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11th Standard Maths Vector Algebra - I English Medium Free Online Test One Mark Questions with Answer Key 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. If \(\overrightarrow{a}+2\overrightarrow{b}\) and \(3\overrightarrow{a}+m\overrightarrow{b}\) are parallel, then the value of m is

    (a)

    3

    (b)

    \(1\over3\)

    (c)

    6

    (d)

    \(1\over6\)

  2. A vector makes equal angle with the positive direction of the coordinate axes. Then each angle is equal to

    (a)

    \(cos^{-1}({1\over 3})\)

    (b)

    \(cos^{-1}({2\over 3})\)

    (c)

    \(cos^{-1}({1\over\sqrt 3})\)

    (d)

    \(cos^{-1}({2\over\sqrt 3})\)

  3. If ABCD is a parallelogram, then \(\overrightarrow{AB}+\overrightarrow{AD}+\overrightarrow{CB}+\overrightarrow{CD}\) is equal to 

    (a)

    \(2(\overrightarrow{AB}+\overrightarrow{AD})\)

    (b)

    \(4\overrightarrow{AC}\)

    (c)

    \(4\overrightarrow{BD}\)

    (d)

    \(\overrightarrow{0}\)

  4. If \(\overrightarrow{a},\overrightarrow{b}\) are the position vectors A and B, then which one of the following points whose position vector lies on AB, is

    (a)

    \(\overrightarrow{a}+\overrightarrow{b}\)

    (b)

    \({2\overrightarrow{a}-\overrightarrow{b}\over 2}\)

    (c)

    \({2\overrightarrow{a}+\overrightarrow{b}\over 3}\)

    (d)

    \({\overrightarrow{a}-\overrightarrow{b}\over 3}\)

  5. If \(\overrightarrow{r}={9\overrightarrow{a}+7\overrightarrow{b}\over16}\) ,then the point P whose position vector \(\overrightarrow{r}\)divides the line joining the points with position vectors \(\overrightarrow{a}\)and \(\overrightarrow{b}\) in the ratio

    (a)

    7: 9 internally

    (b)

    9: 7 internally

    (c)

    9:7 externally

    (d)

    7:9 externally

  6. Two vertices of a triangle have position vectors \(3\hat{i}+4\hat{j}-4\hat{k}\) and\(2\hat{i}+3\hat{j}+4\hat{k}\)If the position vector of the centroid is \(\hat{i}+2\hat{j}+3\hat{k}\) ,then the position vector of the third vertex is

    (a)

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

    (b)

    \(-2\hat{i}-\hat{j}-6\hat{k}\)

    (c)

    \(2\hat{i}-\hat{j}+6\hat{k}\)

    (d)

    \(-2\hat{i}+\hat{j}+6\hat{k}\)

  7. If \(\overrightarrow{a}\)  and \(\overrightarrow{b}\) having same magnitude and angle between them is 60° and their scalar product is \({1\over2}\) then \(|\overrightarrow{a}|\) is

    (a)

    2

    (b)

    3

    (c)

    7

    (d)

    1

  8. If \(|\overrightarrow{a}|=13,|\overrightarrow{b}|=5\)  and \(\overrightarrow{a}.\overrightarrow{b}=60^o\) then \(|\overrightarrow{a}\times\overrightarrow{b}|\) is

    (a)

    15

    (b)

    35

    (c)

    45

    (d)

    25

  9. If   \(\overrightarrow{a}\)  and   \(\overrightarrow{b}\) are two vectors of magnitude 2 and inclined at an angle 60° , then the angle between   \(\overrightarrow{a}\)  and \(\overrightarrow{a}+\overrightarrow{b}\) is 

    (a)

    30°

    (b)

    60°

    (c)

    45°

    (d)

    90°

  10. Find the odd one out of the following

    (a)

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

    (b)

    \(2\hat { i } +4\hat { j } +6\hat { k } \)

    (c)

    \(7\hat { i } +14\hat { j } +21\hat { k } \)

    (d)

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

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