JEE Main January 2024 Mathematics

JEE-Main Examination - January 2024

Mathematics

• Section A:
  • Question 1: 'k' values for Cr = (k^2 - 8)n Cr+1
  • Question 2: Distance of a point from a line
  • Question 3: Differential equations of x(t) and y(t)
  • Question 4: Orthocentre of a triangle
  • Question 5: Sum of coefficients in expansions of (1-3x+10x^2)^n and (1+x^2)^n
  • Question 6: Number of common terms in two arithmetic progressions
  • Question 7: Shortest distance of a parabola from a circle
  • Question 8: Shortest distance between two lines
  • Question 9: Value of 'd' in the equation ∫(x^2 + y^2) dx = a + b^2 + c^3
  • Question 10: Properties of a relation R in a set M
• Section B:
  • Question 11: Solution set of |z-i| = |z+i| = |z-1|
  • Question 12: Circle passing through four points
  • Question 13: Continuity of a function
  • Question 14: Standard deviation of a set of observations
  • Question 15: Length of a chord of an ellipse
  • Question 16: Tangent of an angle in a triangle
  • Question 17: Vector equation of a line
  • Question 18: Limit of a function as x approaches 0
  • Question 19: Properties of a matrix
  • Question 20: Function f(n) = highest prime factor of n
  • Question 21: Angle between two vectors
  • Question 22: Solution of a differential equation
  • Question 23: Solution of a differential equation
  • Question 24: Area of a region bounded by curves
  • Question 25: Value of 'p' in a geometric progression
  • Question 26: Probability of getting a six in repeated tosses of a die
  • Question 27: Solution of an equation in terms of 'p' and 'q'
  • Question 28: Value of a series
  • Question 29: Properties of a matrix
  • Question 30: Solution of an equation in terms of 'A', 'B', and 'C'
• Section A (continued):
  • Question 31: Position of an ant moving in the Y-Z plane
  • Question 32: Viscosity of gases and surface tension of liquids
  • Question 33: Refractive index of a prism
  • Question 34: Force on a proton in an electric and magnetic field
  • Question 35: Acceleration due to gravity on the surface of the earth
  • Question 36: Height of a rail to negotiate a curve
  • Question 37: Reverse-biased circuit
  • Question 38: (Not provided)
  • Question 39: (Not provided)
  • Question 40: (Not provided)

Physics

• Question 34: Electric and magnetic fields
• Question 35: Acceleration due to gravity on the surface of the earth
• Question 36: Height of a rail to negotiate a curve
• Question 37: Reverse-biased circuit
• Question 42: Magnetic field and a rectangular loopHere are the study notes for the text:

Physics

• A body of mass 1000 kg is moving horizontally with a velocity of 6 m/s. If 200 kg extra mass is added, the final velocity is [4 options].
• A plane electromagnetic wave propagating in the x-direction is described by Ey = (200 V/m) sin[1.5 x 10^7t - 0.05x]. The intensity of the wave is [4 options].
• A thin metallic wire having a cross-sectional area of 10^-4 m^2 is used to make a ring of radius 30 cm. A positive charge of 2π C is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the center of the ring. The tension in the ring is [answer].
• A wire of length 10 cm and radius 7 x 10^-4 m is connected across the right gap of a meter bridge. When a resistance of 4.5 Ω is connected on the left gap by using a resistance box, the balance length is found to be at 60 cm from the left end. If the resistivity of the wire is R x 10^-7 Ωm, then the value of R is [4 options].

Chemistry

• Element not showing variable oxidation state is [4 options].
• Highest enol content will be shown by [4 options].
• A solution of two miscible liquids showing negative deviation from Raoult's law will have [4 options].
• A complex ion has the highest magnetic moment if it has [4 options].
• Choose the polar molecule from the following: [4 options].
• The ascending order of acidity of –OH group in the following compounds is [4 options].
• Statement I: The 4f and 5f-series of elements are placed separately in the Periodic table top reserve the principle of classification. Statement II: S-block elements can be found in pure form in nature. [4 options].

Miscellaneous

• A wire of resistance R and length L is cut into 5 equal parts. If these parts are joined in parallel, then the resultant resistance will be [4 options].
• The average kinetic energy of a monatomic molecule is 0.414 eV at a temperature of [4 options].
• Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is [4 options].
• A convex lens of focal length 40 cm forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length 20 cm. The photoelectric current now is [4 options].
• An electric charge 10^-6 µC is placed at the origin of an X-Y co-ordinate system. Two points P and Q are situated at (3, 3) m and (6, 0) m respectively. The potential difference between the points P and Q will be [4 options].

Let me know if you want me to clarify anything!### Acidic/Basic Nature of Salt

• The acidic/basic nature of a salt depends on the Ka and Kb values of the acid and base forming it.
• A salt of a weak acid and weak base can have an acidic or basic nature.

SN1 and SN2 Reactions

• Racemisation occurs in SN1 reactions.
• Inversion occurs in SN2 reactions.

Electronic Configuration of Neodymium

• The atomic number of Neodymium is 60.
• The electronic configuration of Neodymium is [Xe] 4f4 6s2.

Displacement of Oxygen

• The mass of silver displaced by a quantity of electricity that displaces 5600 mL of O2 at S.T.P. is 11 g.

Reaction Kinetics

• The order of the reaction 2HI(g) → H2(g) + I2(g) is determined by the rate of reaction at different concentrations of HI.

Combustion of Methane

• The mass of methane required to produce 22 g of CO2 after complete combustion is dependent on the molar masses of C, H, and O.

Thermodynamic Processes

• Three moles of an ideal gas at 300 K expand isothermally from 30 dm3 to 45 dm3 against a constant opposing pressure of 80 kPa.
• The amount of heat transferred in this process is dependent on the initial and final volumes of the gas.

Organic Compounds

• 3-Methylhex-2-ene reacts with HBr in the presence of peroxide to form an addition product.
• The number of possible stereoisomers for the product is dependent on the structure of 3-Methylhex-2-ene.

Bond Order

• The sum of bond order of CO and NO+ is a specific value.

Oxidation State of Sulphur

• The number of compounds with +4 oxidation state of Sulphur from the given list (SO3, H2SO3, SOCl2, SF4, BaSO4, H2S2O7) is specific.