CBSE [Delhi]_XII_Mathematics_2009_Set I

Write a unit vector in the direction of 

Write the value of p for which  are parallel vector.

If matrix A = (1 2 3 ), write AA’, where A’ is the transpose of matrix A.

Write the value of the determinant 

Using principal value, evaluate the following:

If the binary operation * on the set of integers Z, is defined by a * b = a + 3b², then find the value of 2 * 4.

If A is an invertible matrix of order 3 and |A| = 5, then find |adj A|.