List of top Questions asked in AP PGECET- 2026

An ER model contains:
• Student with attributes: StudentID, Name, Age
• Course with attributes: CourseID, Title
• A many-to-many relationship Enrols between Student and Course, with attribute Grade In the relational design, a separate table is needed to capture the relationship and its attribute.
The correct schema design is?

Two transactions operate on the same data item:
• $T_1$: Read(X), Write(X)
• $T_2$: Read(X), Write(X)
If both execute without proper control, the system may face?

A web developer is creating a webpage where:
• A heading is displayed at the top
• A paragraph of text follows
• A link is provided to navigate to another webpage
Which of the following HTML code snippets correctly represents this structure?

Let $A$ and $B$ be two events of a sample space such that \[ P(A)=\frac{1}{2},\qquad P(A\mid B)=\frac{1}{4},\qquad P(B\mid A)=\frac{1}{2}. \] Then, \[ P(\overline{A}\mid\overline{B})=\_\_\_\_\_, \] where $\overline{A}$ denotes the complement of $A$.

Consider the function $ f(x,y) = (x - 2)^2(y + 3) $. Then:

The value of the improper integral $ \int_0^1 \frac{1}{4\sqrt{1-x}} dx $ is equal to _______.

Consider the following system of equations: \[ \begin{pmatrix} 1 & 3 & 2 2 & 2 & -3 4 & 4 & -6 2 & 5 & 2 \end{pmatrix} \begin{pmatrix} x y z \end{pmatrix} = \begin{pmatrix} 1 1 2 1 \end{pmatrix} \] The value of $ y^2 + z^2 $ is _______.

Let $ G = \mathbb{R}^* \times \mathbb{R} $, where $ \mathbb{R} $ is the set of all real numbers and $ \mathbb{R}^* = \mathbb{R} - \{0\} $. Define an operation $ \circ $ on $ G $ as $ (a,b) \circ (c,d) = (ac, bc + d) $. Then, the identity element of the group $ (G, \circ) $ is _____.

Let $ f(x) = x^3 - x - 2 $. Using the bisection method on the interval $ [1, 2] $, how many iterations are required to approximate a root correct to two decimal places?

In a Boolean algebra theorem which of the following is TRUE?

With the initial guess of $ x_0 = 1, x_1 = 2 $, the first iteration value using secant method for $ f(x) = x^2 + 5x + 4 $ will be _______.

Define two relations $ \sigma_1 $ and $ \sigma_2 $ on the set of all real numbers $ \mathbb{R} $ as follows:
$ a \sigma_1 b \iff a - b $ is a rational number
$ a \sigma_2 b \iff a - b $ is an integer
Which one of the following is correct?

In the context of the Client-Server model, which HTTP response status code indicates that the requested resource was not found on the server?

Let $ 1 < a < 7 $ and $ b > 7 $. If both mean and median of the data set $ \{1, 7, -7, a, b\} $ are equal to 4, then the value of $ b $ is _____.

What is the primary purpose of the XML Document Type Definition (DTD)?