As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.
Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced..

**Q1.**If $\overrightarrow{a}$×($\overrightarrow{b}$×$\overrightarrow{c}$ )=($\overrightarrow{a}$×$\overrightarrow{b}$)×$\overrightarrow{c}$, where $\overrightarrow{a}$, $\overrightarrow{b}$ and $\overrightarrow{c}$ are any three vectors such that $\overrightarrow{a}$.$\overrightarrow{b}$≠0, $\overrightarrow{b}$∙$\overrightarrow{c}$≠0, then $\overrightarrow{a}$ and $\overrightarrow{c}$ are

**Q2.**Let $\overrightarrow{a}$, $\overrightarrow{b}$,$\overrightarrow{c}$ are three non-coplanar vectors such that $\overrightarrow{\mathrm{r1}}$=$\overrightarrow{a}$-$\overrightarrow{b}$+$\overrightarrow{c}$, $\overrightarrow{\mathrm{r2}}$=$\overrightarrow{b}$+$\overrightarrow{c}$-$\overrightarrow{a}$, $\overrightarrow{\mathrm{r3}}$=$\overrightarrow{c}$+$\overrightarrow{a}$+$\overrightarrow{b}$,$\overrightarrow{r}$=2$\overrightarrow{a}$-3$\overrightarrow{b}$+4$\overrightarrow{c}$

**Q3.**If the vectors $\overrightarrow{c}$,$\overrightarrow{a}$=x$\hat{i}$+y$\hat{j}$+z$\hat{k}$and $\overrightarrow{b}$=$\hat{j}$ are such that $\overrightarrow{a}$,$\overrightarrow{c}$ and $\overrightarrow{b}$ from a right handed system, then $\overrightarrow{c}$ is

**Q5.**If the points with position vectors 60$\hat{i}$+3$\hat{j}$,40$\hat{i}$-8$\hat{j}$ and a$\hat{i}$-52$\hat{j}$ are collinear, then a is equal to

**Q7.**The length of the shortest distance between the two lines $\overrightarrow{r}$=(-3$\hat{i}$+6$\hat{j}$)+s(-4$\hat{i}$+3$\hat{j}$+2$\hat{k}$) and $\overrightarrow{r}$=(-$\hat{i}$+7$\hat{k}$)+t(-4$\hat{i}$+$\hat{j}$+$\hat{k}$) is

**Q8.**Let $\hat{u}$ and $\hat{v}$ are unit vectors such that $\hat{u}$∙$\hat{v}$=0 If r ̂ is any vector coplanar with $\hat{u}$ and $\hat{v}$, then the magnitude of the vector $\overrightarrow{r}$×($\hat{u}$×$\hat{v}$ ) is

**Q9.**A force of magnitude √6 acting along the line joining the points A(2,-1,1) and B(3,1,2) displaces a particle from A to B. The work done by the force is

**Q10.**If $\overrightarrow{a}$$\overrightarrow{b}$$\overrightarrow{c}$ and $\overrightarrow{p}$ , $\overrightarrow{q}$ ,$\overrightarrow{r}$ are reciprocal system of vectors, then $\overrightarrow{a}$× $\overrightarrow{p}$ +$\overrightarrow{b}$× $\overrightarrow{q}$ +$\overrightarrow{c}$×$\overrightarrow{r}$ equals