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.**A vector which makes equal angles with the vectors 1/3 ($\hat{i}$-2$\hat{j}$+2$\hat{k}$), 1/5 (-4$\hat{i}$-3$\hat{k}$), and $\hat{j}$, is

**Q2.**If the position vector of A with respect to O is 3$\hat{i}$-2$\hat{j}$+4$\hat{k}$ and $\overrightarrow{\mathrm{AB}}$=3$\hat{i}$-$\hat{j}$+$\hat{k}$ Then the position vector of B with respect to O is

**Q3.**If $\overrightarrow{a}$=2$\hat{i}$-3$\hat{j}$+5$\hat{k}$, $\overrightarrow{b}$=3$\hat{i}$-4$\hat{j}$+5$\hat{k}$ and $\overrightarrow{c}$=5$\hat{i}$-3$\hat{j}$-2$\hat{k}$, then the volume of the parallelopiped with

coterminous edges $\overrightarrow{a}$+$\overrightarrow{b}$,$\overrightarrow{b}$+$\overrightarrow{c}$,$\overrightarrow{c}$+$\overrightarrow{a}$ is

**Q4.**Consider a tetrahedron with faces F

_{1},F

_{2},F

_{3},F

_{4}. Let $\overrightarrow{v}$

_{1}, $\overrightarrow{v}$

_{2}, $\overrightarrow{v}$

_{3}, $\overrightarrow{v}$

_{4}be the vectors whose magnitudes are respectively equal to areas of F

_{1},F

_{2},F

_{3},F

_{4}and whose directions are perpendicular to these faces in outward direction. Then, | $\overrightarrow{v}$

_{1}+ $\overrightarrow{v}$

_{2}+ $\overrightarrow{v}$

_{3}+ $\overrightarrow{v}$

_{4}| equals

Solution

(c)

(c)

**Q5.**If a tetrahedron has vertices at O(0,0,0),A(1,2,1),B(2,1,3) and C(-1,1,2). Then, the

angle between the faces OAB and ABC will be

Solution

(a)

(a)

**Q6.**If $\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ be three non-coplanar vectors and $\overrightarrow{p}$,$\overrightarrow{q}$,$\overrightarrow{r}$ constitute the corresponding reciprocal system of vectors

then for any arbitrary vector$\overrightarrow{\mathrm{\xce\pm}}$

**Q7.**A vector of magnitude 12 units perpendicular to the plane containing the vectors 4$\hat{i}$+6$\hat{j}$-$\hat{k}$ and 3$\hat{i}$+8$\hat{j}$+$\hat{k}$is

**Q8.**If the scalar projection of the vector x$\hat{i}$+$\hat{j}$+$\hat{k}$ on the vector $\hat{i}$-$\hat{j}$+5$\hat{k}$is 1/√30 then the value of x is

**Q9.**If $\overrightarrow{a}$+$\overrightarrow{b}$+$\overrightarrow{c}$ are three unit vectors such that $\overrightarrow{a}$+$\overrightarrow{b}$+$\overrightarrow{c}$=0, where $\overrightarrow{0}$ is null vector, then $\overrightarrow{a}$∙$\overrightarrow{b}$+$\overrightarrow{b}$∙$\overrightarrow{c}$+$\overrightarrow{c}$∙$\overrightarrow{a}$ is

**Q10.**If $\overrightarrow{x}$+ $\overrightarrow{y}$+ $\overrightarrow{z}$= $\overrightarrow{0}$,| $\overrightarrow{x}$ |=| $\overrightarrow{y}$ |+| $\overrightarrow{z}$ |=2, and Î¸ is angle between $\overrightarrow{y}$ and $\overrightarrow{z}$ , then the value of cosec

^{2}Î¸+cot

^{2}Î¸ is equal to