TS PGECET Question Paper 2025 (Available): Download June 18 Shift 2 Question Paper with Answer Key PDF

Determine the rank of the matrix:
\[ \begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{pmatrix} \]

• (1) 1
• (2) 2
• (3) 3
• (4) 0

Evaluate the integral:
\[ \int_0^1 x e^x \, dx \]

• (1) \(e - 1\)
• (2) \(e\)
• (3) \(e - 2\)
• (4) \(2e - 1\)

Solve the differential equation:
\[ \frac{d^2y}{dx^2} - 4y = 0 \]

• (1) \(y = C_1 e^{2x} + C_2 e^{-2x}\)
• (2) \(y = C_1 \cos(2x) + C_2 \sin(2x)\)
• (3) \(y = C_1 e^{x} + C_2 e^{-x}\)
• (4) \(y = C_1 e^{4x} + C_2 e^{-4x}\)

A bag contains 3 red and 2 blue balls. Two balls are drawn without replacement. What is the probability that both are red?

• (1) \(\frac{3}{10}\)
• (2) \(\frac{1}{5}\)
• (3) \(\frac{2}{5}\)
• (4) \(\frac{1}{10}\)

Use Newton-Raphson method to find the root of \(f(x) = x^3 - x - 2 = 0\) starting with \(x_0 = 1\) after one iteration.

• (1) \(1.5\)
• (2) \(1.333\)
• (3) \(1.25\)
• (4) \(1.4\)

What is the time complexity of inserting an element into a balanced binary search tree?

• (1) \(O(\log n)\)
• (2) \(O(n)\)
• (3) \(O(n \log n)\)
• (4) \(O(1)\)

Which algorithm is used for finding the shortest path in a weighted graph with negative edges?

• (1) Bellman-Ford
• (2) Dijkstra’s
• (3) Kruskal’s
• (4) Prim’s

What is the role of the page table in an operating system?

• (1) Maps virtual addresses to physical addresses
• (2) Stores process executable code
• (3) Manages CPU scheduling
• (4) Handles file system operations

What is the purpose of the subnet mask in IP addressing?

• (1) To separate network and host portions of an IP address
• (2) To encrypt data packets
• (3) To assign IP addresses dynamically
• (4) To route packets between networks

What is a primary key in a relational database?

• (1) A unique identifier for each record in a table
• (2) A key used for sorting records
• (3) A key linking two tables
• (4) A key for encrypting data