List of top Questions asked in JEE Advanced- 2024

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 _______

Among V(CO)₆, Cr(CO)₅, Cu(CO)₃, Mn(CO)₅, Fe(CO)₅, [Co(CO)₃]^3-, [Cr(CO)₄]^4-, and Ir(CO)₃, the total number of species isoelectronic with Ni(CO)₄ is _________.
[Given, atomic number: V = 23, Cr=24, Mn 25, Fe 26, Co 27, Ni 28, Cu = 29, Ir = 77]

At room temperature, disproportionation of an aqueous solution of in situ generated nitrous acid (HNO₂) gives the species

Reaction of iso-propylbenzene with O₂ followed by the treatment with H₃O⁺ forms phenol and a by-product P. Reaction of P with 3 equivalents of Cl₂ gives compound Q. Treatment of Q with Ca(OH)₂ produces compound R and calcium salt S.
The correct statement(s) regarding P, Q, R and S is(are)

Let α and β be the distinct roots of the equation x² + x- 1 = 0. Consider the set T = {1, α, β}. For a 3 × 3 matrix M = ( a_ij )_3×3, define R_i = a_i1 + a_i2 + a_i3 and C_j = a_1j + a_2j + a_3j for i = 1, 2, 3 and j = 1, 2, 3.
Match each entry in List-I to the corret entry in List-II.

List - I		List - II
(P)	The number of matrices M = ( aij )3×3 with all entries in T such that Ri = Cj = 0 for all i, j, is	(1)	1
(Q)	The number of symmetric matrices M = ( aij )3×3 with all entries in T such that Cj = 0 for all j, is	(2)	12
(R)	Let M = ( aij )3×3 be a skew symmetric matrix such that aij ∈ T for i > j. Then the number of elements in the set \(\left\{\begin{pmatrix} x \\ y \\ z \end{pmatrix}:x,y,z\in \R, M\begin{pmatrix} x \\ y \\ z \end{pmatrix}=\begin{pmatrix} a_{12} \\ 0 \\ -a_{23} \end{pmatrix}\right\}\) is	(3)	infinite
(S)	Let M = ( aij )3×3 be a matrix with all entries in T such that Ri = 0 for all i. Then the absolute value of the determinant of M is	(4)	6
		(5)	0

The correct option is

A dimensionless quantity is constructed in terms of electronic charge \(e\), permittivity of free space \(\epsilon_0\) , Planck’s constant ℎ, and speed of light c. If the dimensionless quantity is written as \(e^\alpha\epsilon_0^\beta h^\gamma c^\delta\)and n is a non-zero integer, then\((\alpha, \beta,\gamma,\delta)\) is given by

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.

List I		List II
(P)		(1)
(Q)		(2)
(R)		(3)
(S)		(4)
		(5)

Four identical thin, square metal sheets, S1, S2, S3 and S4, each of side a are kept parallel to each other with equal distance \(d (≪ a)\) between them, as shown in the figure. Let \(C_0 = \epsilon_0\frac{a^2}{d}, \)where \(\epsilon_0\) is the permittivity of free space.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

List-I		List-II
P	The capacitance between S1 and S4, with S2 and S3 not connected, is	I	\(3C_0\)
Q	The capacitance between S1 and S4, with S2 shorted to S3, is	II	\(\frac{C_0}{2}\)
R	The capacitance between S1 and S3, with S2 shorted to S4, is	III	\(\frac{C_0}{3}\)
S	The capacitance between S1 and S2, with S3 shorted to S1, and S2 shorted to S4, is	IV	\(2\frac{C_0}{3}\)
			\[2C_0\]

Aspartame, an artificial sweetener, is a dipeptide aspartyl phenylalanine methyl ester. The structure of aspartame is

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.

List I		List II
(P)		(1)
(Q)		(2)
(R)		(3)
(S)		(4)
		(5)

Two large, identical water tanks, 1 and 2, kept on the top of a building of height H, are filled with water up to height ℎ 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 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are t1 and t2, respectively. If \(H = ( \frac{16}{ 9} ) ℎ\), then the ratio t1/t2 is ___

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 CaCl₂ yields Ca-soap R, quantitatively. Starting with one mole of Q, the amount of R produced in gram is ______.
[Given, atomic weight: H = 1, C = 12, N = 14, O = 16, Na = 23, Cl = 35, Ca = 40]

Two uniform strings of mass per unit length \(\mu\) and \(4\mu\), and length \(L\) and \(2L\), respectively, are joined at point \(O\), and tied at two fixed ends \(P\) and \(Q\), as shown in the figure. The strings are under a uniform tension \(T\). If we define the frequency \(v_0 = \frac{1}{2L} \sqrt{\frac{T}{\mu}}\), which of the following statements is(are) correct?

Consider the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\). Let S (p, q) be a point in the first quadrant such that \(\frac{p^2}{9}+\frac{q^2}{4}>1\). Two tangents are drawn from S to the ellipse, of which one meets the ellipse at one end point of the minor axis and the other meets the ellipse at a point T in the fourth quadrant. Let R be the vertex of the ellipse with positive x-coordinate and Obe the center of the ellipse. If the area of the triangle △ORT is \(\frac{3}{2}\) , then which of the following options is correct ?

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 [ \(\epsilon_0 \)is the permittivity of free space.]

A particle of mass m is moving in a circular orbit under the influence of the central force\( f(r) = −kr\), corresponding to the potential energy \(v(r) = \frac{kr^2}{2}\), where \(k\) is a positive force constant and \( r\) is the radial distance from the origin. According to the Bohr’s quantization rule, the angular momentum of the particle is given by \(L= nℏ\), where\( ℏ = ℎ/(2pi), ℎ\) is the Planck’s constant, and \(n\) a positive integer. If \(v\) and \(E\) are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?

A point source \(S\) emits unpolarized light uniformly in all directions. At two points A and B, the ratio \(r = I_A/I_B\) 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 ____

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.]

One mole of a monatomic ideal gas undergoes the cyclic process J→ K→ L→ M→ J, as shown in the P-T diagram.Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option. [ℛ is the gas constant.]

List-I		List-II
P	Work done in the complete cyclic process	I	\(ℛT_0 − 4ℛT_0 ln 2\)
Q	Change in the internal energy of the gas in the process JK	II	\(0\)
R	Heat given to the gas in the process KL	III	\(3ℛT_0\)
S	Change in the internal energy of the gas in the process MJ	IV	\(−2ℛT_0 ln 2\)
			\[−3ℛT_0 ln 2\]

 

Consider the following volume−temperature (V−T) diagram for the expansion of 5 moles of an ideal monoatomic gas.

Considering only P-V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence X→Y→Z is ______.
[Use the given data: Molar heat capacity of the gas for the given temperature range, C_V,_m = 12 J K⁻¹mol⁻¹ and gas constant, R=8.3 JK⁻¹ mol⁻¹]

An infinitely long wire, located on the z-axis, carries a current I along the +z-direction and produces the magnetic field \(\bar{B}\) . The magnitude of the line integral \(∫ \overrightarrow{B}.\overrightarrow{dl}\) along a straight line from the point \( (−√3a, a, 0) \)to \((a, a, 0)\) is given by [\(\mu_0\) is the magnetic permeability of free space.]

The option(s) in which at least three molecules follow Octet Rule is(are)

A group of 9 students, s₁, s₂,…., s₉, is to be divided to form three teams X, Y and Z of sizes 2, 3, and 4, respectively. Suppose that s₁ cannot be selected for the team X and s₂ cannot be selected for the team Y. Then the number of ways to form such teams, is _______.