Evaluate \(\begin{pmatrix} 2 & 3 \\ 4 & 1 \end{pmatrix} \begin{pmatrix} 2 \\ 3 \end{pmatrix}\).
(13, 11)
(11, 13)
\(\begin{pmatrix} 13 \\ 11 \end{pmatrix}\)
\(\begin{pmatrix} 11 \\ 13 \end{pmatrix}\)
Correct answer is C
\(\begin{pmatrix} 2 & 3 \\ 4 & 1 \end{pmatrix} \begin{pmatrix} 2 \\ 3 \end{pmatrix}\)
= \(\begin{pmatrix} 2 \times 2 + 3 \times 3 \\ 4 \times 2 + 1 \times 3 \end{pmatrix}\)
= \(\begin{pmatrix} 13 \\ 11 \end{pmatrix}\)
Simplify \(2\log_{3} 8 - 3\log_{3} 2\)
\(-\log_{3} 4\)
\(-\log_{3} 2\)
\(3\log_{3} 2\)
\(3\log_{3} 4\)
Correct answer is C
\(2\log_{3} 8 - 3\log_{3} 2 = \log_{3} 8^{2} - \log_{3} 2^{3}\)
= \(\log_{3}(\frac{64}{8}) \)
= \(\log_{3} 8 = \log_{3} 2^{3}\)
= \(3 \log_{3} 2\)
58°
72°
74°
87°
Correct answer is B
\(a . b = |a||b| \cos \theta\)
\(\begin{pmatrix} 13 \\ 1 \end{pmatrix}. \begin{pmatrix} 1 \\ 4 \end{pmatrix} = 13 \times 1 + 1 \times 4 = 13 + 4 = 17\)
\(17 = (\sqrt{13^{2} + 1^{2}})(\sqrt{1^{2} + 4^{2}}) \cos \theta\)
\(17 = (\sqrt{170})(\sqrt{17}) \cos \theta\)
\(\cos \theta = \frac{17}{17\sqrt{10}} = \frac{\sqrt{10}}{10} = 0.3162\)
\(\theta = \cos^{-1} 0.3162 = 72°\)
\(\frac{1}{3}\)
\(\frac{1}{4}\)
\(\frac{1}{6}\)
\(\frac{1}{12}\)
Correct answer is B
P(even in 1 dice) = \(\frac{3}{6} = \frac{1}{2}\)
P(even in 2 fair die) = \(\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\)
The position vectors of A and B are (2i + j) and (-i + 4j) respectively; find |AB|.
\(3\sqrt{2}\)
\(\sqrt{34}\)
\(\sqrt{34}\)
\(9\sqrt{2}\)
Correct answer is A
No explanation has been provided for this answer.