List of top Questions asked in JEE Main

Let \( A \) be a \( 2 \times 2 \) real matrix and \( I \) be the identity matrix of order 2. If the roots of the equation \[ |A - xI| = 0 \] be \( -1 \) and \( 3 \), then the sum of the diagonal elements of the matrix \( A^2 \) is .....

If the area of the region \[ \{(x,y) : 0 \leq y \leq \min\{2x, 6x - x^2\}\} \] is \( A \), then \( 12A \) is equal to \ldots

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12. If \( \mu \) and \( \sigma^2 \) denote the mean and variance of the correct observations respectively, then \( 15(\mu + \mu^2 + \sigma^2) \) is equal to \(\ldots\)

If $y = y(x)$ is the solution curve of the differential equation $$ (x^2 - 4) \, dy - (y^2 - 3y) \, dx = 0, $$ with $x > 2$, $y(4) = \frac{3}{2}$ and the slope of the curve is never zero, then the value of $y(10)$ equals: 

Let \( A \) and \( B \) be two finite sets with \( m \) and \( n \) elements respectively. The total number of subsets of the set \( A \) is 56 more than the total number of subsets of \( B \). Then the distance of the point \( P(m, n) \) from the point \( Q(-2, -3) \) is:

If \( \alpha, \beta \) are the roots of the equation \( x^2 - x - 1 = 0 \) and \( S_n = 2023 \alpha^n + 2024 \beta^n \), then:

If \[ \lim_{x \to 0} \frac{3 + \alpha \sin x + \beta \cos x + \log(1 - x)}{3 \tan^2 x} = \frac{1}{3}, \] then \( 2\alpha - \beta \) is equal to:

Let \( g(x) = 3f\left(\frac{x}{3}\right) + f(3 - x) \) and \( f''(x) >0 \) for all \( x \in (0, 3) \). If \( g \) is decreasing in \( (0, \alpha) \) and increasing in \( (\alpha, 3) \), then \( 8\alpha \) is:

Let \( R \) be the interior region between the lines \( 3x - y + 1 = 0 \) and \( x + 2y - 5 = 0 \) containing the origin. The set of all values of \( a \), for which the points \( (a^2, a + 1) \) lie in \( R \), is:

Considering only the principal values of inverse trigonometric functions, the number of positive real values of \( x \) satisfying \[ \tan^{-1}(x) + \tan^{-1}(2x) = \frac{\pi}{4} \] is:

Let \(\alpha, \beta, \gamma\) be the foot of perpendicular from the point \((1, 2, 3)\) on the line \(\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}\). Then \(19(\alpha + \beta + \gamma)\) is equal to:

The compound formed by the reaction of ethanal with semicarbazide contains _____number of nitrogen atoms.

On a thin layer chromatographic plate, an organic compound moved by 3.5 cm, while the solvent moved by 5 cm. The retardation factor of the organic compound is \( \_\_\_\_ \times 10^{-1} \).

If IUPAC name of an element is “Unununnium” then the element belongs to nth group of periodic table. The value of n is______

The pH at which Mg(OH)\(_2\) \([K_{sp} = 1 \times 10^{-11}]\) begins to precipitate from a solution containing 0.10 M Mg\(^{2+}\) ions is \( \_\_\_\_ \).

Choose the correct statements from the following:
A Ethane-1,2-diamine is a chelating ligand.
B Metallic aluminium is produced by electrolysis of aluminium oxide in presence of cryolite.
C Cyanide ion is used as a ligand for leaching of silver.
D Phosphine acts as a ligand in Wilkinson catalyst.
E The stability constants of \( \text{Ca}^{2+} \) and \( \text{Mg}^{2+} \) are similar to EDTA complexes.

The Lassaigne’s extract is boiled with dil HNO\(_3\) before testing for halogens because

Following is a confirmatory test for aromatic primary amines. Identify reagent (A) and (B)

Match List-I with List-II
\[ \begin{array}{|c|c|} \hline \text{List-I (Species)} & \text{List-II (Electronic distribution)} \\ \hline \text{(A) Cr}^{+2} & \text{(I) } 3d^8 \\ \text{(B) Mn}^{+} & \text{(II) } 3d^3 4s^1 \\ \text{(C) Ni}^{+2} & \text{(III) } 3d^4 \\ \text{(D) V}^{+} & \text{(IV) } 3d^5 4s^1 \\ \hline \end{array} \]

What happens to freezing point of benzene when small quantity of napthalene is added to benzene?

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

In the given reactions identify the reagent A and reagent B

Structure of 4-Methylpent-2-enal is

Example of vinylic halide is

Given below are the two statements: one is labelled as Assertion (A) and the other is labeled as Reason (R).
Assertion (A): There is a considerable increase in covalent radius from N to P. However from As to Bi only a small increase in covalent radius is observed.
Reason (R): covalent and ionic radii in a particular oxidation state increases down the group.
In the light of the above statement, choose the most appropriate answer from the options given below: