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 the vectors $\overrightarrow{\mathrm{r1}}$=a$\hat{i}$+$\hat{j}$+$\hat{k}$, $\overrightarrow{\mathrm{r2}}$=$\hat{i}$+b$\hat{j}$+$\hat{k}$, $\overrightarrow{\mathrm{r3}}$=$\hat{i}$+$\hat{j}$+c$\hat{k}$ (a≠1,b≠1,c≠1) are coplanar,

then the value of 1/(1-a)+1/(1-b)+1/(1-c), is

**Q2.**If $\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are non-coplanar vectors and Î» be a real number, then the vectors $\overrightarrow{a}$+2$\overrightarrow{b}$+3$\overrightarrow{c}$,Î» $\overrightarrow{b}$+4 $\overrightarrow{c}$ and (2Î»-1) $\overrightarrow{c}$ are non-coplanar for

**Q3.**The value of a so that the volume of parallelopiped formed by $\hat{i}$+a$\hat{j}$+$\hat{k}$, $\hat{j}$+a$\hat{k}$ and a$\hat{i}$+$\hat{k}$ becomes minimum is

**Q4.**The area of parallelogram constructed on the vectors $\overrightarrow{a}$= $\overrightarrow{p}$ +2 $\overrightarrow{q}$ and $\overrightarrow{b}$=2 $\overrightarrow{p}$ + $\overrightarrow{q}$ , where $\overrightarrow{p}$ and $\overrightarrow{q}$ are unit vectors forming an angle of 30° is

Solution

(a)

(a)

**Q5.**If |$\overrightarrow{a}$ |=3,|$\overrightarrow{b}$ |=4, then a value of Î» for which $\overrightarrow{a}$+Î»$\overrightarrow{b}$ is perpendicular to $\overrightarrow{a}$-Î»$\overrightarrow{b}$ is

**Q6.**Given, $\overrightarrow{p}$=3$\hat{i}$+2$\hat{j}$+4$\hat{k}$, $\overrightarrow{a}$=$\hat{i}$+$\hat{j}$, $\overrightarrow{b}$=$\hat{j}$+$\hat{k}$, $\overrightarrow{c}$=$\hat{i}$+$\hat{k}$and $\overrightarrow{p}$=x$\overrightarrow{a}$+ y$\overrightarrow{b}$+z$\overrightarrow{b}$ , then x,y,z are respectively

**Q7.**If $\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are three vectors such that $\overrightarrow{a}$=$\overrightarrow{b}$+$\overrightarrow{c}$ and the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is Ï€/2, then

Solution

(a)

(a)

**Q8.**The values of x for which the angle between the vectors $\overrightarrow{a}$=x$\hat{i}$-3$\hat{j}$-$\hat{k}$and $\overrightarrow{b}$=2x$\hat{i}$+x$\hat{j}$-$\hat{k}$is acute

and the angle between the vector $\overrightarrow{b}$ and the y-axis lies between Ï€/2 and Ï€ are

**Q9.**If $\overrightarrow{p}$=$\hat{i}$+$\hat{j}$, $\overrightarrow{q}$=4$\hat{k}$-$\hat{j}$ and $\overrightarrow{r}$=$\hat{i}$+$\hat{k}$,then the unit vector in the direction of 3$\overrightarrow{p}$+$\overrightarrow{q}$-2$\overrightarrow{r}$ is

**Q10.**If ABCDEF is a regular hexagon with $\overrightarrow{a}$B=$\overrightarrow{a}$ and $\overrightarrow{b}$C=$\overrightarrow{b}$, then $\overrightarrow{c}$E equals