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11th Standard Maths Vector Algebra - I English Medium Free Online Test One Mark Questions 2020 - 2021

11th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. The value of \(\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{DA}+\overrightarrow{CD}\) is

    (a)

    \(\overrightarrow{AD}\)

    (b)

    \(\overrightarrow{CA}\)

    (c)

    \(\overrightarrow{0}\)

    (d)

    \(-\overrightarrow{AD}\)

  2. The unit vector parallel to the resultant of the vectors \(\hat{i}+\hat{j}-\hat{k}\) and \(\hat{i}-2\hat{j}+\hat{k}\) is

    (a)

    \({\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)

    (b)

    \({2\hat{i}+\hat{j}\over\sqrt{5}}\)

    (c)

    \({2\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)

    (d)

    \({2\hat{i}-\hat{j}\over\sqrt{5}}\)

  3. The vectors \(\overrightarrow{a}-\overrightarrow{b},\overrightarrow{b}-\overrightarrow{c},\overrightarrow{c}-\overrightarrow{a}\) are

    (a)

    parallel to each other

    (b)

    unit vectors

    (c)

    mutually perpendicular vectors

    (d)

    coplanar vectors.

  4. If \(\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k},|\overrightarrow{b}|=5\) and the angle between \(\overrightarrow{a}\) and \(\overrightarrow{b}\) is \({\pi\over 6},\) then the area of the triangle formed by these two vectors as two sides, is

    (a)

    \(7\over4\)

    (b)

    \(15\over4\)

    (c)

    \(3\over4\)

    (d)

    \(17\over4\)

  5. The vectors from origin to the points A and B are \(2\hat { i } -3\hat { j } +2\hat { k } \) and \(2\hat { i } +3\hat { j } +\hat { k } \) respectively, then the area of \(\Delta\)OAB is equal to

    (a)

    340

    (b)

    5

    (c)

    \(\sqrt { 229 } \)

    (d)

    \(\frac { 1 }{ 2 } \sqrt { 229 } \)

  6. The vector in the direction of the vector\(\hat{i}-2\hat{j}+2\hat{k}\) that has magnitude 9 is

    (a)

    \(\hat{i}-2\hat{j}+2\hat{k}\)

    (b)

    \(\frac { \hat { i } -2\hat { j } +2\hat { k } }{ 3 } \)

    (c)

    3(\(\hat{i}-2\hat{j}+2\hat{k}\))

    (d)

    9(\(\hat{i}-2\hat{j}+2\hat{k}\))

  7. The angle between two vectors\(\vec{a}\) and\(\vec{b}\) with magnitudes\(\sqrt{3}\) and 4 respectively and \(\vec{a}.\vec{b}=2\sqrt{3}\) is

    (a)

    \(\frac{\pi}{6}\)

    (b)

    \(\frac { \pi }{ 3 } \)

    (c)

    \(\frac { \pi }{ 2 } \)

    (d)

    \(\frac { 5\pi }{ 2 } \)

  8. If m \(\left( \overset { \rightarrow }{ 2 } +\overset { \rightarrow }{ j } +\overset { \rightarrow }{ k } \right) \) is a unit vector then the value of m is

    (a)

    \(\pm \frac { 1 }{ \sqrt { 3 } } \)

    (b)

    \(\pm \frac { 1 }{ \sqrt { 5 } } \)

    (c)

    \(\pm \frac { 1 }{ \sqrt { 6 } } \)

    (d)

    \(\pm \frac { 1 }{ {2 } } \)

  9. Assertion (A): If ABCD is a parallelogram, \(\overset { \rightarrow }{ AB } +\overset { \rightarrow }{ AD } +\overset { \rightarrow }{ CB } +\overset { \rightarrow }{ CD } \) then is equal zero.

    Reason (R): \(\overset { \rightarrow }{ AB } \) and \(\overset { \rightarrow }{ CD } \) are equal in magnitude and opposite in direction. Also\( \overset { \rightarrow }{ AD } \) and \( \overset { \rightarrow }{ CB } \) are equal in magnitude and opposite in direction

    (a)

    Both A and R are true and R is the correct explanation of A

    (b)

    Both A and R are true and R is not a correct explantion of A

    (c)

    A is true but R is false

    (d)

    A is false but R is true

  10. Assertion (A) : \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \) are the position vector three collinear points then 2 \(\overset { \rightarrow }{ a }=\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \)
    Reason (R): Collinear points, have same direction

    (a)

    Both A and R are true and R is the correct explanation of A

    (b)

    Both A and R are true and R is not a correct explantion of A

    (c)

    A is true but R is false

    (d)

    A is false but R is true

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