List of top Questions asked in JEE Main

Let: $\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=\hat{i}-\hat{j}+2 \hat{k}$ and $\vec{c}=5 \hat{i}-3 \hat{j}+3 \hat{k}$ be there vectors If $\vec{r}$ is a vector such that, $\vec{r} \times \vec{b}=\vec{c} \times \vec{b}$ and $\vec{r} \cdot \vec{a}=0$, then $25|\vec{r}|^2$ is equal to

$\displaystyle \lim _{n \rightarrow \infty}\left[\frac{1}{1+n}+\frac{1}{2+n}+\frac{1}{3+n}+\ldots+\frac{1}{2 n}\right]$ is equal to

The mean and variance of $5$ observations are $5$ and $8$ respectively If $3$ observations are $1,3,5$, then the sum of cubes of the remaining two observations is

Let $S$ be the set of all solutions of the equation $\cos ^{-1}(2 x)-2 \cos ^{-1}\left(\sqrt{1-x^2}\right)=\pi$, $x \in\left[-\frac{1}{2}, \frac{1}{2}\right]$ Then $\displaystyle\sum_{x \in S} 2 \sin ^{-1}\left(x^2-1\right)$ is equal to

Let $S=x: x∈R$ and $\left(\sqrt{3}+\sqrt{2})^{x^2-4}+(\sqrt{3}-\sqrt{2})^{x^2-4}=10\right\}$Then $n(S)$ is equal to

The sum to $10$ terms of the series $\frac{1}{1+1^2+1^4}+\frac{2}{1+2^2+2^4}+\frac{3}{1+3^2+3^4}+\ldots $ is

Let $x=(8 \sqrt{3}+13)^{13}$ and $y=(7 \sqrt{2}+9)^9$ If $[t]$ denotes the greatest integer $\leq t$, then

Let $\lambda \in R , \vec{a}=\lambda \hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=\hat{i}-\lambda \hat{j}+2 \hat{k}$.If $((\vec{a}+\vec{b}) \times(\vec{a} \times \vec{b})) \times(\vec{a}-\vec{b})=8 \hat{i}-40 \hat{j}-24 \hat{k}$, then $|\lambda(\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})|^2$ is equal to

Given below are two statements:
Statement I: Tropolone is an aromatic compound and has 8л electrons.
Statement II: electrons of >C = O group in tropolone is involved in aromaticity.
In the light of the above statements, choose the correct answer from the options given below

Match the List I with List II

	List I		List II
(A)	Weak intermolecular forces of attraction	I	Hexamethylenedia mine + adipic acid
(B)	Hydrogen bonding	II	AlEt₃+ TiCl₄
(C)	Heavily branched polymer	III	2-chloro-1, 3-butadiene
(D)	High density polymer	III	phenol+ formaldehyde

choose the correct answer from the options given below:

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The diameter of colloidal particles in solution should not be much smaller than wavelength of light to show Tyndall effect.
Reason R : The light scatters in all directions when the size of particles is large enough.
In the light of the above statements, choose the correct answer from the options given below

Given below are two statements:
Statement I: SO$_2$ and H$_2$O both possess V-shaped structures.
Statement II: The bond angle of SO$_2$ is less than that of H$_2$O. In the light of the above statements, choose the most appropriate answer from the options given below:

The naturally occurring amino acid that contains only one basic functional group in its chemical structure is:

What happens when methane undergoes combustion in systems A and B respectively?

The covalency and oxidation state respectively of boron in [BF₄]^-, are

Match the List I with List II
1- Bromopropane is reacted with regents in List I to give products in List II

	List I-Reagent		List II-Product
(A)	KOH(alc)	I	Nitrile
(B)	KCL(alc)	II	Ester
(C)	AgNo₂	III	Alkene
(D)	H₃CC00A_g	III	Nitroalkane

Choose the correct answer from the options given below: