GATE EE 2017 Question Paper (11-Feb-2017) (Shift 1)

The matrix A = ≤ft[ {*20c 3/2&0&1/2\\ 0& - 1&0\\ 1/2&0&3/2 } ] has three distinct Eigen values and one of its Eigen vectors is ≤ft[ {*20c 1\\ 0\\ 1 } ]. Which one of the following can be another Eigen vector of A?

For a complex number z, *20c lim\\ z → i {z^2 + 1}{{z^3 + 2z - i≤ft( z^2 + 2 )}} is

Let z(t) = x(t) y(t), where “ ” denotes convolution. Let c be a positive real-valued constant. Choose the correct expression for z(ct).

A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will

Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the centre of the line joining the electron and proton. At t = 0 , the particles are released but are constrained to move along the same straight line. Which of these will collide first?