PYQs Based Test - 11 : Engineering Mathematics

The determinant of the matrix M is shown below is ____.

M=≤ft[ {*20c 1&2&0&0\\ 3&4&0&0\\ 0&0&4&3\\ 0&0&2&1 } ]

Given A = ≤ft( {*20c 2&5\\ 0&3 } ). The value of the determinant |A⁴ -5A³ + 6A² + 2I| = ______

A player throws a ball at a basket kept at a distance. The probability that the ball falls into the basket in a single attempt is 0.1. The player attempts to throw the ball twice. Considering each attempt to be independent, the probability that this player puts the ball into the basket only in the second attempt (rounded off to two decimal places) is

Consider the matrix A = ≤ft( {*20c 2&1&1\\ 2&3&4\\ - 1& - 1& - 2 } ) whose eigenvalues are 1, -1 and 3. Then Trace of (A³ – 3A²) is _________.

Consider the following system of linear equations:

3x + 2ky = -2

Kx + 6y = 2

Here x and y are the unknowns and k is a real constant. The value of k for which there are infinite number of solutions is