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
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  B)
  13 N, 5 N
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  C)
  10 N, 8 N
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  D)
  16 N, 2 N
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• question_answer2) Which of the following atoms has the lowest ionisation potential?                 [AIEEE 2003]
  A)
  \[_{7}^{14}N\]
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  B)
  \[_{55}^{133}Cs\]
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  C)
  \[_{18}^{40}Ar\]
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  D)
  \[_{8}^{16}O\]
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• question_answer3) If\[A\times B=B\times A,\]then the angle between A and B is                                              [AIEEE 2004]
  A)
  \[\pi \]
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  B)
  \[\pi /3\]
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  C)
  \[\pi /2\]
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  D)
  \[\pi /4\]
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• 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)
              \[\frac{4}{3}\]
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  B)
  \[\frac{16}{9}\]
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  C)
              \[\frac{3}{4}\]
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  D)
  \[\frac{9}{16}\]
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• 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
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  B)
  \[|\vec{A}|\left( 1-\frac{{{\Delta }_{\theta }}2}{2} \right)\]
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  C)
  \[|\vec{A}|\Delta \theta \]
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  D)
  \[|\vec{B}|\Delta \theta -|\vec{A}|\]
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• 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)
  \[\sqrt{\frac{5}{9}}\]
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  B)
  \[\sqrt{\frac{10}{9}}\]
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  C)
  \[\sqrt{\frac{20}{9}}\]   
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  D)
  \[\sqrt{\frac{9}{12}}\]   
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• 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)
  \[\frac{1}{2}a\,(\widehat{k}-\widehat{i})\]
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  B)
  \[\frac{1}{2}a\,(\widehat{j}-\widehat{i})\]
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  C)
  \[\frac{1}{2}a\,(\widehat{j}-\widehat{k})\]
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  D)
  \[\frac{1}{2}a\,(\widehat{i}-\widehat{k})\]
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• 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)
  \[{{\sin }^{-1}}\,\left[ \frac{n-1}{n+1} \right]\]
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  B)
  \[{{\sin }^{-1}}\,\left[ \frac{{{n}^{2}}-1}{{{n}^{2}}+1} \right]\]
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  C)
  \[{{\cos }^{-1}}\,\left[ \frac{{{n}^{2}}-1}{{{n}^{2}}+1} \right]\]
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  D)
  \[{{\cos }^{-1}}\,\left[ \frac{n-1}{n+1} \right]\]
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• 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]
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• 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 \[\overrightarrow{r}\]
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  B)
  \[\overrightarrow{v}\] is perpendicular to \[\overrightarrow{r}\] and \[\overrightarrow{a}\] is directed towards the origin
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  C)
  \[\overrightarrow{v}\] and \[\overrightarrow{a}\] both are parallel to \[\overrightarrow{r}\]
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  D)
  None of these
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• 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)
  \[60\]
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  B)
  \[32\]
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  C)
  \[40\]
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  D)
  \[50\]
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