List of practice Questions

The values of \( \mu \) which satisfy the equation \( A^{100} \vec{x} = \mu \vec{x} \), where \( A = \begin{bmatrix} 2 & -1 \\ 0 & -2 \\ 1 & 1 \end{bmatrix} \) are
The number of flip-flops used in a decade counter is _____
A solution of the ODE \( \frac{d^2y}{dx^2} + \frac{dy}{dx} = 0 \) is such that \( y(0) = 2 \) and \( y'(0) = 3 \). The value of \( y''(0) \) is
Complete integral of the partial differential equation \( 2\frac{\partial^2 f}{\partial q^2} + 3\frac{\partial f}{\partial q} = 6x + 2y \) is
The radius of convergence of Taylor's series expansion of \( f(z) = \frac{1}{(z - 1)^2} \) in powers of \( (z - 1) \) is ...
Evaluate \( \int_C \frac{dz}{z^2 + 9} \), where \( C \) is \( |z - 3| = 4 \)
A die is thrown at random, find the probability of getting 5 or a number greater than 2 and is even
For any two arbitrary events \( A \) and \( B \), which of the following is true?
The primary advantage of using a rectangular waveguide over other transmission line types is
Fundamental principle behind the propagation of light in dielectric waveguides and optical fibers is
What is the radiation pattern of a point source antenna in free space?
The purpose of using a transmission line segment with a length of \( \lambda/4 \) in impedance matching is
Determine the value of \( p \) such that the rank of matrix \( A \) is 2:
\[ A = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 0 & 2 & p \\ 1 & 0 & p & 7 \end{bmatrix} \]
The matrix \( A = \begin{bmatrix} 3 & -1 & 1 \\ 1 & -5 & 1 \\ 1 & -1 & 3 \end{bmatrix} \) has eigenvalues 2, 3, 6 then the eigenvalues of \( A^4 \) are
The curl of a vector field \( F \) is zero throughout a region of space. What does this imply about the behavior of \( F \)?
Which of the following assertions accurately describes Gauss's theorem?
Which of the following is not a source of magnetostatic fields?
Which one of the following field patterns represents a TEM wave traveling in the positive \( z \)-direction?
If an electromagnetic wave travels in the positive \( x \)-direction, and its electric field oscillates in the \( y \)-direction, what is the polarization of the wave?
In which scenario would you expect the highest amount of refraction to occur when an electromagnetic wave passes from one medium to another?
In a transmission line with a characteristic impedance \( Z_0 \), what happens if the load impedance \( Z_L \) matches \( Z_0 \)?
Which of the following statement is correct with respect to Latch?
The output of each stage of flip-flop is connected to input of next stage flip-flop and the complement output of the last stage flip-flop is again connected to the input of first stage flip-flop then this is called
Add the two numbers 87H and 79H in the 8085 microprocessors, then
Which theorem relates the line integral of a vector field over a closed curve to the surface integral of the curl of the field over the surface bounded by the curve?