JEE Main 2024 (Online) 4th April Morning Shift — Question Paper

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Physics

• Two forces F̅₁ and F̅₂ are acting on a body. One force has magnitude thrice that of the…
• Twelve wires each having resistance 2 Ω are joined to form a cube. A battery of 6 V emf…
• In an experiment to measure focal length (f) of convex lens, the least counts of the…
• The resistances of the platinum wire of a platinum resistance thermometer at the ice…
• The equation of stationary wave is : y=2a sin (2πnt/λ)cos ((2π x)/λ). Which of the…
• A body travels 102.5 m in nᵗʰ second and 115.0 m in (n+2)ᵗʰ second. The acceleration is :
• Which figure shows the correct variation of applied potential difference (V) with…
• The co-ordinates of a particle moving in x-y plane are given by : x=2+4 t, y=3 t+8 t²…
• A metal wire of uniform mass density having length L and mass M is bent to form a…
• The value of net resistance of the network as shown in the given figure is :
• Two wavelengths λ₁ and λ₂ are used in Young's double slit experiment. λ₁=450 nm and…
• An effective power of a combination of 5 identical convex lenses which are kept in…
• An infinitely long positively charged straight thread has a linear charge density λ…
• The electric field in an electromagnetic wave is given by E⃗=î 40 cos ω(t-z / c) NC⁻¹…
• To measure the internal resistance of a battery, potentiometer is used. For R=10 Ω, the…
• A hydrogen atom changes its state from n=3 to n=2. Due to recoil, the percentage change…
• The magnetic field existing in a region is given by B⃗=0.2(1+2 x) k̂. A square loop of…
• Given below are two statements : Statement I : When speed of liquid is zero everywhere…
• In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is…
• An electron is projected with uniform velocity along the axis inside a current carrying…
• P-T diagram of an ideal gas having three different densities ρ₁, ρ₂, ρ₃ (in three…
• An elastic spring under tension of 3 N has a length a. Its length is b under tension 2…
• Which of the following nuclear fragments corresponding to nuclear fission between…
• An infinite plane sheet of charge having uniform surface charge density +σₛ C / m² is…
• If a rubber ball falls from a height h and rebounds upto the height of h / 2. The…
• A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it…
• A alternating current at any instant is given by i=[6+√56 sin (100 π t+π / 3)] A. The r…
• A solid sphere and a hollow cylinder roll up without slipping on same inclined plane…
• On celcius scale the temperature of body increases by 40° C. The increase in temperature…

Chemistry

• Number of complexes from the following with even number of unpaired "d" electrons is…
• The enthalpy of formation of ethane (C₂ H₆) from ethylene by addition of hydrogen where…
• Which among the following is incorrect statement?
• Number of molecules/ions from the following in which the central atom is involved in sp³…
• Which of the following is the correct structure of L-Glucose?
• Consider the following reaction MnO₂+KOH+O₂ → A+H₂ O . Product 'A' in neutral or acidic…
• Which one of the following molecules has maximum dipole moment?
• The element which shows only one oxidation state other than its elemental form is :
• The Molarity (M) of an aqueous solution containing 5.85 g of NaCl in 500 mL water is…
• The correct order of first ionization enthalpy values of the following elements is : (A)…
• The de-Broglie's wavelength of an electron in the 4ᵗʰ orbit is ________ π a₀. (a₀=…
• What will be the decreasing order of basic strength of the following conjugate bases?…
• Number of elements from the following that CANNOT form compounds with valencies which…
• In the precipitation of the iron group (III) in qualitative analysis, ammonium chloride…
• One of the commonly used electrode is calomel electrode. Under which of the following…
• The correct sequence of ligands in the order of decreasing field strength is :
• Match List I with List II : LIST I Mechanism steps | LIST II Effect; A. | | I. | - E…
• Consider the following transformation involving first order elementary reaction in each…
• Given below are two statements : Statements I : Acidity of α-hydrogens of aldehydes and…
• Xg of ethylamine is subjected to reaction with NaNO₂ / HCl followed by water; evolved…
• Which of the following nitrogen containing compound does not give Lassaigne's test ?
• Only 2 mL of KMnO₄ solution of unknown molarity is required to reach the end point of a…
• Number of molecules/species from the following having one unpaired electron is ________…
• The number of different chain isomers for C₇H₁₆ is __________.
• The number of the correct reaction(s) among the following is _______.
• What pressure (bar) of H₂ would be required to make emf of hydrogen electrode zero in…
• 2.5 g of a non-volatile, non-electrolyte is dissolved in 100 g of water at 25° C. The…

Mathematics

• Let f: R → R be a function given by f(x)= (1-cos 2 x)/x², x < 0 ; α, x=0, ; (β √(1-cos…
• Let the solution y=y(x) of the differential equation (d y)/(d x)-y=1+4 sin x satisfy…
• If the domain of the function sin ⁻¹((3 x-22)/(2 x-19))+log ₑ((3 x²-8 x+5)/(x²-3 x-10))…
• If the shortest distance between the lines (x+2)/2=(y+3)/3=(z-5)/4 and…
• If the solution y=y(x) of the differential equation (x⁴+2 x³+3 x²+2 x+2) d y-(2 x²+2…
• Let a unit vector which makes an angle of 60° with 2 î+2 ĵ-k̂ and an angle of 45° with…
• Let α and β be the sum and the product of all the non-zero solutions of the equation…
• There are 5 points P₁, P₂, P₃, P₄, P₅ on the side A B, excluding A and B, of a triangle…
• Let ABC be a triangle of area 15 √2 and the vectors AB⃗=î+2 ĵ-7 k̂, BC⃗=a î+b ĵ+c k̂ and…
• Let A be a square matrix of order 2 such that |A|=2 and the sum of its diagonal elements…
• Let A be a 3 × 3 matrix of non-negative real elements such that A[1; 1; 1]=3[1; 1; 1]…
• Let f(x)=x⁵+2 e^(x / 4) for all x ∈ R. Consider a function g(x) such that (g ° f)(x)=x…
• Let the sum of the maximum and the minimum values of the function f(x)=(2 x²-3 x+8)/(2…
• Let the point, on the line passing through the points P(1,-2,3) and Q(5,-4,7), farther…
• If 2 and 6 are the roots of the equation a x²+b x+1=0, then the quadratic equation…
• If 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…
• The sum of all rational terms in the expansion of (2^(1/5)+5^(1/3))¹⁵ is equal to :
• Let the first three terms 2, p and q, with q ≠ 2, of a G.P. be respectively the 7ᵗʰ, 8ᵗʰ…
• If the system of equations x+(√2 sin α) y+(√2 cos α) z=0 ; x+(cos α) y+(sin α) z=0…
• Let α, β ∈ R. Let the mean and the variance of 6 observations -3,4,7,-6, α, β be 2 and…
• Let α ∈(0, ∞) and A=[1, 2, α; 1, 0, 1; 0, 1, 2]. If det(adj(2 A-Aᵀ) · adj(A-2 Aᵀ))=2⁸…
• If ∫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…
• One of the points of intersection of the curves y=1+3x-2x² and y=1/x is (1/2,2). Let the…
• The vertices of a triangle are A(-1,3),B(-2,2) and C(3,-1). A new triangle is formed by…
• In a survey of 220 students of a higher secondary school, it was found that at least 125…
• Let a=1+(² C₂)/(3 !)+(³ C₂)/(4 !)+(⁴ C₂)/(5 !)+...., b=1+(¹ C₀+ ¹ C₁)/(1 !)+(² C₀+ ² C₁+…
• Let the length of the focal chord PQ of the parabola y²=12 x be 15 units. If the…
• A square is inscribed in the circle x²+y²-10 x-6 y+30=0. One side of this square is…
• Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls…

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