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

Find the inverse of the matrix:

\[ \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \]

• (1) \(\begin{pmatrix} 4 & -3 \\ -1 & 2 \end{pmatrix}\)
• (2) \(\begin{pmatrix} 4 & 3 \\ -1 & 2 \end{pmatrix}\)
• (3) \(\begin{pmatrix} 2 & -3 \\ -1 & 4 \end{pmatrix}\)
• (4) \(\begin{pmatrix} -4 & 3 \\ 1 & -2 \end{pmatrix}\)

Evaluate the limit:
\[ \lim_{x \to 0} \frac{\sin x - x}{x^3} \]

• (1) \(-\frac{1}{6}\)
• (2) \(\frac{1}{6}\)
• (3) \(0\)
• (4) \(\infty\)

Solve the differential equation:
\[ \frac{dy}{dx} + y = e^x \]

• (1) \(y = \frac{e^x}{2} + C e^{-x}\)
• (2) \(y = e^x + C e^{-x}\)
• (3) \(y = \frac{e^x}{2} + C e^x\)
• (4) \(y = e^x + C e^x\)

If a fair die is rolled twice, what is the probability that the sum is at least 10?

• (1) \(\frac{1}{12}\)
• (2) \(\frac{1}{6}\)
• (3) \(\frac{1}{9}\)
• (4) \(\frac{1}{4}\)

Use the bisection method to find the root of \(f(x) = x^2 - 2 = 0\) in \([1, 2]\) with an error less than 0.01.

• (1) \(1.414\)
• (2) \(1.5\)
• (3) \(1.732\)
• (4) \(1.618\)

Which of the following correctly describes a binary search tree (BST)?

• (1) A tree where each node has at most two children, with left child \(<\) node \(<\) right child
• (2) A tree where each node has exactly two children
• (3) A tree where all leaves are at the same level
• (4) A tree where the root is the smallest value

What is the time complexity of merge sort in the worst case?

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

Which of the following are necessary conditions for a deadlock?

• (1) Mutual Exclusion and Hold and Wait
• (2) Preemption and Circular Wait
• (3) Mutual Exclusion and No Preemption
• (4) Hold and Wait and Preemption

Which of the following correctly describes the TCP/IP model?

• (1) A 4-layer model: Application, Transport, Internet, Network Access
• (2) A 7-layer model including Physical and Data Link layers
• (3) A 5-layer model including Session and Presentation layers
• (4) A 3-layer model: Application, Transport, Network

What is normalization in database design?

• (1) Process of organizing data to eliminate redundancy
• (2) Process of indexing tables for faster queries
• (3) Process of encrypting database records
• (4) Process of backing up database files