List of practice Questions

Define the dielectric constant of a medium.

Define Curie temperature in magnetism.

Using Gauss’s law, obtain an expression for the electric field at a point due to a uniformly charged infinite plane sheet.

State Gauss’s law. Determine the electric field intensity at a point due to an infinitely long uniformly charged straight wire.

State Huygens’ Principle. Use it to prove the laws of reflection or laws of refraction at a plane surface.

A JK flip-flop has inputs $J = 1$ and $K = 1$. 
The clock input is applied as shown. Find the output clock cycles per second (output frequency). 
 

f(w, x, y, z) =\( \Sigma\) (0, 2, 5, 7, 8, 10, 13, 14, 15) 
Find the correct simplified expression. 
 

Given the state-space system:
\[ \dot{x} = \begin{bmatrix} -4 & -1.5 \\ 4 & 0 \end{bmatrix} x + \begin{bmatrix} 2 \\ 0 \end{bmatrix} u \] \[ y = \begin{bmatrix} 0.15 & 0.625 \end{bmatrix} x \] Find the Transfer Function (TF).
The value of \[ \frac{{}^{100}C_{50}}{51} + \frac{{}^{100}C_{51}}{52} + \cdots + \frac{{}^{100}C_{100}}{101} \] is:
Which of the following recurrence relations represents the average case time complexity of QuickSort?
Consider a binary tree whose preorder traversal is \[ P, Q, S, E, R, F, G \] and inorder traversal is \[ S, Q, E, P, F, R, G. \] Which of the following statements is correct?
In a data warehouse, a 3D cube initially has dimensions: Product type, Month, and Country. After visualization, the dimension Country is refined into State. Which OLAP operation is performed?
Node size = 4096 B
Node pointer = 10 B
Search key = 11 B
Record pointer = 12 B
Find the maximum number of node pointers.
Consider the ER model:
E1 (A11, A12, A13)
E2 (A21, A22, A23)
Where:
- A21 is the key of E2
- A22 is a multivalued attribute
- R12 is a many-to-many relationship between E1 and E2
Find the minimum number of relations required to convert this ER model into tables.
Consider the relation \( R(A, B, C, D, E) \)
Functional Dependencies:
\[ A \rightarrow BC \] \[ CD \rightarrow E \] \[ E \rightarrow A \] Find the number of candidate keys.
Which of the following logical statements is not valid?
Let \( P \) be a \(6 \times 4\) matrix and \( Q \) be a \(4 \times 6\) matrix such that \( PQ = 0 \). Which of the following statements is correct?
Given that the solution of \[ \frac{d^2y}{dx^2} + \alpha \frac{dy}{dx} + \beta y = -e^{-x} \] is \[ y(x) = C_1 e^{-x} + C_2 e^{2x} + x e^{-x}, \] find the values of $\alpha$ and $\beta$.
There are four different types of bananas. In how many ways can 12 children select bananas so that at least one child selects different types of bananas?
If the function \( f(x) \) satisfies \[ f'(x) = f(x) - \pi x + \pi, \] then the possible value of \( f(1) \) is
Find the radius of convergence of the series
\[ \sum_{n=0}^{\infty} \frac{\binom{n}{6}^2}{(2n)!} x^n \]
Given \[ y = -3x - 3 + m e^{2x} \] Find the Orthogonal Trajectories (O.T.).
Let \[ A = \begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 0 \end{pmatrix}. \] Which of the following statements is correct?
If \[ f(x) = \big( f(x) - \pi x \big) + \pi, \] then the possible value(s) of \( f(3) - f(2) \) is/are:
Evaluate: \[ {}^{5}C_{0} + {}^{6}C_{1} + {}^{7}C_{2} + {}^{8}C_{3} + {}^{9}C_{4} + {}^{10}C_{5} + {}^{11}C_{6}. \]