Question 1

Find the angle between two vectors:
$\vec{a}=3\hat{i}-5\hat{j}+2\hat{k}$,
$\vec{b}=3\hat{i}+3\hat{j}-2\hat{k}$

Accepted Answer

$110^{0}$

Answer

$120^{0}$

Answer

$130^{0}$

Answer

$100^{0}$

Question 2

Find the resultant of two vectors:
$\vec{a}=3\hat{i}-5\hat{j}+2\hat{k}$,
$\vec{b}=3\hat{i}+3\hat{j}-2\hat{k}$

Accepted Answer

$9\hat{i}-2\hat{j}$

Answer

$6\hat{i}-2\hat{j}$

Answer

$5\hat{i}-4\hat{j}$

Answer

$3\hat{i}-3\hat{j}$

Question 3

Find the cross-product between two vectors:
$\vec{a}=3\hat{i}-5\hat{j}+2\hat{k}$,
$\vec{b}=3\hat{i}+3\hat{j}-2\hat{k}$

Accepted Answer

$12\hat{i}-60\hat{j}+48\hat{k}$

Answer

$13\hat{i}-50\hat{j}+38\hat{k}$

Answer

$22\hat{i}-30\hat{j}+28\hat{k}$

Answer

$11\hat{i}-65\hat{j}+42\hat{k}$

Question 4

Find the magnitude of the following vector:
$\vec{a}=3\hat{i}-5\hat{j}+2\hat{k}$,

Accepted Answer

$|a|=\sqrt{38}$

Answer

$|a|=\sqrt{30}$

Answer

$|a|=\sqrt{35}$

Answer

$|a|=\sqrt{32}$

Question 5

Find the probability that when three regular dice are rolled all three show a value of 1.

Accepted Answer

$\frac{1}{216}$

Answer

$\frac{1}{236}$

Answer

$\frac{1}{226}$

Answer

$\frac{1}{206}$

Question 6

70% of the houses on a street have a freezer. 
If two houses are picked at random find
the probability that one has freezer but the other does not.

Accepted Answer

21%

Answer

18%

Answer

28%

Answer

24%

Question 7

A box contains marbles. 30% are red the rest are blue. If 5 marbles are picked at random find the probability that 2 are red.

Accepted Answer

31%

Answer

42%

Answer

34%

Answer

38%

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