Find the angle between i + 5j and 5i - J
0\(^o\)
45\(^o\)
60\(^o\)
90\(^o\)
Correct answer is D
a = i + 5j and b = 5i - j
cos\(\theta\) = \(\frac{a.b}{|a|.|b|}\)
= \(\frac{(1 \times 5) + (5x - 1)}{(\sqrt{1^2 + 5^2}) (5^2 + (-1))^2}\)
= \(\frac{5 - 5}{\sqrt{26}\times \sqrt{26}}\) = 0
x = cos\(^{-1}\)(0), x = 90\(^o\)
\(\frac{2}{3}\)
\(\frac{1}{2}\)
\(\frac{1}{3}\)
\(\frac{1}{6}\)
Correct answer is B
x -5 -2 4 8
-5 25 10 -20 -40
-2 10 4 -8 -16
4 10 4 -8 -16
4 -20 -8 16 32
8 -40 -16 32 64
Pr(Two numbers is positive) = \(\frac{8}{16}\)
= \(\frac{1}{2}\)
Find the median of the numbers 9,7, 5, 2, 12,9,9, 2, 10, 10, and 18.
7
9
10
11
Correct answer is B
Rearrange;
2, 2, 5, 7, 9, 9, 9, 10, 10, 11, 12, 18
Median = 9
\(\frac{117}{125}\)
\(\frac{24}{25}\)
\(\frac{3}{5}\)
\(\frac{7}{25}\)
Correct answer is C
Cos (x + y)
= cos x cos y - sin x sin y
cos (x + y) = \(\frac{4}{5} \times \frac{24}{25} - \frac{3}{5} \times \frac{7}{25}\)
= \(\frac{96}{125} - \frac{21}{125} = \frac{96 - 21}{125}\)
= \(\frac{75}{125}\)
= \(\frac{3}{5}\)
4
6
8
10
Correct answer is A
P = {1, 2, 3, 4, 5, 6}
Q = {3, 4 , 5, 6, 7, 8, 9}
P \(\cap\) Q = {3, 4, 5, 6}
n(P \(\cup\) Q) = 4