List of practice Questions

The complete integral of the partial differential equation \( pz^2 \sin^2 x + qz^2 \cos^2 y = 1 \) is:
The area between the parabolas \( y^2 = 4 - x \) and \( y^2 = x \) is given by:
The value of the integral \[ \iiint\limits_{0}^{a, b, c} e^{x+y+z} \, dz \, dy \, dx \] is:
If \( \nabla \phi = 2xy^2 \hat{i} + x^2z^2 \hat{j} + 3x^2y^2z^2 \hat{k} \), then \( \phi(x,y,z) \) is:
The only function from the following that is analytic is:
The value of \( m \) so that \( 2x - x^2 + m y^2 \) may be harmonic is:
The value of \( \oint_C \frac{1}{z} dz \), where \( C \) is the circle \( z = e^{i\theta}, 0 \leq \theta \leq \pi \), is:
The Region of Convergence (ROC) of the signal \( x(n) = \delta(n - k), k>0 \) is:
The Laplace transform of a signal \( X(t) \) is \[ X(s) = \frac{4s + 1}{s^2 + 6s + 3}. \] The initial value \( X(0) \) is:
Given the inverse Fourier transform of \(f(s) = \begin{cases} a - |s|, & |s| \leq a \\ 0, & |s|>a \end{cases}\).The value of \[ \int_0^\pi \left( \frac{\sin x}{x} \right)^2 dx \] is:
If \( A = [a_{ij}] \) is the coefficient matrix for a system of algebraic equations, then a sufficient condition for convergence of Gauss-Seidel iteration method is:
For applying Simpson's \( \frac{1}{3} \) rule, the given interval must be divided into how many number of sub-intervals?
A program that converts Source Code into machine code is called
Which of the following can adsorb larger volume of hydrogen gas?
Which one of the following flows in the internal circuit of a galvanic cell?
Which one of the following is not a primary fuel?
Which of the following molecules will not display an infrared spectrum?
Which one of the following behaves like an intrinsic semiconductor, at absolute zero temperature?
The energy gap (eV) at 300K of the material GaAs is
Which of the following ceramic materials will be used for spark plug insulator?
In unconventional superconductivity, the pairing interaction is
What is the magnetic susceptibility of an ideal superconductor?
The Rayleigh scattering loss, which varies as _______ in a silica fiber.
What is the near field length \(N\) that can be calculated from the relation (if \(D\) is the diameter of the transducer and \(\lambda\) is the wavelength of sound in the material)?
Which one of the following represents an open thermodynamic system?