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

Let \( A, B \) be two events of a sample space such that \( P(A) = \frac{1}{4} \), \( P(B|A) = \frac{1}{2} \), \( P(A|B) = \frac{1}{4} \). If \( \overline{B} \) is the complement of \( B \), then \( P(A | \overline{B}) \) is _____
In a workshop of 100 machines, 25 machines are defective. Assuming the Poisson law for the number of defective machines, the probability that a random sample of 5 machines will have no defective machine is
In a town, the probability that a person attends a gym on weekdays is 0.7, the probability that a person attends the gym on weekends is 0.4, and the probability that a person attends the gym on weekdays or weekends, or both is 0.3. What is the probability that a person attends the gym on both weekdays and weekends?
Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be a function such that \( f(0) = 3 \) and \( |f'(x)| \leq 2 \), \( \forall x \in \mathbb{R} \). Then \( f(2) \) lies in which of the following intervals?
A complex function \( f(z) = u + iv \) with \( u = \operatorname{Re}(z) + \operatorname{Im}(z) \) is analytic if \( v = \) ________
Let \( f(x) = x^3 - \dfrac{9}{2}x^2 + 6x - 2 \) be a function defined on the closed interval \( [0, 3] \). Then, the global maximum value of \( f(x) \) is
Given \( f(z) = \dfrac{-z}{(z - 2)^2} \), which of the following is the Laurent series expansion of \( f(z) \) around \( z = 2 \)?
The directional derivative of the function \( f(x, y) = 2x^2 + y^2 \) along a line directed from \( (0, 0) \) to \( (1, 1) \), evaluated at the point \( x = 1, y = 1 \), is ___
Consider the system of equations: \[ \begin{aligned} x + y + z &= 6 \\ 2x + 2y + 3z &= 13 \\ 3x + 4y + 5z &= 20 \end{aligned} \] Which of the following statements is true about the solution to this system?
If \( A \) and \( B \) are two non-zero square matrices of same size such that the product matrix \( AB \) is a zero matrix, then which of the following must be true?
A fair coin is flipped three times. What is the probability of getting exactly two heads?
Find the eigenvalues of the matrix:
Matrix \[ A = \begin{bmatrix} 4 & 1 & 2 \\ 1 & 3 & 0 \\ 2 & 0 & 5 \end{bmatrix} \]
The value of \( \int_0^3 \int_0^0 (x^2 + 3y^2) \, dy \, dx \) is
If the mean and variance of a binomial variate are 12 & 4, then the distribution is _____

The variance for continuous probability function \(f(x) = x^2 e^{-x}\) when \(x \ge 0\) is

If \(f = \text{Tan}^{-1}(xy)\) then \((\frac{\partial f}{\partial x})_{(1,2)}\) = _____ .

Line of Regression of y on x
Let S be a closed surface for which \( \oiint_S \vec{r} \cdot \hat{n} \, dS = 1 \), then the volume enclosed by the surface is ____ .
Cauchy Riemann Equations for an Analytic function are
For the function \( \frac{\sin z}{z^4} \), the point z = 0 is
In Method of Variation of Parameters, \( A = -\int \frac{y_2 R dx}{W} \). If \( V = \sin x, R = \sec x, W = 1 \) then A= ____ .
Auxiliary Equation for the Cauchy Euler Equation \( (x^2 D^2 + xD + 4)y = 0 \) is ____ .
The general solution of the differential equation \( x^2 \frac{d^2y}{dx^2} - 2x \frac{dy}{dx} + 2y = 4 \) is
The system AX=B has a unique solution if
If \( A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \), \( B = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} \) and \( C = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix} \) then