Delhi-2015

Find λ if the vectors and are coplanar.

If a line makes angles 90^o, 60^o and θ with x, y and z-axis respectively, where θ is acute, then find θ.

Write the element a₂₃ of a 3 × 3 matrix A = (a_jj) whose elements a_ij are given by

Find the differential equation representing the family of curves where A and B are arbitrary constants.

Find the integrating factor of the differential equation

If find A² – 5A + 4I and hence find a matrix X such that A² – 5A + 4I + X = O.

OR

If find (A’)^-1.

If using properties of determinants find the value of f(2x) – f(x).

Find :

OR

Integrate the following w.r.t. x

Evaluate :