A force (10i + 4j)N acts on a body of mass 2kg which is at rest. Find the velocity after 3 seconds.
(5i3+2j3)ms−1
(10i3+4j3)ms−1
(5i+2j)ms−1
(15i+6j)ms−1
Correct answer is D
Recall, F=mass×acceleration⟹acceleration=forcemass
= 10i+4j2=(5i+2j)ms−2
= v=u+at⟹vat 3 seconds=0+(5i+2j×3)
= (15i+6j)ms−1
Given that a = 5i + 4j and b = 3i + 7j, evaluate (3a - 8b).
9i + 44j
-9i + 44j
-9i - 44j
9i - 44j
Correct answer is C
= 3(5i+4j)−8(3i+7j)=15i+12j−24i−56j
= −9i−44j
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 12 | 18 | y | 30 | 2y | 45 |
Given the table above as the result of tossing a fair die 150 times, find the mode.
3
4
5
6
Correct answer is D
The mode is the occurrence with the highest frequency which, from the table, is 45 (the occurrence of obtaining a 6).
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 12 | 18 | y | 30 | 2y | 45 |
Given the table above as the results of tossing a fair die 150 times. Find the probability of obtaining a 5.
110
16
15
310
Correct answer is C
Probability of obtaining a 5 = frequency of 5total frequency
12+18+y+30+2y+45=150⟹105+3y=150
3y=45;y=15
Probability of 5 = 2×15150=15
Given that a=(23) and b=(−14), evaluate (2a−14b)
(1747)
(1745)
(1743)
(1742)
Correct answer is B
a=(23); b=(−14)
⟹2×a=(46) and 14×b=(−141)
∴
= \begin{pmatrix} \frac{17}{4} \\ 5 \end{pmatrix}