Organisation : Indian Institute of Technology IIT Madras
Exam Name : JEE (Advanced) 2024 Joint Entrance Examination
Announcement : Question Paper
Year : 2024
Website : https://www.jeeadv.ac.in/
IIT Madras JEE (Advanced) Question Paper
SECTION 1 (Maximum Marks: 12)
** This section contains FOUR (04) questions.
** Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is the correct answer.
** For each question, choose the option corresponding to the correct answer.
** Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct option is chosen;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : −1 In all other cases.
Related / Similar Question Paper : AIISH Entrance Examination Model Question Paper & Mock Test
SECTION 2 (Maximum Marks: 12)
** This section contains THREE (03) questions.
** Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) correct answer(s).
** For each question, choose the option(s) corresponding to (all) the correct answer(s).
** Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 ONLY if (all) the correct option(s) is(are) chosen;
Partial Marks : +3 If all the four options are correct but ONLY three options are chosen;
Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct;
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : −2 In all other cases.
** For example, in a question, if (A), (B) and (D) are the ONLY three options corresponding to correct answers, then
choosing ONLY (A), (B) and (D) will get +4 marks;
choosing ONLY (A) and (B) will get +2 marks;
choosing ONLY (A) and (D) will get +2 marks;
choosing ONLY (B) and (D) will get +2 marks;
choosing ONLY (A) will get +1 mark;
choosing ONLY (B) will get +1 mark;
choosing ONLY (D) will get +1 mark;
choosing no option (i.e. the question is unanswered) will get 0 marks; and
choosing any other combination of options will get −2 marks.
SECTION 3 (Maximum Marks: 24)
** This section contains SIX (06) questions.
** The answer to each question is a NON-NEGATIVE INTEGER.
** For each question, enter the correct integer corresponding to the answer using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer.
** Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If ONLY the correct integer is entered;
Zero Marks : 0 In all other cases.
SECTION 4 (Maximum Marks: 12)
** This section contains FOUR (04) Matching List Sets.
** Each set has ONE Multiple Choice Question.
** Each set has TWO lists: List-I and List-II.
** List-I has Four entries (P), (Q), (R) and (S) and List-II has Five entries (1), (2), (3), (4) and (5).
** FOUR options are given in each Multiple Choice Question based on List-I and List-II and ONLY ONE of these four options satisfies the condition asked in the Multiple Choice Question.
** Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 ONLY if the option corresponding to the correct combination is chosen;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : −1 In all other cases.
Chemistry :
1. A closed vessel contains 10 g of an ideal gas X at 300 K, which exerts 2 atm pressure. At the same temperature, 80 g of another ideal gas Y is added to it and the pressure becomes 6 atm. The ratio of root mean square velocities of X and Y at 300 K is
(A) 2√2 : √3
(B) 2√2 : 1
(C) 1 : 2
(D) 2 : 1
2. At room temperature, disproportionation of an aqueous solution of in situ generated nitrous acid
(HNO2) gives the species
(A) H3O+ , NO3− and NO
(B) H3O+ , NO3− and NO2
(C) H3O+ , NO− and NO2
(D) H3O+ , NO3− and N2O
3. Among the following, the correct statement(s) for electrons in an atom is(are)
(A) Uncertainty principle rules out the existence of definite paths for electrons.
(B) The energy of an electron in 2s orbital of an atom is lower than the energy of an electron that is infinitely far away from the nucleus.
(C) According to Bohr’s model, the most negative energy value for an electron is given by n = 1, which corresponds to the most stable orbit.
(D) According to Bohr’s model, the magnitude of velocity of electrons increases with increase in values of n.
4. 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 p-toluenesulfonic acid (PTSA) gives product R. Sum of the number of methylene groups (-CH2-) and oxygen atoms in R is ______.
5. 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.
List-I List-II
(P) XeF2 (1) Trigonal bipyramidal and two lone pair of electrons
(Q) XeF 4 (2) Tetrahedral and one lone pair of electrons
(R) XeO3 (3) Octahedral and two lone pair of electrons
(S) XeO3F2 (4) Trigonal bipyramidal and no lone pair of electrons
(5) Trigonal bipyramidal and three lone pair of electrons
(A) P-5, Q-2, R-3, S-1
(B) P-5, Q-3, R-2, S-4
(C) P-4, Q-3, R-2, S-1
(D) P-4, Q-2, R-5, S-3
Mathematics :
1. 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 1/2 Also assume that the probability of the answer for a question being guessed, given that the student’s answer is correct, is 1/6 Then the probability that the student knows the answer of a randomly chosen question is
(A) 1/12
(B) 1/7
(C) 5/7
(D) 5/12
Physics :
1. A dimensionless quantity is constructed in terms of electronic charge 𝑒, permittivity of free space 𝜀0 , Planck’s constant ℎ, and speed of light 𝑐. If the dimensionless quantity is written as 𝑒 𝛼 𝜀0𝛽 ℎ 𝛾 𝑐 𝛿 and 𝑛 is a non-zero integer, then (𝛼, 𝛽, 𝛾, 𝛿) is given by
(A) (2𝑛, −𝑛, −𝑛, −𝑛)
(B) (𝑛, −𝑛, −2𝑛, −𝑛)
(C) (𝑛, −𝑛, −𝑛, −2𝑛)
(D) (2𝑛, −𝑛, −2𝑛, −2𝑛)
2. Two beads, each with charge 𝑞 and mass 𝑚, are on a horizontal, frictionless, non-conducting, circular hoop of radius 𝑅. 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 [𝜀0 is the permittivity of free space.]
(A) 𝑞 2 /(4𝜋𝜀0 𝑅 3 𝑚)
(B) 𝑞 2 /(32𝜋𝜀0 𝑅 3 𝑚)
(C) 𝑞 2 /(8𝜋𝜀0 𝑅 3 𝑚)
(D) 𝑞 2 /(16𝜋𝜀0 𝑅 3 𝑚)
3. A block of mass 5 kg moves along the x-direction subject to the force 𝐹 = (−20𝑥 + 10) N, with the value of 𝑥 in metre. At time 𝑡 = 0 s, it is at rest at position 𝑥 = 1 m. The position and momentum of the block at 𝑡 = (𝜋/4) s are
(A) −0.5 m, 5 kg m/s
(B) 0.5 m, 0 kg m/s
(C) 0.5 m, −5 kg m/s
(D) −1 m, 5 kg m/s
4. The specific heat capacity of a substance is temperature dependent and is given by the formula 𝐶 = 𝑘𝑇, where 𝑘 is a constant of suitable dimensions in SI units, and 𝑇 is the absolute temperature. If the heat required to raise the temperature of 1 kg of the substance from −73 ° C to 27 ° C is 𝑛𝑘, the value of 𝑛 is _____.
[Given: 0 K = −273 ° C.]
5. A point source S emits unpolarized light uniformly in all directions. At two points A and B, the ratio 𝑟 = 𝐼𝐴 /𝐼𝐵 of the intensities of light is 2. If a set of two polaroids having 45° angle between their pass-axes is placed just before point B, then the new value of 𝑟 will be _____.
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JEE (Advanced) Syllabus
MATHEMATICS :
Sets, Relations and Functions :
Sets and their representations, different kinds of sets (empty, finite and infinite), algebra of sets, intersection, complement, difference and symmetric difference of sets and their algebraic properties, De-Morgan’s laws on union, intersection, difference (for finite number of sets) and practical problems based on them.
Cartesian product of finite sets, ordered pair, relations, domain and codomain of relations, equivalence relation Function as a special case of relation, functions as mappings, domain, codomain, range of functions, invertible functions, even and odd functions, into, onto and one-to-one functions, special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer etc.), sum, difference, product and composition of functions.
Algebra :
Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.
Statement of fundamental theorem of algebra, Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.
Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite arithmetic and geometric progressions, infinite geometric series, sum of the first n natural numbers, sums of squares and cubes of the first n natural numbers.
Logarithms and their properties, permutations and combinations, binomial theorem for a positive integral index, properties of binomial coefficients.
Matrices :
Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, elementary row and column transformations, determinant of a square matrix of order up to three, adjoint of a matrix, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.
Probability and Statistics :
Random experiment, sample space, different types of events (impossible, simple, compound), addition and multiplication rules of probability, conditional probability, independence of events, total probability, Bayes Theorem, computation of probability of events using permutations and combinations.
Measure of central tendency and dispersion, mean, median, mode, mean deviation, standard deviation and variance of grouped and ungrouped data, analysis of the frequency distribution with same mean but different variance, random variable, mean and variance of the random variable.
Trigonometry :
Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.
Inverse trigonometric functions (principal value only) and their elementary properties.
Analytical Geometry :
Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.
Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; Centroid, orthocentre, incentre and circumcentre of a triangle.
Equation of a circle in various forms, equations of tangent, normal and chord. Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.
Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal.
Locus problems.
Three dimensions: Distance between two points, direction cosines and direction ratios, equation of a straight line in space, skew lines, shortest distance between two lines, equation of a plane, distance of a point from a plane, angle between two lines, angle between two planes, angle between a line and the plane, coplanar lines.
Differential Calculus :
Limit of a function at a real number, continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L’Hospital rule of evaluation of limits of functions.
Continuity of composite functions, intermediate value property of continuous functions.
Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.
Tangents and normals, increasing and decreasing functions, derivatives of order two, maximum and minimum values of a function, Rolle’s theorem and Lagrange’s mean value theorem, geometric interpretation of the two theorems, derivatives up to order two of implicit functions, geometric interpretation of derivatives.
Integral Calculus :
Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals as the limit of sums, definite integral and their properties, fundamental theorem of integral calculus.
Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas bounded by simple curves. Formation of ordinary differential equations, solution of homogeneous differential equations of first order and first degree, separation of variables method, linear first order differential equations.
Vectors :
Addition of vectors, scalar multiplication, dot and cross products, scalar and vector triple products, and their geometrical interpretations.