#### 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)

$\hat { i } +3\hat { j } +2\hat { k }$