\(\frac{2}{3}\)
2
3
\(\frac{3}{2}\)
Correct answer is D
For perpendicular vectors, their dot product = 0.
\((4i - kj). (3i + 8j) = 12 - 8k = 0\)
\(8k = 12 \implies k = \frac{3}{2}\)
\(2\sqrt{2}\)
\(\sqrt{13}\)
\(5\)
\(\sqrt{29}\)
Correct answer is D
\(p = \begin{pmatrix} 2 \\ -2 \end{pmatrix} , q = \begin{pmatrix} 3 \\ 4 \end{pmatrix}\)
\(\frac{1}{2}p = \begin{pmatrix} 1 \\ -1 \end{pmatrix}\)
\(q - \frac{1}{2}p = \begin{pmatrix} 3 \\ 4 \end{pmatrix} - \begin{pmatrix} 1 \\ -1 \end{pmatrix} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}\)
\(|q - \frac{1}{2}p| = \sqrt{2^{2} + 5^{2}} = \sqrt{29}\)
If n items are arranged two at a time, the number obtained is 20. Find the value of n.
5
10
15
40
Correct answer is A
\(^{n}P_{2} = \frac{n!}{(n - 2)!} = 20 \)
\(\frac{n(n - 1)(n - 2)!}{(n - 2)!} = 20\)
\(n(n - 1) = 20 \implies n^{2} - n - 20 = 0\)
\(n^{2} - 5n + 4n - 20 = 0\)
\(n(n - 5) + 4(n - 5) = 0\)
\(n = \text{5 or -4}\)
\(n = 5\)
50 m
250 m
350 m
500 m
Correct answer is B
\(s = ut + \frac{1}{2} at^{2}\)
\(u = 0, t = 10 secs, a = 5 ms^{-2}\)
\(s = 0 + \frac{1}{2} 5 \times 10^{2}\)
\(s = 250 m\)
40
25
15
10
Correct answer is C
The first 6 questions can only be selected in 1 way.
The remaining 4 questions can be selected in \(^{6}C_{4}\) ways.
= \(\frac{6!}{(6 - 4)! 4!} = 15\)