JEE Main 2024 (Online) 1st February Morning Shift — Question Paper

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Physics

• A galvanometer has a resistance of 50 Ω and it allows maximum current of 5 mA. It can be…
• Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific…
• The reading in the ideal voltmeter (V) shown in the given circuit diagram is :
• The radius (r), length (l) and resistance (R) of a metal wire was measured in the…
• A particle is moving in one dimension (along x axis) under the action of a variable…
• A parallel plate capacitor has a capacitance C=200 pF. It is connected to 230 V ac…
• A monochromatic light of wavelength 6000 Å is incident on the single slit of width 0.01…
• A ball of mass 0.5 kg is attached to a string of length 50 cm. The ball is rotated on a…
• A rectangular loop of sides 12 cm and 5 cm, with its sides parallel to the x-axis and…
• A tuning fork resonates with a sonometer wire of length 1 m stretched with a tension of…
• 10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the…
• If R is the radius of the earth and the acceleration due to gravity on the surface of…
• With rise in temperature, the Young's modulus of elasticity :
• The de Broglie wavelengths of a proton and an α particle are λ and 2 λ respectively. The…
• Two identical charged spheres are suspended by strings of equal lengths. The strings…
• Two identical capacitors have same capacitance C. One of them is charged to the…
• A plane is in level flight at constant speed and each of its two wings has an area of 40…
• Three identical spheres each of mass 2 M are placed at the corners of a right angled…
• A particle moving in a circle of radius R with uniform speed takes time T to complete…
• In series LCR circuit, the capacitance is changed from C to 4 C. To keep the resonance…
• A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet…
• The distance between object and its 3 times magnified virtual image as produced by a…
• Consider a block and trolley system as shown in figure. If the coefficient of kinetic…
• The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another…
• The current in a conductor is expressed as I=3 t²+4 t³, where I is in Ampere and t is in…
• The minimum energy required by a hydrogen atom in ground state to emit radiation in…
• The pressure and volume of an ideal gas are related as PV^(3/2)=K (Constant). The work…
• In the given circuit if the power rating of Zener diode is 10 mW, the value of series…
• The dimensional formula of angular impulse is :

Chemistry

• The number of white coloured salts, among the following is (a) SrSO₄ (b) Mg(NH₄)PO₄ (c)…
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• Total number of deactivating groups in aromatic electrophilic substitution reaction…
• Kₐ for CH₃ COOH is 1.8 × 10⁻⁵ and K_b for NH₄ OH is 1.8 × 10⁻⁵. The pH of ammonium…
• The number of molecules/ion/s having trigonal bipyramidal shape is _______. PF₅, BrF₅…
• Given below are two statements : Statement (I) : The NH₂ group in Aniline is ortho and…
• In Kjeldahl's method for estimation of nitrogen, CuSO₄ acts as :
• Ionic reactions with organic compounds proceed through : (A) homolytic bond cleavage (B)…
• Given below are two statements : Statement (I) : A solution of [Ni(H₂ O)₆]²⁺ is green in…
• Choose the correct option for free expansion of an ideal gas under adiabatic condition…
• According to the wave-particle duality of matter by de-Broglie, which of the following…
• The potential for the given half cell at 298 K is (-) __________ × 10⁻² V 2 H_((aq))⁺+2…
• Among the following oxides of p-block elements, number of oxides having amphoteric…
• Which of the following reactions are disproportionation reactions? (A) Cu⁺ → Cu²⁺+Cu (B)…
• In acidic medium, K₂ Cr₂ O₇ shows oxidising action as represented in the half reaction…
• The ratio of (¹⁴ C)/(¹² C) in a piece of wood is 1/8 part that of atmosphere. If half…
• Given below are two statements : Statement (I) : Potassium hydrogen phthalate is a…
• Arrange the bonds in order of increasing ionic character in the molecules. LiF, K₂ O…
• Which of the following complex is homoleptic?
• We have three aqueous solutions of NaCl labelled as ' A ', ' B ' and ' C ' with…
• Number of optical isomers possible for 2-chlorobutane ________.
• Given below are two statements: one is labelled as Assertion (A ) and the other is…
• If one strand of a DNA has the sequence ATGCTTCA, sequence of the bases in complementary…
• In case of isoelectronic species the size of F⁻, Ne and Na⁺is affected by :
• Consider the following reaction : 3 PbCl₂+2(NH₄)₃ PO₄ → Pb₃(PO₄)₂+6 NH₄ Cl If 72 mmol of…
• The lowest oxidation number of an atom in a compound A₂ B is -2 . The number of…
• Given below are two statements : Statement (I) : Aminobenzene and aniline are same…
• Which of the following compound will most easily be attacked by an electrophile?

Mathematics

• Let S={x ∈ R:(√3+√2)ˣ+(√3-√2)ˣ=10}. Then the number of elements in S is :
• If 5 f(x)+4 f(1/x)=x²-2, ∀ x ≠ 0 and y=9 x² f(x), then y is strictly increasing in :
• The value of the integral ∫₀^(π / 4) (x d x)/(sin ⁴(2 x)+cos ⁴(2 x)) equals :
• Let y=y(x) be the solution of the differential equation (d y)/(d x)=2 x(x+y)³-x(x+y)-1…
• Let P={z ∈ ℂ:|z+2-3 i| ≤ 1} and Q={z ∈ ℂ: z(1+i)+z̄(1-i) ≤-8}. Let in P ∩ Q, |z-3+2 i|…
• Let the median and the mean deviation about the median of 7 observation…
• If the Coefficient of x³⁰ in the expansion of (1+1/x)⁶(1+x²)⁷(1-x³)⁸ ; x ≠ 0 is α, then…
• If the system of equations 2 x+3 y-z=5 ; ; x+α y+3 z=-4 ; ; 3 x-y+β z=7 has infinitely…
• Let a⃗=-5 î+ĵ-3 k̂, b⃗=î+2 ĵ-4 k̂ and c⃗=(((a⃗ × b⃗) × î) × î) × î. Then c⃗ ·(-î+ĵ+k̂)…
• If A=[√2, 1; -1, √2], B=[1, 0; 1, 1], C=ABAᵀ and X=Aᵀ C² A, then det X is equal to :
• The number of elements in the set S={(x, y, z): x, y, z ∈ Z, x+2 y+3 z=42, x, y, z ≥ 0}…
• Let S=|z ∈ C:| z-1 |=1 and (√2-1)(z+z̄)-i(z-z̄)=2 √2 |. Let z₁, z₂ ∈ S be such that…
• Let f: R → R and g: R → R be defined as f(x)={log ₑ x,, x>0; e⁻ˣ,, x ≤ 0 and g(x)={x,, x…
• If x=x(t) is the solution of the differential equation (t+1) d x=(2 x+(t+1)⁴) dt…
• Let 3,7,11,15, …, 403 and 2,5,8,11, …, 404 be two arithmetic progressions. Then the sum…
• Let C: x²+y²=4 and C′: x²+y²-4 λ x+9=0 be two circles. If the set of all values of λ so…
• Let A={1,2,3, …, 20}. Let R₁ and R₂ two relation on A such that R₁={(a, b): b is…
• Let f: R → R be defined as : f(x)= (a-b cos 2 x)/x² ; x<0 ; ; x²+c x+2 ; 0 ≤ x ≤ 1 ; ; 2…
• Let the line L: √2 x+y=α pass through the point of the intersection P (in the first…
• Let x²/a²+y²/b²=1, a>b be an ellipse, whose eccentricity is 1/√2 and the length of the…
• The area enclosed by the curves xy+4y=16 and x+y=6 is equal to :
• If the shortest distance between the lines (x-λ)/-2=(y-2)/1=(z-1)/1 and…
• Let the line of the shortest distance between the lines L₁: r⃗=(î+2 ĵ+3 k̂)+λ(î-ĵ+k̂)…
• For 0<θ<π / 2, if the eccentricity of the hyperbola x²-y² cosec² θ=5 is √7 times…
• Let 3, a, b, c be in A.P. and 3, a-1, b+1, c+9 be in G.P. Then, the arithmetic mean of…
• Let {x} denote the fractional part of x and f(x)=(cos ⁻¹(1-{x}²) sin…
• If ∫_(-π / 2)^(π / 2) (8 √2 cos x d x)/(1+eˢⁱⁿˣ)(1+sin ⁴ x)=α π+β log ₑ(3+2 √2), where…
• A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at…
• If n is the number of ways five different employees can sit into four indistinguishable…
• If tan A=1/√x(x²+x+1),tan B=√x/√(x²+x+1) and tan C=(x⁻³+x⁻²+x⁻¹)^(1/2),0<A,B,C<π/2, then…

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