Dbatu Previous Year Question Paper Questions & Answers

Preparing for exams with previous years’ question papers can greatly enhance understanding and confidence. For students at DBATU (Dr. Babasaheb Ambedkar Technological University), revisiting past question papers is a proven strategy for better results. Below are questions and answers from various subjects to help students prepare comprehensively.

Applied Mathematics

Question: Explain Rolle’s Theorem with an example.
Answer: Rolle’s Theorem states that if a function is continuous on [a, b], differentiable on (a, b), and f(a) = f(b), there exists at least one c in (a, b) such that f'(c) = 0. Example: f(x) = x² – x – 2 on [-1, 2].

Question: What is the Laplace transform of e^(-at)?
Answer: The Laplace transform of e^(-at) is 1/(s + a).

Question: Solve the differential equation dy/dx = y.
Answer: The solution is y = Ce^x, where C is an integration constant.

Question: Define eigenvalues and eigenvectors.
Answer: Eigenvalues are scalars λ such that Ax = λx for matrix A and vector x. Eigenvectors are the corresponding vectors x.

Question: What is a Taylor series expansion?
Answer: It is the representation of a function as an infinite sum of terms, derived from the derivatives of the function at a single point.

Question: Explain the significance of Green’s Theorem.
Answer: Green’s Theorem relates a line integral around a closed curve to a double integral over the plane region it encloses.

Question: Find the derivative of x³ + 3x² + 5.
Answer: The derivative is 3x² + 6x.

Question: State the conditions for a function to be analytic.
Answer: A function is analytic if it is differentiable everywhere in its domain and satisfies the Cauchy-Riemann equations.

Question: What is the Fourier series of f(x) = x on [-π, π]?
Answer: The Fourier series is a summation of sine terms, as the function is odd.

Question: Solve the integral ∫x²dx.
Answer: The solution is (x³/3) + C, where C is the constant of integration.

Question: What is the probability density function?
Answer: It is a function that describes the likelihood of a random variable to take a specific value.

Question: Define a random variable.
Answer: A random variable is a variable whose values are determined by the outcome of a random phenomenon.

Question: What is the significance of the mean value theorem?
Answer: It guarantees at least one point where the instantaneous rate of change equals the average rate of change over an interval.

Question: Differentiate sin²x.
Answer: The derivative is 2sinxcosx or sin(2x).

Question: What are the basic laws of probability?
Answer: They include addition law, multiplication law, and Bayes’ theorem.

Question: Define a Markov process.
Answer: A Markov process is a stochastic process where the future state depends only on the present state, not on the history.

Question: Find the integral of e^x dx.
Answer: The solution is e^x + C.

Question: What is an ordinary differential equation (ODE)?
Answer: An ODE is an equation involving a function and its derivatives with respect to one variable.

Question: Solve y” + y = 0.
Answer: The solution is y = C₁cosx + C₂sinx.

Data Structures

Question: Define a stack.
Answer: A stack is a linear data structure that follows the Last In, First Out (LIFO) principle.

Question: What is a queue?
Answer: A queue is a linear data structure that follows the First In, First Out (FIFO) principle.

Question: Explain the concept of linked lists.
Answer: Linked lists consist of nodes, where each node contains data and a pointer to the next node.

Question: Differentiate between a stack and a queue.
Answer: Stack is LIFO, while queue is FIFO.

Question: What is a binary search tree?
Answer: It is a tree data structure where each node has at most two children, and the left child is less than the parent, and the right is greater.

Question: Explain hashing.
Answer: Hashing is a technique to map data to a fixed-size table using a hash function.

Question: Define a graph.
Answer: A graph is a collection of nodes (vertices) connected by edges.

Question: What is depth-first search (DFS)?
Answer: DFS is a graph traversal technique that explores as far as possible along a branch before backtracking.

Question: What is breadth-first search (BFS)?
Answer: BFS is a graph traversal method that explores all neighbors at the current depth before moving deeper.

Question: Explain dynamic programming.
Answer: It is a method for solving complex problems by breaking them into subproblems and solving each subproblem only once.

Question: What is recursion?
Answer: Recursion is a function calling itself directly or indirectly to solve a smaller instance of the problem.

Question: Define a circular queue.
Answer: A circular queue is a linear data structure in which the last position is connected to the first position to make a circle.

Question: What are AVL trees?
Answer: AVL trees are self-balancing binary search trees where the difference between heights of left and right subtrees cannot be more than one.

Question: What is a priority queue?
Answer: A priority queue is a type of queue where each element is associated with a priority, and elements with higher priority are dequeued before others.

Question: What is hashing collision?
Answer: A hashing collision occurs when two keys hash to the same index in a hash table.

Question: Explain Kruskal’s algorithm.
Answer: It is a minimum spanning tree algorithm that adds edges in increasing order of weight, ensuring no cycles are formed.

Question: What is a doubly linked list?
Answer: It is a linked list where each node has two pointers, one to the next node and another to the previous node.

Question: What is a heap?
Answer: A heap is a complete binary tree where the value of each node is greater than or equal to (max heap) or less than or equal to (min heap) its children.

Question: Explain the concept of adjacency matrix.
Answer: An adjacency matrix is a 2D array used to represent a graph, where the cell (i, j) indicates whether there is an edge between vertex i and vertex j.

Electronics and Communication

Question: What is Ohm’s Law?
Answer: Ohm’s Law states that V = IR, where V is voltage, I is current, and R is resistance.

Question: Define a diode.
Answer: A diode is a semiconductor device that allows current to flow in one direction only.

Question: What is a transistor?
Answer: A transistor is a semiconductor device used to amplify or switch electronic signals.

Question: Explain Kirchhoff’s current law (KCL).
Answer: KCL states that the total current entering a junction equals the total current leaving the junction.

Question: Define modulation.
Answer: Modulation is the process of varying one or more properties of a carrier signal based on the message signal.

Question: What is amplitude modulation (AM)?
Answer: In AM, the amplitude of the carrier wave varies with the amplitude of the input signal.

Question: What is frequency modulation (FM)?
Answer: In FM, the frequency of the carrier wave is varied according to the input signal.

Question: Explain the working of an operational amplifier.
Answer: An operational amplifier is a high-gain voltage amplifier with differential inputs and a single-ended output.

Question: What is an inductor?
Answer: An inductor is a passive component that stores energy in its magnetic field when current flows through it.

Question: Define capacitance.
Answer: Capacitance is the ability of a capacitor to store charge per unit voltage.

Question: What is a rectifier?
Answer: A rectifier is a device that converts AC to DC.

Question: Explain the concept of resonance.
Answer: Resonance occurs when a system oscillates at its natural frequency with maximum amplitude.

Question: Define bandwidth.
Answer: Bandwidth is the range of frequencies within which a circuit operates effectively.

Question: What is a filter?
Answer: A filter is a circuit that passes certain frequencies and attenuates others.

Question: Explain pulse width modulation (PWM).
Answer: PWM is a technique to encode a message into a pulsing signal by varying the pulse width.

Question: What is a Zener diode?
Answer: A Z