JEE Main 2023 (Online) 31st January Evening Shift — Question Paper

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Physics

• A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the breaking…
• Match List I with List II LIST I | LIST II ; A. | Angular momentum | I. | [ML² T⁻²]; B…
• The number of turns of the coil of a moving coil galvanometer is increased in order to…
• A ball is dropped from a height of 20 m. If the coefficient of restitution for the…
• A body of mass 10 kg is moving with an initial speed of 20 m / s. The body stops after 5…
• Under the same load, wire A having length 5.0 m and cross section 2.5 × 10⁻⁵ m²…
• The H amount of thermal energy is developed by a resistor in 10 s when a current of 4 A…
• If the binding energy of ground state electron in a hydrogen atom is 13.6 eV, then, the…
• Given below are two statements : Statement I: In a typical transistor, all three regions…
• An alternating voltage source V=260 sin (628 t ) is connected across a pure inductor of…
• A series LCR circuit consists of R=80 Ω, X_L=100 Ω, and X_C=40 Ω. The input voltage is…
• Two light waves of wavelengths 800 and 600 nm are used in Young's double slit experiment…
• For a solid rod, the Young's modulus of elasticity is 3.2 × 10¹¹ Nm⁻² and density is 8 ×…
• Two discs of same mass and different radii are made of different materials such that…
• Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant…
• A water heater of power 2000 W is used to heat water. The specific heat capacity of…
• The displacement equations of two interfering waves are given by y₁=10 sin (ω t+π/3) cm…
• A microscope is focused on an object at the bottom of a bucket. If liquid with…
• Two bodies are projected from ground with same speeds 40 ms⁻¹ at two different angles…
• A long conducting wire having a current I flowing through it, is bent into a circular…
• If the two metals A and B are exposed to radiation of wavelength 350 nm. The work…
• The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd…
• A body is moving with constant speed, in a circle of radius 10 m. The body completes one…
• For the given circuit, in the steady state, |V_B-V_D|= ________ V.
• A body weight W, is projected vertically upwards from earth's surface to reach a height…
• Considering a group of positive charges, which of the following statements is correct ?
• Match List I with List II LIST I | LIST II ; A. | Microwaves | I. | Physiotherapy; B. |…
• Two parallel plate capacitors C₁ and C₂ each having capacitance of 10 μ F are…
• A hypothetical gas expands adiabatically such that its volume changes from 08 litres to…

Chemistry

• In Dumas method for the estimation of N₂, the sample is heated with copper oxide and the…
• Given below are two statements : Statement I: Upon heating a borax bead dipped in cupric…
• Which of the following compounds are not used as disinfectants ? A. Chloroxylenol B…
• Evaluate the following statements for their correctness. A. The elevation in boiling…
• The number of molecules which gives the haloform test among the following molecules is…
• Cyclohexylamine when treated with nitrous acid yields (P). On treating (P) with PCC…
• A hydrocarbon ' X ' with formula C₆ H₈ uses two moles of H₂ on catalytic hydrogenation…
• The rate constant for a first order reaction is 20 min⁻¹. The time required for the…
• Amongst the following, the number of species having the linear shape is _________. XeF₂…
• When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen…
• The number of alkali metal(s), from Li, K, Cs, Rb having ionization enthalpy greater…
• A sample of a metal oxide has formula M_(0.83) O_(1.00). The metal M can exist in two…
• Match List I with List II LIST I | LIST II ; A. | Physisorption | I. | Single Layer…
• Given below are two statements : Statement I : H₂ O₂ is used in the synthesis of…
• The resistivity of a 0.8 M solution of an electrolyte is 5 × 10⁻³ Ω cm. Its molar…
• Which one of the following statements is incorrect?
• The element playing significant role in neuromuscular function and interneuronal…
• Assume carbon burns according to the following equation : 2 C₍ₛ₎+O_(2( g)) → 2 CO(g)…
• If the CFSE of [Ti(H₂ O)₆]³⁺ is -96.0 kJ / mol, this complex will absorb maximum at…
• The normal rain water is slightly acidic and its pH value is 5.6 because of which one of…
• At 298 K, the solubility of silver chloride in water is 1.434 × 10⁻³ g L⁻¹. The value of…
• In the following halogenated organic compounds, the one with the maximum number of…
• Enthalpies of formation of CCl₄( g), H₂ O(g), CO₂( g) and HCl(g) are -105,-242,-394 and…
• Arrange the following orbitals in decreasing order of energy. A. n=3, l=0, m=0 B. n=4…
• The Lewis acid character of boron tri halides follows the order :
• Which of the following elements have half-filled f-orbitals in their ground state?…
• An organic compound [A](C₄H₁₁ N), shows optical activity and gives N₂ gas on treatment…
• Compound A, C₅ H₁₀ O₅, given a tetraacetate with Ac₂ O and oxidation of A with Br₂-H₂ O…
• The incorrect statement for the use of indicators in acid-base titration is :

Mathematics

• Let A be the event that the absolute difference between two randomly choosen real…
• Let S be the set of all a ∈ N such that the area of the triangle formed by the tangent…
• The foot of perpendicular from the origin O to a plane P which meets the co-ordinate…
• The set of all values of a² for which the line x+y=0 bisects two distinct chords drawn…
• If φ(x)=1/√x ∫_(π/4)ˣ(4 √2 sin t-3 φ′(t)) d t, x>0, then ∅′(π/4) is equal to :
• The coefficient of x⁻⁶, in the expansion of ((4 x)/5+5/(2 x²))⁹, is
• Let the mean and standard deviation of marks of class A of 100 students be respectively…
• If ²ⁿ⁺¹ Pₙ₋₁: ²ⁿ⁻¹ Pₙ=11: 21, then n²+n+15 is equal to :
• If the constant term in the binomial expansion of (x^(5/2)/2-4/xˡ)⁹ is -84 and the…
• Let H be the hyperbola, whose foci are (1 ± √2, 0) and eccentricity is √2. Then the…
• Among the relations S={(a, b): a, b ∈ ℝ-{0}, 2+a/b>0} and T={(a, b): a, b ∈ ℝ, a²-b² ∈ ℤ},
• Let α>0. If ∫₀^α x/(√(x+α)-√x) d x=(16+20 √2)/15, then α is equal to :
• Let A=[aᵢⱼ], aᵢⱼ ∈ ℤ ∩[0,4], 1 ≤ i, j ≤ 2. The number of matrices A such that the sum of…
• Let A be a n × n matrix such that |A|=2. If the determinant of the matrix Adj(2 · Adj(2…
• The absolute minimum value, of the function f(x)=|x²-x+1|+[x²-x+1], where [t] denotes…
• Let P be the plane, passing through the point (1,-1,-5) and perpendicular to the line…
• If a point P(α, β, γ) satisfying ( α, β, γ )( 2, 10, 8; 9, 3, 8; 8, 4, 8 ) = ( 0, 0, 0 )…
• The sum 1²-2 · 3²+3 · 5²-4 · 7²+5 · 9²-…+15 · 29² is _________.
• Let a₁, a₂, a₃, … be an A.P. If a₇=3, the product a₁ a₄ is minimum and the sum of its…
• Let (a, b) ⊂(0,2 π) be the largest interval for which sin ⁻¹(sin θ)-cos ⁻¹(sin θ)>0, θ…
• Let a⃗=î+2 ĵ+3 k̂, b⃗=î-ĵ+2 k̂ and c⃗=5 î-3 ĵ+3 k̂ be three vectors. If r⃗ is a vector…
• Let a⃗, b⃗, c⃗ be three vectors such that |a⃗|=√31, 4|b⃗|=|c⃗|=2 and 2(a⃗ × b⃗)=3(c⃗ ×…
• Let y=y(x) be the solution of the differential equation (3 y²-5 x²) y d x+2 x(x²-y²) d…
• lim(x → ∞) ((√(3 x+1)+√(3 x-1))⁶+(√(3 x+1)-√(3 x-1))⁶)/((x+√(x²-1))⁶+(x-√(x²-1))⁶) x³
• The equation e⁴ˣ+8 e³ˣ+13 e²ˣ-8 eˣ+1=0, x ∈ ℝ has :
• The complex number z=(i-1)/(cos π/3+i sin π/3) is equal to :
• Let f: ℝ-{2,6} → ℝ be real valued function defined as f(x)=(x²+2 x+1)/(x²-8 x+12). Then…
• Let the area of the region {(x,y):|2x-1|≤ y≤ |x²-x|,0≤ x≤ 1} be A. Then (6 A+11)² is…
• Let the plane P: 8 x+α₁ y+α₂ z+12=0 be parallel to the line L: (x+2)/2=(y-3)/3=(z+4)/5…

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