JEE Main January 2024 Mathematics
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Questions and Answers

If A denotes the sum of all the coefficients in the expansion of (1 – 3x + 10x^2)^n and B denotes the sum of all the coefficients in the expansion of (1 + x^2)^n, then:

  • 3A = B
  • A = 3B (correct)
  • B = A
  • A = B^3

    • The number of common terms in the progressions 4, 9, 14, 19, ...... up to the 25th term and 3, 6, 9, 12, ...... up to 37th term is:

    7

    If the shortest distance of the parabola y^2 = 4x from the centre of the circle x^2 + y^2 – 4x – ______y + 64 = 0 is d, then d^2 is equal to:

    16

    If the shortest distance between the lines x − 4y + z = 0 and x − λy + z − 2 = 0 is trisected, then the sum of all possible values of λ is:

    <p>8</p> Signup and view all the answers

    If ∫(3 + x + 1/x + x^2) dx = a + b/2 + c/3, where a, b, c are rational numbers, then 2a + 3b – 4c is equal to:

    <p>7</p> Signup and view all the answers

    The intensity of the plane electromagnetic wave described by Ey = (200 Vm–1) sin[1.5 × 107t – 0.05 x] in the x-direction is:

    <p>26.6 Wm–2</p> Signup and view all the answers

    In the statements, which one is true?

    <p>Both Statement I and Statement II are true</p> Signup and view all the answers

    If a resistance of 4.5 Ω is connected on the left gap of a meter bridge, and the balance length is found to be at 60 cm from the left end, what is the value of the resistivity of the wire?

    <p>66</p> Signup and view all the answers

    The resultant resistance when a wire of resistance R and length L is cut into 5 equal parts and joined parallelly will be ____.

    <p>R/5</p> Signup and view all the answers

    At what temperature will the average kinetic energy of a monatomic molecule be 0.414 eV?

    <p>1600 K</p> Signup and view all the answers

    Given the statements, which is the most appropriate answer?

    <p>Both Statement I and Statement II are false</p> Signup and view all the answers

    Then m + n is equal to

    <p>4</p> Signup and view all the answers

    Cyclohexene is what type of organic compound?

    <p>Alicyclic</p> Signup and view all the answers

    The function f : N – {1} → N; defined by f(n) =

    <p>one-one only</p> Signup and view all the answers

    What is the product formed when yellow compound of lead chromate gets dissolved in hot NaOH solution?

    <p>Tetraanionic complex with coordination number six</p> Signup and view all the answers

    Carbonate is basic.

    <p>True</p> Signup and view all the answers

    What is the least positive integral value of α for which the angle between the vectors αi − 2j + 2k and αi + 2αj − 2k is acute?

    <p>1</p> Signup and view all the answers

    Which statement is true about the viscosity of gases and surface tension of liquids?

    <p>Statement I is correct but statement II is incorrect</p> Signup and view all the answers

    Salt of weak acid and weak base forming a solution can be acidic or basic.

    <p>True</p> Signup and view all the answers

    Calculate the magnitude and direction of the velocity for an ant moving in the Y-Z plane at t = 1s, given S = 2t^2j + 5k

    <p>16 m/s in y-direction</p> Signup and view all the answers

    The mass of silver displaced by a quantity of electricity that displaces 5600 mL of O2 at S.T.P will be _____ g.

    <p>108</p> Signup and view all the answers

    What is the electronic configuration for Neodymium?

    <p>[Xe] 4f4 6s2</p> Signup and view all the answers

    If the refractive index of a prism material is given by cot(A/2), what is the angle of minimum deviation?

    <p>π - A</p> Signup and view all the answers

    Which circuit is reverse-biased?

    <p>c)</p> Signup and view all the answers

    Match the following:

    <p>HI (mol L-1) = Rate (mol L s-1) 0.005 = 7.5 × 10-1 0.01 = 3.0 × 10-4 0.02 = 1.2 × 10-2</p> Signup and view all the answers

    What physical quantity cannot be measured using a spherometer?

    <p>Thickness of thin plates</p> Signup and view all the answers

    What is the mass of methane required to produce 22 g of CO2 after complete combustion?

    <p>32</p> Signup and view all the answers

    What is the change in internal energy when 0.08 kg of air is heated at constant volume through 5°C?

    <p>318 J</p> Signup and view all the answers

    If three moles of an ideal gas at 300 K expand against a constant opposing pressure of 80 kPa, then the amount of heat transferred is ______ J.

    <p>2400</p> Signup and view all the answers

    What is the radius of the third stationary orbit of an electron for Bohr's atom if the radius of the fourth stationary orbit is R?

    <p>4R</p> Signup and view all the answers

    Study Notes

    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.

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    Solve this JEE Main mathematics test paper from January 2024. Questions cover various math topics.

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