List of top Engineering Mathematics Questions asked in AP PGECET

What is the 2's complement representation of the decimal number -5 in 8-bit binary?
In a simple undirected graph, the sum of the degrees of all vertices is 20. How many edges are present in the graph?
Which of the following propositions is logically equivalent to $p \rightarrow q$?
Which of the following circuits is a sequential circuit?
Two graphs $G_1$ and $G_2$ are isomorphic if which of the following conditions is satisfied?
If a graph G has 10 vertices and each vertex has degree 3, how many edges does G have?
A graph is said to be Eulerian if it contains a closed trail that includes every:
How many different 5-character passwords can be formed using the digits 0-9 and lowercase letters a-z if the first character must be a letter and repetitions are allowed?
For a connected planar graph with 10 vertices and 15 edges, how many faces does the graph have?
The number of ways to distribute 10 identical apples among 4 children such that every child receives at least one apple 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 \( A, B \) 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
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?
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?
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
A complex function \( f(z) = u + iv \) with \( u = \operatorname{Re}(z) + \operatorname{Im}(z) \) is analytic if \( v = \) ________
Given \( f(z) = \dfrac{-z}{(z - 2)^2} \), which of the following is the Laurent series expansion of \( f(z) \) around \( z = 2 \)?
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 \[ A = \begin{bmatrix} 4 & 1 & 2 \\ 1 & 3 & 0 \\ 2 & 0 & 5 \end{bmatrix} \]
If \( A = \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix} \), then eigen value and its corresponding eigen vector
Let E and F be the events of a sample space S of an experiment, if $ P(S/F) = P(F/F) $, then $ P(S/F) $ is equal to:
Evaluate the limit $$ \lim_{x \to \infty} \frac{\sin x}{x} $$