Express the force F = (8 N, 150°) in the form (a i + b j) where a and b are constants
\(4\sqrt{3} i - 4j\)
\(4 i - 4\sqrt{3} j\)
\(- 4 i + 4\sqrt{3} j\)
\(- 4\sqrt{3} i + 4j\)
Correct answer is D
\(F = F\cos \theta i + F \sin \theta j\)
\((8 N, 150°) = 8 \cos 150 i + 8 \sin 150 j\)
= \(- 8 \cos 30 i + 8 \sin 30 j\)
= \(-8(\frac{\sqrt{3}}{2}) i + 8(\frac{1}{2} j\)
= \(-4\sqrt{3} i + 4 j\)
36 N
48 N
72 N
108 N
Correct answer is C
\(F = ma \)
\(a = \frac{v - u}{t}\)
\(\therefore F = m(\frac{v - u}{t})\)
\(F = 12(\frac{35 - 5}{5}) = 12 \times 6 = 72 N\)
\(\frac{5}{33}\)
\(\frac{13}{66}\)
\(\frac{8}{53}\)
\(\frac{19}{66}\)
Correct answer is D
\(P(\text{two same color balls}) = P(\text{2 red}) + P(\text{2 white}) + P(\text{2 black})\)
\(P(\text{2 red}) = \frac{3}{12} \times \frac{2}{11} = \frac{1}{22}\)
\(P(\text{2 white}) = \frac{4}{12} \times \frac{3}{11} = \frac{1}{11}\)
\(P(\text{2 black}) = \frac{5}{12} \times \frac{4}{11} = \frac{5}{33}\)
\(P(\text{2 same color balls}) = \frac{1}{22} + \frac{1}{11} + \frac{5}{33} = \frac{19}{66}\)
Eight football clubs are to play in a league on home and away basis. How many matches are possible?
14
28
56
128
Correct answer is C
Number of matches possible = \(2 \times ^{8}C_{2}\) (Home and away repitition of the matches)
= \(2 \times \frac{8!}{(8 - 2)! 2!}\)
= \(2 \times 28\)
= 56
If the mean of -1, 0, 9, 3, k, 5 is 2, where k is a constant, find the median of the set of numbers.
\(\frac{3}{2}\)
0
\(\frac{7}{2}\)
6
Correct answer is A
\(\frac{-1 + 0 + 9 + 3 + k + 5}{6} = 2 \implies 16 + k = 12\)
\(k = -4\)
Arranging -1, 0, 9, 3, -4, 5 in order: -4, -1, 0, 3, 5, 9
Median = \(\frac{0 + 3}{2} = \frac{3}{2}\)