Vectors & Basic Mathematics: JEE Main Physics Previous Year Questions

153 previous year questions from Vectors & Basic Mathematics. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. 1.A force is represented by $F=a{x}^2+b{t}^{1/2}$ Where $x=$ distance and $t=$ time. The dimensions of $b^2/a$ are :
2. 2.A = $3\hat{i}+4\hat{j}$ Find a vector perpendicular to $\vec{A}$ in the plane of $\vec{A}$
3. 3.Given below are two statements : Statement (I) : Planck's constant and angular momentum have same dimensions. Statement (II) : Linear momentum and moment of force have sa…
4. 4.If $A=3i+j+2k$ and $B=2i-2j+4k$ then value of $\text{|}A\times B\text{|}$ will be-
5. 5.The position of a particle is given by $r=\text{(}i+2j-k\text{)}$ and momentum $p=\text{(}3i+4j-2k\text{)}$. The angular momentum is perpendicular to the
6. 6.Consider two physical quantities $A$ and $B$ related to each other as $E=\frac{B-x^2}{\text{At}}$ where $E\text{,}x$ and $t$ have dimensions of energy, length an…
7. 7.What is the angle between $\text{(}P+Q\text{)}$ and $\text{(}P\times Q\text{)}$
8. 8.Two vectors $A$ and $B$ have equal magnitudes. The magnitude of $(A+B)$ is ‘n’ times the magnitude of $(A-B)$ The angle between $A$and $B$is
9. 9.The torque of the force $F=\text{(}2i-3j+4k\text{)}N$ acting at the point $r=\text{(}3i+2j+3k\text{)}$ m about the origin be
10. 10.Match List-I with List-II (matching question)
11. 11.If $a_1$ and $a_2$ are two non collinear unit vectors and if $(a_1+a_2)=\sqrt{3}$, then the value of $(a_1-a_2)$. $(2a_1+a_2)$ is -
12. 12.Force acting on a particle is $\text{(}2i+3j\text{)}N$. Work done by this force is zero, when a particle is moved on the line $3y+\text{kx}=5$. Here value of $k$ is -
13. 13.If G be the gravitational constant and u be the energy density then which of the following quantity have the dimensions as that of the $\sqrt{\text{uG}}$ :
14. 14.The number of density of molecules of a gas depends on their distance r from the origin as, $n\text{(}r\text{)}=n_0{e}^{-\text{αr}4}$. Then the total number o…
15. 15.The value of $\text{(}A+B\text{)}\times \text{(}A-B\text{)}$ is
16. 16.Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ have equal magnitudes. If magnitude of $\overrightarrow{A}+\overrightarrow{B}$ is equal to two times the magnitu…
17. 17.A force $F=3i+cj+2k$ acting on a particle causes a displacement $S=-4i+2j-3k$ in its own direction. If the work done is 6J, then the value of c will be
18. 18.Two particles are located at equal distance from origin. The position vectors of those are represented by $A=2i+3nj+2k$ and $B=2i-2j+4pk$, respectively. If both the vec…
19. 19.If two vectors $A$ and $B$ having equal magnitude $R$ are inclined at angle $\theta$, then
20. 20.The angle between the vectors $\text{(}i+j\text{)}$ and $\text{(}j+k\text{)}$ is
21. 21.A physical quantity $Q$ is found to depend on quantities $a\text{,}b\text{,}c$ by the relation $Q=\frac{a^4{b}^3}{c^2}$. The percentage error in…
22. 22.The angle between vector $Q$ and the resultant of $\text{(}2Q+2P\text{)}$ and $\text{(}2Q-2P\text{)}$ is :
23. 23.Dot product of two mutual perpendicular vector is
24. 24.A force vector applied on a mass is represented as $F=6i-8j+10k$ and accelerates with $1m/s^2$. What will be the mass of the body in kg.
25. 25.The equation of stationary wave is :…