List of top Questions asked in JEE Main

\[\text{If } \lambda>0, \text{ let } \theta \text{ be the angle between the vectors }\vec{a} = \hat{i} + \lambda \hat{j} - 3 \hat{k} \text{ and } \vec{b} = 3 \hat{i} - \hat{j} + 2 \hat{k}.\text{ If the vectors } \vec{a} + \vec{b} \text{ and } \vec{a} - \vec{b} \text{ are mutually perpendicular, then the value of } (14 \cos \theta)^2 \text{ is equal to.}\]

Let \( PQ \) be a chord of the parabola \( y^2 = 12x \) and the midpoint of \( PQ \) be at \( (4, 1) \). Then, which of the following points lies on the line passing through the points \( P \) and \( Q \)?

Let \( P \) be the point of intersection of the lines \[ \frac{x - 2}{1} = \frac{y - 4}{5} = \frac{z - 2}{1} \quad \text{and} \quad \frac{x - 3}{2} = \frac{y - 2}{3} = \frac{z - 3}{2}. \] Then, the shortest distance of \( P \) from the line \( 4x = 2y = z \) is:

If the area of the region \[ \left\{(x, y) : \frac{a}{x^2} \leq y \leq \frac{1}{x}, \, 1 \leq x \leq 2, \, 0<a<1 \right\} \] is \[ (\log 2) - \frac{1}{7}, \] then the value of $7a - 3$ is equal to:

A circle is inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed in this circle are \( m \) and \( n \), respectively, then \( m + n^2 \) is equal to:

Let $P$ be a point on the ellipse \[\frac{x^2}{9} + \frac{y^2}{4} = 1.\]Let the line passing through $P$ and parallel to the $y$-axis meet the circle \[x^2 + y^2 = 9\]at point $Q$ such that $P$ and $Q$ are on the same side of the $x$-axis. Then, the eccentricity of the locus of the point $R$ on $PQ$ such that $PR : RQ = 4 : 3$ as $P$ moves on the ellipse, is:

In chromatographic techniques, which of the following follows preferential adsorption?

1. Column chromatography
2. Thin layer chromatography
3. Paper chromatography

Match the following : 

(a) \([Cr(H_2O)_6]^{+3}\)	(i) \(t^2_{2g}eg^0\)
(b) \([Fe(H_2O)_6]^{+3}\)	(ii) \(t^3_{2g}eg^0\)
\((c) [Ni(H_2O)_6]^{+2}\)	(iii) \(t^3_{2g}eg^2\)
(d) \([V(H_2O)_6]^{+3}\)	(iv) \(t^6_{2g}eg^2\)

The final product A formed in the following multistep reaction sequence is

Which of the following acts as a strong reducing agent? (Atomic number : Ce = 58, Eu = 63, Gd = 64, Lu = 71)

Given below are two statements:
Statement I: Bromination of phenol in a solvent with low polarity such as CHCl\(_3\) or CS\(_2\) requires a Lewis acid catalyst.
Statement II: The Lewis acid catalyst polarizes the bromine to generate \( \text{Br}^+ \).
In light of the above statements, choose the correct answer from the options given below:

What is the structure of C ?

Given below are two statements:
Statement (I) : A Buffer solution is the mixture of a salt and an acid or a base mixed in any particular quantities.
Statement (II) : Blood is naturally occurring buffer solution whose pH is maintained by $H_2CO_3/HCO_3^-$ concentrations.
In the light of the above statements, choose the correct answer from the options given below.

The solution from the following with highest depression in freezing point/lowest freezing point is

What is the structure of Mn₂(CO)₁₀?

The correct order of the first ionization enthalpy is

While preparing crystals of Mohr's salt, dil. \(H_2SO_4\) is added to a mixture of ferrous sulphate and ammonium sulphate, before dissolving this mixture in water, dil. \(H_2SO_4\) is added here to:

Given below are two statements:
Statement I : Picric acid is 2, 4, 6-trinitrotoluene.
Statement II : Phenol-2, 4-disulphuric acid is treated with conc. HNO₃ to get picric acid.
In the light of the above statement, choose the most appropriate answer from the options given below:

Which of the following compounds has intramolecular hydrogen bonding in it?

The correct statements from following are:
A. The strength of anionic ligands can be explained by crystal field theory. 
B. Valence bond theory does not give a quantitative interpretation of kinetic stability of coordination compounds. 
C. The hybridization involved in formation of \([Ni(CN)_4​]^{2−}\) complex is \(dsp^2\). 
D. The number of possible isomer(s) of \(cis-[PtCl_2​(en)_2​]^{2+}\) is one.
Choose the correct answer from the options given below:

Match List I with List II

LIST-I (Cell)	LIST-II (Use/Property/Reaction)
A. Leclanche cell	IV. Reaction at anode Zn → Zn2+ + 2e-
B. Ni-Cd cell	III. Rechargeable
C. Fuel cell	I. Converts energy of combustion into electrical energy
D. Mercury cell	II. Does not involve any ion in solution and is used in hearing aids

Choose the correct answer from the options given below:

A first row transition metal in its +2 oxidation state has a spin-only magnetic moment value of 3.86 BM. The atomic number of the metal is

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

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): NH$_3$ and NF$_3$ molecule have pyramidal shape with a lone pair of electrons on nitrogen atom. The resultant dipole moment of NH$_3$ is greater than that of NF$_3$.
Reason (R): In NH$_3$, the orbital dipole due to lone pair is in the same direction as the resultant dipole moment of the N$-$H bonds. F is the most electronegative element.
In the light of the above statements, choose the correct answer from the options given below: