List of top Questions asked in Andhra Pradesh Post Graduate Engineering Common Entrance Test

The probability of a component being defective is 0.01. There are 100 such components in a machine. Then the probability of two or more defective components in the machine is _______

If the function \( f(z) = -x^2 + xy + y^2 + i(ax^2 + bxy + cy^2) \) of complex variable \(z = x + iy\) is analytic in the complex plane, then the values of \(a, b, c\) are _______

Let \( f(x,y) = e^{-x} \sin(-y), g(x,y) = e^{-x} cos(-y) \), and \( C \) be the square with vertices at \( (0,0), (\frac{\pi}{2},0), (\frac{\pi}{2},\frac{\pi}{2}), (0,\frac{\pi}{2}) \). Then, the value of the line integral \( \oint_C [f(x,y)dx + g(x,y)dy] \) is _______

Let \( A \) be a \(3 \times 3\) matrix and \( B = 2A^2 + A^{-1} - I \), where \( I \) is a \(3 \times 3\) identity matrix. If the eigenvalues of \( A \) are 1, –1 and 2, then the trace of \( B \) is ________