List of top Questions asked in JEE Main- 2024

Let $\alpha \beta \neq 0$ and $A = \begin{bmatrix} \beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2\alpha \end{bmatrix}$. If $B = \begin{bmatrix} 3\alpha & -9 & 3\alpha \\ -\alpha & 7 & -2\alpha \\ -2\alpha & 5 & -2\beta \end{bmatrix}$ is the matrix of cofactors of the elements of A, then det(AB) is equal to:

Let $A = \begin{bmatrix} 2 & -1 \\ 1 & 1 \end{bmatrix}$. If the sum of the diagonal elements of $A^{13}$ is $3^n$, then $n$ is equal to _____.

Let \( f(x) = \int_0^x g(t) \log_e \left( \frac{1 - t}{1 + t} \right) dt \), where \( g \) is a continuous odd function. If \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( f(x) + \frac{x^2 \cos x}{1 + e^x} \right) dx = \left( \frac{\pi}{\alpha} \right)^2 - \alpha, \] then \( \alpha \) is equal to .....

Ail organic compound has 42.1% carbon, 6.4% hydrogen and remainder is oxygen. If its molecular weight is 342, then its molecular formula is :

Let \( A = \{2, 3, 6, 7\} \) and \( B = \{4, 5, 6, 8\} \). Let \( R \) be a relation defined on \( A \times B \) by \((a_1, b_1) R (a_2, b_2)\) if and only if \(a_1 + a_2 = b_1 + b_2\). Then the number of elements in \( R \) is __________.

Match List - I with List - II.

List - I (Pair of Compounds)	List - II (Isomerism)
(A) n-propanol and Isopropanol	(I) Metamerism
(B) Methoxypropane and ethoxyethane	(IV) Functional Isomerism
(C) Propanone and propanal	(III) Position Isomerism
(D) Neopentane and Isopentane	(II) Chain Isomerism

What will be the reactivity order of following compounds towards electrophilic substitution reaction ?

The total number of ‘Sigma’ and Pi bonds in 2 formylhex-4-enoic acid is ____.

Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is:

Two identical conducting spheres P and S with charge Q on each, repel each other with a force 16N. A third identical uncharged conducting sphere R is successively brought in contact with the two spheres. The new force of repulsion between P and S is :

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is \(\frac{A}{3}\) and the height is d, the capacitance of the arrangement is:

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is :

The relation between time \( t \) and distance \( x \) is \( t = \alpha x^2 + \beta x \), where \( \alpha \) and \( \beta \) are constants. The relation between acceleration \( a \) and velocity \( v \) is:

Number of carbocation from the following that are not stabilized by hyperconjugation is _________ .

Two vertices of a triangle \( \triangle ABC \) are \( A(3, -1) \) and \( B(-2, 3) \), and its orthocentre is \( P(1, 1) \). If the coordinates of the point \( C \) are \( (\alpha, \beta) \) and the centre of the circle circumscribing the triangle \( \triangle PAB \) is \( (h, k) \), then the value of \[ (\alpha + \beta) + 2(h + k) \] equals:

Given below are two statements :
Statement-I: When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be 0°.
Statement-II: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well : In the light of above statement.
Choose the correct answer from the options given below.

Match List - I with List - II.

List - I(Number)	List - II(Significant figure)
(A) 1001	(I) 3
(B) 010.1	(II) 4
(C) 100.100	(III) 5
(D) 0.0010010	(IV) 6

Choose the correct answer from the options given below :

In the following sequence of reaction, the major products B and C respectively are :

Which of the following elements has the highest 1st ionization energy ?

Given below are two statements:
Statement I: Aniline reacts with con. \( H_2SO_4 \) followed by heating at 453–473 K gives p-aminobenzene sulphonic acid, which gives blood red colour in the 'Lassaigne's test'.
Statement II: In Friedel-Craft's alkylation and acylation reactions, aniline forms salt with the \( AlCl_3 \) catalyst. Due to this, nitrogen of aniline acquires a positive charge and acts as a deactivating group.
In the light of the above statements, choose the correct answer from the options given below:

Given below are two statement one is labeled as Assertion (A) and the other is labeled as Reason (R).
Assertion (A): CH₂ = CH – CH₂ – Cl is an example of allyl halide
Reason (R): Allyl halides are the compounds in which the halogen atom is attached to sp² hybridised carbon atom.
In the light of the two above statements, choose the most appropriate answer from the options given below

$\textbf{The orange colour of } \text{K}_2\text{Cr}_2\text{O}_7 \textbf{ and purple colour of KMnO}_4 \textbf{ is due to}$

KMnO₄ decomposes on heating at 513 K to form O₂ along with