PYQs Based Test - 11 : Engineering Mathematics

A 3 × 3 matrix has eigenvalues 1, 2 and 5. The determined of the matrix is _________.

Let 𝑁 be a 3 by 3 matrix with real number entries. The matrix 𝑁 is such that 𝑁² = 0. The eigen values of N are

Consider the following equations

$\frac{\partial V\left(x,y\right)}{\partial x}=p{x}^2+y^2+2xy$

$\frac{\partial V\left(x,y\right)}{\partial y}=x^2+q{y}^2+2xy$

Where p and q are constants. V (x, y) that satisfies the above equations is

An urn contains 5 red and 7green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour. The probability of getting a red ball in the next draw is

Let $f(z)=\frac{1}{z^2+6z+9}$ defined in the complex plane. The integral ∮${}_c$ f(z)dz over the contour of a circle c with center at the origin and unit radius is ___.