Question

Write the value of the determinant $\begin{vmatrix}p & p+1 \\ p-1 & p\end{vmatrix}$

Write the differential equation formed from the equation y = mx + c, where m and c are arbitrary constants.

If A = {1, 2, 3}, B = {4, 5, 6, 7} and f = {(1, 4), (2, 5),(3, 6)} is a function from A to B. State whether f is one-one or not.

If $\begin{vmatrix}x+1 & x-1 \\ x-3 & x+2\end{vmatrix}$ = $\begin{vmatrix}4 & -1 \\ 1 & 3\end{vmatrix}$ , then write the value of x.

Find a vector in the direction of vector $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$which has magnitude 21 units.

If f : R → R is defined by f(x) = $(3-x^{3})^{1/3},$ then find fof(x).

The value of the determinant of a matrix A of order 3 × 3 is 4. Find the value of |5A|.