List of top Mathematics Questions asked in TS PGECET

Evaluate \[ \iint_D x^2y\,dx\,dy, \] where \[ D:\;x^2+y^2\le16. \]
If \[ \overline{V}=x^{2}y\,\overline{i}-yz^{2}\,\overline{j}+xyz\,\overline{k} \] is the linear velocity of a particle in circular motion at the point \((1,1,1)\), then its angular velocity is
Evaluate \[ \oint_C \frac{z+2}{z^2+2z+2}\,dz, \] where \(C\) is the circle \[ |z-\alpha|=1, \qquad \alpha=-1+\frac{3}{2}i. \]
If the solution of \[ \frac{d^2y}{dt^2} = -\frac54y+\frac{dy}{dt}, \] satisfying \[ y(0)=1, \qquad \left(\frac{dy}{dt}\right)_{t=0}=0, \] is \(y(t)\), then \(y(\pi)=\)

Consider the linear system of equations \[ \begin{bmatrix} 3 & -1 & 4 \\ 6 & 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \end{bmatrix}. \] In this system of equations, if \(x\) is always a fixed constant, then the system has:& nbsp;