Solved papers for JEE Main & Advanced Physics Vectors JEE PYQ - Vectors

done JEE PYQ - Vectors Total Questions - 11

• question_answer1) Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then, the magnitudes of the forces are                                     [AIEEE 2002]

A)
12 N. 6 N

B)
13 N, 5 N

C)
10 N, 8 N

D)
16 N, 2 N

• question_answer2) Which of the following atoms has the lowest ionisation potential?                 [AIEEE 2003]

A)
$_{7}^{14}N$

B)
$_{55}^{133}Cs$

C)
$_{18}^{40}Ar$

D)
$_{8}^{16}O$

• question_answer3) If$A\times B=B\times A,$then the angle between A and B is                                              [AIEEE 2004]

A)
$\pi$

B)
$\pi /3$

C)
$\pi /2$

D)
$\pi /4$

• question_answer4) Two springs of force constants 300 N/m (Spring A) and 400 N/m (Spring B) are joined together in compressed by 8.75 cm. The ratio of energy stored in A and B is$\frac{{{E}_{A}}}{{{E}_{B}}}$. The  ${}^{{{E}_{A}}}/{}_{{{E}_{B}}}$is equal to: [JEE ONLINE 09-04-2013]

A)
$\frac{4}{3}$

B)
$\frac{16}{9}$

C)
$\frac{3}{4}$

D)
$\frac{9}{16}$

• question_answer5) A vector $\vec{A}$ is rotated by a small angle$\Delta \theta$radians $(\Delta \theta <<1)$ to get a new vector $\vec{B}.$ In that case$|\vec{B}-\vec{A}|$is:  [JEE MAIN 11-04-2015]

A)
0

B)
$|\vec{A}|\left( 1-\frac{{{\Delta }_{\theta }}2}{2} \right)$

C)
$|\vec{A}|\Delta \theta$

D)
$|\vec{B}|\Delta \theta -|\vec{A}|$

• question_answer6) So, $\left| \vec{B}-\vec{A} \right|=\left| {\vec{B}} \right|\Delta \theta =\left| {\vec{A}} \right|\Delta \theta$ Let$\vec{A}=(\hat{i}+\hat{j})$and$\vec{B}=(\hat{i}-\hat{j}).$The magnitude of a coplanar vector$\vec{C}$such that$\vec{A}.\vec{C}=\vec{B}.\vec{C}=\vec{A}.\vec{B},$  is given by [JEE Main Online 16-4-2018]

A)
$\sqrt{\frac{5}{9}}$

B)
$\sqrt{\frac{10}{9}}$

C)
$\sqrt{\frac{20}{9}}$

D)
$\sqrt{\frac{9}{12}}$

• question_answer7)  In the cube of side a shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be [JEE Main 10-Jan-2019 Morning] A)
$\frac{1}{2}a\,(\widehat{k}-\widehat{i})$

B)
$\frac{1}{2}a\,(\widehat{j}-\widehat{i})$

C)
$\frac{1}{2}a\,(\widehat{j}-\widehat{k})$

D)
$\frac{1}{2}a\,(\widehat{i}-\widehat{k})$

• question_answer8) Two vectors  $\overrightarrow{A}\text{ }and\text{ }\overrightarrow{B}$ have equal magnitudes. The magnitude of $\left( \overrightarrow{A}+\text{ }\overrightarrow{B} \right)$ is n times the magnitude of$\left( \overrightarrow{A}-\overrightarrow{B} \right)$. The angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is-       [JEE Main 10-Jan-2019 Evening]

A)
${{\sin }^{-1}}\,\left[ \frac{n-1}{n+1} \right]$

B)
${{\sin }^{-1}}\,\left[ \frac{{{n}^{2}}-1}{{{n}^{2}}+1} \right]$

C)
${{\cos }^{-1}}\,\left[ \frac{{{n}^{2}}-1}{{{n}^{2}}+1} \right]$

D)
${{\cos }^{-1}}\,\left[ \frac{n-1}{n+1} \right]$

• question_answer9) The sum of two forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ such that$\left| {\vec{R}} \right|=\left| {\vec{P}} \right|$. The angle $\theta$ (in degrees) that the resultant of $2\vec{P}$and  $\vec{Q}$ will make with $\vec{Q}$is_________. [JEE MAIN Held on 07-01-2020 Evening]

• question_answer10) A particle moves such that its position vector $\vec{r}\left( t \right)=cos\omega t\,\hat{i}\text{+}sin\omega t\,\hat{j}$ where $\omega$ is a constant and t is time. Then which of the following statements is true for the velocity $\vec{v}(t)$ and acceleration $\vec{a}(t)$  of the particle

A)
$\overrightarrow{v}$and $\overrightarrow{a}$both are perpendicular to $\overrightarrow{r}$

B)
$\overrightarrow{v}$ is perpendicular to $\overrightarrow{r}$ and $\overrightarrow{a}$ is directed towards the origin

C)
$\overrightarrow{v}$ and $\overrightarrow{a}$ both are parallel to $\overrightarrow{r}$

D)
None of these

• question_answer11) A particle starts from the origin at $t=0$with an initial velocity of $3.0\,\hat{i}\,\,m\text{/}s$ and moves in the $x\text{-}y$plane with a constant acceleration$\left( 6.0\,\hat{i}+4.0\hat{j} \right)m\text{/}{{s}^{2}}$. The x-coordinate of the particle at the instant when its y-coordinate is $32\text{ }m$is D meters. The value of D is [JEE MAIN Held on 09-01-2020 Evening]

A)
$60$

B)
$32$

C)
$40$

D)
$50$

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