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JEE Advanced2024Paper 1

JEE Advanced 2024 — Paper 1

51 questions with step-by-step solutions. All free.

PHY-I

  1. Q1 A dimensionless quantity is constructed in terms of electronic charge , permittivity of free space , Planck's constant
  2. Q2 An infinitely long wire, located on the -axis, carries a current along the -direction and produces the magnetic field
  3. Q3 Two beads, each with charge and mass , are on a horizontal, frictionless, non-conducting, circular hoop of radius . One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by [
  4. Q4 A block of mass 5 kg moves along the -direction subject to the force

PHY-II

  1. Q1 A particle of mass is moving in a circular orbit under the influence of the central force , corresponding to the potential energy …
  2. Q2 Two uniform strings of mass per unit length and , and length and , respectively, are joined at point
  3. Q3 A glass beaker has a solid, plano-convex base of refractive index , as shown in the figure. The radius of curvature of the convex surface (SPU) is cm, while the planar surface (STU) acts as a mirror. This beaker is filled with a liquid of refractive index up to the level QPR. If the image of a point object O at a height of (OT in the figure) is formed onto …

PHY-III

  1. Q1 The specific heat capacity of a substance is temperature dependent and is given by the formula , where is a constant of suitable dimensions in SI units, and
  2. Q2 A disc of mass and radius is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass and radius
  3. Q3 A point source emits unpolarized light uniformly in all directions. At two points and , the ratio
  4. Q4 A source () of sound has frequency Hz. When the observer () and the source move towards each other at a speed with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be …
  5. Q5 Two large, identical water tanks, and , kept on the top of a building of height , are filled with water up to height in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank …
  6. Q6 A thin uniform rod of length and certain mass is kept on a frictionless horizontal table with a massless string of length fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point . If a horizontal impulse is imparted to the rod at a …

PHY-IV

  1. Q1 One mole of a monatomic ideal gas undergoes the cyclic process
  2. Q2 Four identical thin, square metal sheets, ,
  3. Q3 A light ray is incident on the surface of a sphere of refractive index at an angle of incidence . The ray partially refracts into the sphere with angle of refraction …
  4. Q4 The circuit shown in the figure contains an inductor , a capacitor , a resistor

CHEM-I

  1. Q1 A closed vessel contains g of an ideal gas X at K, which exerts atm pressure. At the same temperature, g of another ideal gas Y is added to it and the pressure becomes …
  2. Q2At room temperature, disproportionation of an aqueous solution of in situ generated nitrous acid (HNO) gives the species
  3. Q3Aspartame, an artificial sweetener, is a dipeptide aspartyl phenylalanine methyl ester. The structure of aspartame is
  4. Q4 Among the following options, select the option in which each complex in Set-I shows geometrical isomerism and the two complexes in Set-II are ionization isomers of each other. [en = HNCH

CHEM-II

  1. Q1Among the following the correct statement(s) for electrons in an atom is(are)
  2. Q2 Reaction of iso-propylbenzene with followed by the treatment with
  3. Q3The option(s) in which at least three molecules follow Octet Rule is(are)

CHEM-III

  1. Q1 Consider the following volumetemperature () diagram for the expansion of moles of an ideal monoatomic gas. Considering only …
  2. Q2 Consider the following reaction,
  3. Q3 Complete reaction of acetaldehyde with excess formaldehyde, upon heating with conc. NaOH solution, gives P and Q. Compound P does not give Tollens' test, whereas Q on acidification gives positive Tollens' test. Treatment of P with excess cyclohexanone in the presence of catalytic amount of -toluenesulfonic acid (PTSA) gives product R. Sum of the number of methylene groups (-CH
  4. Q4 Among V(CO), Cr(CO)
  5. Q5 In the following reaction sequence, the major product P is formed. Glycerol reacts completely with excess P in the presence of an acid catalyst to form Q. Reaction of Q with excess NaOH followed by the treatment with CaCl yields Ca-soap R, quantitatively. Starting with one mole of Q, the amount of R produced in gram is…
  6. Q6 Among the following complexes, the total number of diamagnetic species is ______.

CHEM-IV

  1. Q1 In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration, and the conductance is measured after each addition. The limiting ionic conductivity () values (in mS m
  2. Q2 Based on VSEPR model, match the xenon compounds given in List-I with the corresponding geometries and the number of lone pairs on xenon given in List-II and choose the correct option. …
  3. Q3 List-I contains various reaction sequences and List-II contains the possible products. Match each entry in List-I with the appropriate entry in List-II and choose the correct option. …
  4. Q4 List-I contains various reaction sequences and List-II contains different phenolic compounds. Match each entry in List-I with the appropriate entry in List-II and choose the correct option. …

MATH-I

  1. Q1 Let be a continuously differentiable function on the interval such that
  2. Q2 A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question, he gives the correct answer. Assume that the probability of the student giving the correct answer for a question, given that he has guessed it, is
  3. Q3Let be such that . Then is equal to
  4. Q4 Consider the ellipse

MATH-II

  1. Q1Let , and . Then which of the following statements is (are) TRUE?
  2. Q2 Let denote . Let
  3. Q3 Let denote the three-dimensional space. Take two points

MATH-III

  1. Q1Let and . If are such that and , then is equal to ________.
  2. Q2 Let
  3. Q3 Let
  4. Q4 A group of 9 students,
  5. Q5 Let
  6. Q6 Let be a random variable, and let denote the probability that

MATH-IV

  1. Q1 Let and be the distinct roots of the equation
  2. Q2 Let the straight line touch a circle with center ,
  3. Q3 Let be such that the lines
  4. Q4 Let and

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