A test consists of 12 questions out of which candidates are to answer 10. If the first 6 are compulsory, in how many ways can each candidate select her questions?
A body starts from rest and moves in a straight line with uniform acceleration of \(5 ms^{-2}\). How far, in metres, does it go in 10 seconds?
If n items are arranged two at a time, the number obtained is 20. Find the value of n.
If \(p = \begin{pmatrix} 2 \\ -2 \end{pmatrix} \) and \(q = \begin{pmatrix} 3 \\ 4 \end{pmatrix}\), find \(|q - \frac{1}{2}p|\).
Find the value of the constant k for which \(a = 4 i - k j\) and \(b = 3 i + 8 j\) are perpendicular.
