Mathematics Past Questions and Answers

If the binary operation \(\ast\) is defined by m \(\ast\) n = mn + m + n for any real number m and n, find the identity of the elements under this operation

p = \(\begin{vmatrix} x & 3 & 0 \\ 2 & y & 3\\ 4 & 2 & 4 \end{vmatrix}\)
Q = \(\begin{vmatrix} x & 2 & z \\ 3 & y & 2\\ 0 & 3 & z \end{vmatrix}\) Where p^T is the transpose P calculate /p^T/ when x = 0, y = 1 and z = 2

p = \(\begin{vmatrix} x & 3 & 0 \\ 2 & y & 3\\ 4 & 2 & 4 \end{vmatrix}\)
Q = \(\begin{vmatrix} x & 2 & z \\ 3 & y & 2\\ 0 & 3 & z \end{vmatrix}\)
PQ is equivalent to

If the angles of quadrilateral are (p + 10)°, (2p - 30)°, (3p + 20)° and 4p°, find p.

Determine the distance on the earth's surface between two town P (lat 60°N, Long 20°E) and Q(Lat 60°N, Long 25°W) (Radius of the earth = 6400km)