5)) and passing through the…Coordinate Geometry
Q40If ∫ 1/(5√((x-1)⁴(x+3)⁶)) ~d x=A((α x-1)/(β x+3))^(B)+C, where C is the constant of integration, then the value of α+β+20 AB is _ _ _ _ _.Integral Calculus
Q42If α= lim x → 0⁺ ((e^(√(tan x))-e^(√(x)))/(√(tan x)-√(x))) and β= lim x → 0 (1+ sin x)^(1/2 cot x) are the roots of the quadratic equation a x²+b x-√(e)=0…Limit, Continuity and Differentiability
Q47The number of distinct real roots of the equation |x+1||x+3|-4|x+2|+5=0, is _ _ _ _Complex Numbers and Quadratic Equations
Q50Let a, b, c N and a< b< c. Let the mean, the mean deviation about the mean and the variance of the 5 observations 9,25, a, b, c be 18, 4 and 136/5…Statistics and Probability
Q52Let a ray of light passing through the point (3,10) reflects on the line 2 x+y=6 and the reflected ray passes through the point (7,2). If the equation of the…Coordinate Geometry
Q2537If the shortest distance between the lines (x-λ)/2=(y-4)/3=(z-3)/4 and (x-2)/4=(y-4)/6=(z-7)/8 is 13/(√(29)), then a value of λ is:Three Dimensional Geometry
Q2687If the function f(x)=2 x³-9 ax²+12 a² x+1, a> 0 has a local maximum at x=α and a local minimum at x=α², then α and α² are the roots of the equation:Limit, Continuity and Differentiability
Q2873The area of the region in the first quadrant inside the circle x²+y²=8 and outside the parabola y²=2 x is equal to:Integral Calculus
Q2948If the term independent of x in the expansion of (√(a) x²+1/(2 x³))¹⁰ is 105, then a² is equal to:Binomial Theorem and Its Simple Applications
Q3030If the image of the point (-4,5) in the line x+2 y=2 lies on the circle (x+4)²+(y-3)²=r², then r is equal to:Coordinate Geometry
Q3170The sum of all possible values of θ [-π, 2 π], for which (1+i cos θ)/(1-2 i cos θ) is purely imaginary, is equal to:Complex Numbers and Quadratic Equations
Q3483Let ∫_α^(log e 4) (d x)/(√(eˣ-1))=(π)/6. Then e^α and e^(-α) are the roots of the equation:Integral Calculus
Q3649Let y=y(x) be the solution curve of the differential equation sec y (d y)/(~d x)+2 x sin y=x³ cos y, y(1)=0. Then y(√(3)) is equal to:Differential Equations
Q3855Let f(x)=\ ccc-a if -a ≤ x ≤ 0 x+a if 0< x ≤ a. where a> 0 and g(x)=(f(|x|)-|f(x)|) / 2. Then the function g:[-a, a] →[-a, a] isSets, Relations and Functions
Q4165For a, b>0, let f(x)= (tan ((a+1) x)+b tan x)/x, x< 0 3, x=0 (√(a x+b² x²)-√(a x))/(~b √(a) x √(x)), x> 0 be a continuous function at x=0. Then b/a is equal to:Limit, Continuity and Differentiability
Q4547If α ≠ a, β ≠ b, γ ≠ c and | lllα b c a β c a b γ |=0, then a/(α-a)+b/(β-b)+(γ)/(γ-c) is equal to:Matrices and Determinants
Q4639If the system of equations x+4 y-z=λ, 7 x+9 y+μ z=-3,5 x+y+2 z=-1 has infinitely many solutions, then (2 μ+3 λ) is equal to:Matrices and Determinants
Q4783The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal…Permutations and Combinations
Q4865There are three bags X, Y and Z. Bag X contains 5 one-rupee coins and 4 five-rupee coins; Bag Y contains 4 one-rupee coins and 5 five-rupee coins and Bag Z…Statistics and Probability
Q5276In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 70/3 and the product of the third and fifth terms is 49…Sequence and Series
Q5396Let A=\2,3,6,8,9,11 and B=\1,4,5,10,15. Let R be a relation on A × B defined by (a, b) R(c, d) if and only if 3 a d-7 b c is an even integer. Then the…Sets, Relations and Functions
Q5506If the line segment joining the points (5,2) and (2, a) subtends an angle (π)/4 at the origin, then the absolute value of the product of all possible values…Coordinate Geometry
Q5675If the value of (3 cos 36^(°)+5 sin 18^(°))/(5 cos 36^(°)-3 sin 18^(°)) is (a √(5)-b)/c, where a, b, c are natural numbers and gcd(a, c)=1, then a+b+c is…Trigonometry
Q5788Let a=i+2 j+3 k, b=2 i+3 j-5 k and c=3 i-j+λ k be three vectors. Let r be a unit vector along b+c. If r · a=3, then 3 λ is equal to:Vector Algebra
Q5856Let a=4 i-j+k, b=11 i-j+k and c be a vector such that (a+b) × c=c ×(-2 a+3 b). If (2 a+3 b) · c=1670, then |c|² is equal to:Vector Algebra