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JEE Main 2024 4 Apr Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 20244 Apr, Morning shift

Physics 22Chemistry 23Mathematics 30

Physics

Q55A alternating current at any instant is given by i=[6+√(56) sin (100 π t+π / 3)] A. The r m s value of the current is _ _ _ A.Electromagnetic Induction and Alternating Currents
Q56A hydrogen atom changes its state from n=3 to n=2. Due to recoil, the percentage change in the wave length of emitted light is approximately 1 × 10⁻ⁿ. The…Atoms and Nuclei
Q60An infinite plane sheet of charge having uniform surface charge density +σ s C / m² is placed on x - y plane. Another infinitely long line charge having…Electrostatics
Q66Two forces F₁ and F₂ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of…Laws of Motion
Q70An elastic spring under tension of 3 ~N has a length a. Its length is b under tension 2 ~N. For its length (3 a-2 b), the value of tension will be _ _ _ N.Properties of Solids and Liquids
Q71A soap bubble is blown to a diameter of 7 ~cm. 36960 ~erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/ cm then the…Properties of Solids and Liquids
Q72A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed v. The sphere and the cylinder reaches upto…Rotational Motion
Q74Two wavelengths λ₁ and λ₂ are used in Young's double slit experiment. λ₁=450 ~nm and λ₂=650 ~nm. The minimum order of fringe produced by λ₂ which overlaps…Optics
Q5929In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to: A. pure…Electromagnetic Induction and Alternating Currents
Q6064Which of the following nuclear fragments corresponding to nuclear fission between neutron (₀¹ n) and uranium isotope (₉₂²³⁵ U) is correct:Atoms and Nuclei
Q6505To measure the internal resistance of a battery, potentiometer is used. For R=10 Ω, the balance point is observed at l=500 ~cm and for R=1 Ω the balance point…Current Electricity
Q6827The electric field in an electromagnetic wave is given by E=i 40 cos ω(t-z / c) NC⁻¹. The magnetic field induction of this wave is (in SI unit):Electromagnetic Waves
Q7056An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is 25 D. Focal length of each of the…Optics
Q7057In an experiment to measure focal length (f) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of…Optics
Q7285A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the…Gravitation
Q7348On celcius scale the temperature of body increases by 40^(°) C. The increase in temperature on Fahrenheit scale is:Thermodynamics
Q7525The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are 8 Ω and 10 Ω respectively. After inserting in a…Properties of Solids and Liquids
Q7767An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then:Magnetic Effects of Current and Magnetism
Q7807The co-ordinates of a particle moving in x - y plane are given by: x=2+4 t, y=3 t+8 t². The motion of the particle is:Kinematics
Q7853A body travels 102.5 ~m in n^(th) second and 115.0 ~m in (n+2)^(th) second. The acceleration is:Kinematics
Q8282The equation of stationary wave is: y=2 a sin ((2 π nt)/(λ)) cos ((2 π x)/(λ)). Which of the following is NOT correct:Units and Measurements
Q8595If a rubber ball falls from a height h and rebounds upto the height of h / 2. The percentage loss of total energy of the initial system as well as velocity…Work, Energy and Power

Chemistry

Q4The number of different chain isomers for C ₇ H ₁₆ is _ _ _ _ _.Some Basic Principles of Organic Chemistry
Q7Number of molecules/species from the following having one unpaired electron is _ _ _ _. O₂, O₂⁻¹, NO, CN⁻¹, O₂²⁻Chemical Bonding and Molecular Structure
Q11Consider the following reaction MnO₂+KOH+O₂ → A+H₂ O. Product ' A ' in neutral or acidic medium disproportionate to give products ' B ' and ' C ' along with…d- and f-Block Elements
Q18Only 2 ~mL of KMnO₄ solution of unknown molarity is required to reach the end point of a titration of 20 ~mL of oxalic acid (2 M) in acidic medium. The…Redox Reactions and Electrochemistry
Q192.5 ~g of a non-volatile, non-electrolyte is dissolved in 100 ~g of water at 25^(°) C. The solution showed a boiling point elevation by 2^(°) C. Assuming the…Solutions
Q21Xg of ethylamine is subjected to reaction with NaNO₂ / HCl followed by water; evolved dinitrogen gas which occupied 2.24 ~L volume at STP. X is _ _ _ _ _ ×…Some Basic Concepts in Chemistry
Q22The de-Broglie's wavelength of an electron in the 4^(th) orbit is _ _ _ _ π a₀. (a₀= Bohr's radius)Atomic Structure
Q23The enthalpy of formation of ethane (C₂ H₆) from ethylene by addition of hydrogen where the bond-energies of C-H, C-C, C=C, H-H are 414 ~kJ, 347 ~kJ, 615 ~kJ…Chemical Thermodynamics
Q50Given below are two statements: Statements I: Acidity of α -hydrogens of aldehydes and ketones is responsible for Aldol reaction. Statement II: Reaction…Organic Compounds Containing Oxygen
Q76What will be the decreasing order of basic strength of the following conjugate bases? ⁻ OH, R O, CH₃ CO O, ClSome Basic Principles of Organic Chemistry
Q90Which among the following is incorrect statement?Some Basic Principles of Organic Chemistry
Q272Which one of the following molecules has maximum dipole moment?Chemical Bonding and Molecular Structure
Q324Number of molecules/ions from the following in which the central atom is involved in sp³ hybridization is _ _ _ _. NO₃⁻, BCl₃, ClO₂⁻, ClO₃⁻Chemical Bonding and Molecular Structure
Q553Which of the following nitrogen containing compound does not give Lassaigne's test ?Organic Compounds Containing Nitrogen
Q655Number of complexes from the following with even number of unpaired " d " electrons is _ _ _ _ [V(H₂ O)₆]³⁺,[Cr(H₂ O)₆]²⁺,[Fe(H₂ O)₆]³⁺,[Ni(H₂ O)₆]³⁺,[Cu(H₂…Coordination Compounds
Q656The correct sequence of ligands in the order of decreasing field strength is:Coordination Compounds
Q906The element which shows only one oxidation state other than its elemental form is:d- and f-Block Elements
Q1007One of the commonly used electrode is calomel electrode. Under which of the following categories, calomel electrode comes?Redox Reactions and Electrochemistry
Q1008What pressure (bar) of H₂ would be required to make emf of hydrogen electrode zero in pure water at 25^(°) C ?Redox Reactions and Electrochemistry
Q1624The correct order of first ionization enthalpy values of the following elements is: (A) O (B) N (C) Be (D) F (E) B Choose the correct answer from the options…Classification of Elements and Periodicity in Properties
Q1667Number of elements from the following that CANNOT form compounds with valencies which match with their respective group valencies is _ _ _ _. B, C, N, S, O…Classification of Elements and Periodicity in Properties
Q1782In the precipitation of the iron group (III) in qualitative analysis, ammonium chloride is added before adding ammonium hydroxide to:Principles Related to Practical Chemistry
Q2052The Molarity (M) of an aqueous solution containing 5.85 ~g of NaCl in 500 ~mL water is: (Given: Molar Mass Na: 23 and Cl: 35.5 ~gmol⁻¹)Some Basic Concepts in Chemistry

Mathematics

Q28Let a=1+(² C₂)/(3 !)+(³ C₂)/(4 !)+(⁴ C₂)/(5 !)+...., b=1+(¹ C₀+ ¹ C₁)/(1 !)+(² C₀+ ² C₁+ ² C₂)/(2 !)+(³ C₀+ ³ C₁+ ³ C₂+ ³ C₃)/(3 !)+.... Then (2 b)/(a²) is…Binomial Theorem and Its Simple Applications
Q32If the shortest distance between the lines (x+2)/2=(y+3)/3=(z-5)/4 and (x-3)/1=(y-2)/(-3)=(z+4)/2 is 38/(3 √(5)) k, and ∫₀^(k)[x²] d x=α-√(α), where [x]…Integral Calculus
Q33If ∫₀^((π)/4) (sin ² x)/(1+ sin x cos x) ~d x=1/a log e (a/3)+(π)/(b √(3)), where a, b N, then a+b is equal to _ _ _ _ _.Integral Calculus
Q34Let the solution y=y(x) of the differential equation (d y)/(~d x)-y=1+4 sin x satisfy y(π)=1. Then y((π)/2)+10 is equal to _ _ _ _ _.Differential Equations
Q39If lim x → 1 ((5 x+1)^(1 / 3)-(x+5)^(1 / 3))/((2 x+3)^(1 / 2)-(x+4)^(1 / 2))=(m √(5))/(n(2 n)^(2 / 3)), where gcd(m, n)=1, then 8 ~m+12 n is equal to _ _ _ _.Limit, Continuity and Differentiability
Q41Let A be a 3 × 3 matrix of non-negative real elements such that A[ l1 1 1 ]=3[ l1 1 1 ]. Then the maximum value of det(A) is _ _ _ _ _.Matrices and Determinants
Q43Let A be a square matrix of order 2 such that |A|=2 and the sum of its diagonal elements is - 3. If the points (x, y) satisfying A²+x ~A+y I=O lie on a…Matrices and Determinants
Q44Let the length of the focal chord PQ of the parabola y²=12 x be 15 units. If the distance of PQ from the origin is p, then 10 p² is equal to _ _ _ _ _.Coordinate Geometry
Q49In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most…Sets, Relations and Functions
Q53Let ABC be a triangle of area 15 √(2) and the vectors AB=i+2 j-7 k, BC=a i+b j+c k and AC=6 i+d j-2 k, ~d>0. Then the square of the length of the largest side…Vector Algebra
Q2535Let the point, on the line passing through the points P(1,-2,3) and Q(5,-4,7), farther from the origin and at a distance of 9 units from the point P, be (α…Three Dimensional Geometry
Q2685Let the sum of the maximum and the minimum values of the function f(x)=(2 x²-3 x+8)/(2 x²+3 x+8) be m/n, where gcd(m, n)=1. Then m+n is equal to:Limit, Continuity and Differentiability
Q2871One of the points of intersection of the curves y=1+3 x-2 x² and y=1/x is (1/2, 2). Let the area of the region enclosed by these curves be 1/24(l √(5)+m)-n…Integral Calculus
Q2889The sum of all rational terms in the expansion of (2^(1/5)+5^(1/3))¹⁵ is equal to:Binomial Theorem and Its Simple Applications
Q3029A square is inscribed in the circle x²+y²-10 x-6 y+30=0. One side of this square is parallel to y=x+3. If (x i, y i) are the vertices of the square, then Σ(x…Coordinate Geometry
Q3169Let α and β be the sum and the product of all the non-zero solutions of the equation (z)²+|z|=0, z C. Then 4(α²+β²) is equal to:Complex Numbers and Quadratic Equations
Q3481Let f(x)=\ lr -2, -2 ≤ x ≤ 0 x-2, 0< x ≤ 2 and h(x)=f(|x|)+|f(x)|. Then ∫₋₂² ~h(x) d x. is equal to:Integral Calculus
Q3647If the solution y=y(x) of the differential equation (x⁴+2 x³+3 x²+2 x+2) d y-(2 x²+2 x+3) d x=0 satisfies y(-1)=-(π)/4, then y(0) is equal to:Differential Equations
Q3660Let f(x)=x⁵+2 e^(x / 4) for all x R. Consider a function g(x) such that (g° f)(x)=x for all x R. Then the value of 8 g^()(2) is:Limit, Continuity and Differentiability
Q4070If the domain of the function sin ⁻¹((3 x-22)/(2 x-19))+ log e ((3 x²-8 x+5)/(x²-3 x-10)) is (α, β], then 3 α+10 β is equal to:Trigonometry
Q4163Let f: R → R be a function given by f(x)= (1- cos 2 x)/(x²), x < 0 α, x=0, (β √(1- cos x))/x, x>0 where α, β R. If f is continuous at x=0, then α²+β² is equal…Limit, Continuity and Differentiability
Q4428Let α (0, ∞) and A=[ lll1 2 α 1 0 1 0 1 2 ]. If det(adj(2 A-A^(T)) · adj(A-2 A^(T)))=2⁸, then (det(A))² is equal to:Matrices and Determinants
Q4638If the system of equations x+(√(2) sin α) y+(√(2) cos α) z=0 x+(cos α) y+(sin α) z=0 x+(sin α) y-(cos α) z=0 has a non-trivial solution, then α (0, (π)/2) is…Matrices and Determinants
Q4836There are 5 points P₁, P₂, P₃, P₄, P₅ on the side A B, excluding A and B, of a triangle A B C. Similarly there are 6 points P₆, P₇,, P₁₁ on the side BC and 7…Permutations and Combinations
Q4864Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn…Statistics and Probability
Q5170If 2 and 6 are the roots of the equation a x²+b x+1=0, then the quadratic equation, whose roots are 1/(2 a+b) and 1/(6 a+b), is:Complex Numbers and Quadratic Equations
Q5275Let the first three terms 2, p and q, with q ≠ 2, of a G.P. be respectively the 7^(th), 8^(th) and 13^(th) terms of an A.P. If the 5^(th) term of the G.P. is…Sequence and Series
Q5496Let α, β R. Let the mean and the variance of 6 observations -3,4,7,-6, α, β be 2 and 23, respectively. The mean deviation about the mean of these 6…Statistics and Probability
Q5559The vertices of a triangle are A(-1,3), B(-2,2) and C(3,-1). A new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the…Coordinate Geometry
Q5786Let a unit vector which makes an angle of 60^(°) with 2 i+2 j-k and an angle of 45^(°) with i-k be C. Then C+(-1/2 i+1/(3 √(2)) j-(√(2))/3 k) is:Vector Algebra