Four non –zero vectors will always be a.  linearly dependent                 b. linearly independent c. either a or b                           d. none of these

For any non-zero vectors vec(a)andvec(b)vec(a)xxvec(b) is

b. A convex mirror always produces a virtual image independent of the location of the object.

In which of the following type of matrix inverse does not exist always? a. idempotent b. orthogonal c. involuntary d. none of these

If vec a , vec ba n d vec c are three non-zero vectors, no two of which ar collinear, vec a+2 vec b is collinear with vec c and vec b+3 vec c is collinear with vec a , then find the value of | vec a+2 vec b+6 vec c|dot

If the vectors vec a and vec b are linearly independent and satisfying (sqrt3tantheta+1)vec a + (sqrt3sectheta-2)vec b=vec 0 ,then the most general values of theta are:

A lot contains 50 defective and 50 non-defectivebulbs. Two bulbs are drawn at random one at a time withreplacementevents A, and as first bul. The B C are defined theis defective, the second bulb is non-defective, the two banboth defective or non-defective, respectively. Then,(a) A, B and C are pairwise independent(b) A, B and C are pairwise not independent(c) A, B and C are independent(d) None of the above

If vec a and vec b are non - zero vectors and |vec a+ vec b| = |vec a - vec b| , then the angle between vec a and vec b is

Three Non-zero numbers a, b and c will be in G.P. If and only if ____.

If the vector product of a constant vector vec O A with a variable vector vec O B in a fixed plane O A B be a constant vector, then the locus of B is a. a straight line perpendicular to vec O A b. a circle with centre O and radius equal to | vec O A| c. a straight line parallel to vec O A d. none of these

For any non-zero vectors vec(a),vec(b)andvec(c),(vec(a)xxvec(b)).vec(c) is