List of practice Questions

Choose the correct statement of Reciprocity theorem in single source network:
If BW is bandwidth, \( \omega_r \) is resonant frequency and Q is quality factor of a resonant circuit, then Selectivity is defined as:
The response of a 1-$\phi$ R-L series circuit is \( i(t) = Ae^{-\frac{R}{L}t} + I_m \sin(\omega t - \theta) \). Then the supply voltage should be:
Point charges \( Q_1 = 1\text{nC} \) and \( Q_2 = 2\text{nC} \) are at a distance apart. Which of the following statement is \textbf{incorrect?
If \( \vec{D} = \epsilon \vec{E} \) and \( \vec{V} = \sigma \vec{E} \) in a given material, the material is said to be:
A source voltage of 100 V dc is applied across a RLC series circuit. Under steady-state conditions, voltages across each element is
The equivalent inductance of two equal inductances when connected in series aiding is 14 H and when connected in series opposing is 6 H. What is the coefficient of coupling?
Certain resistors connected in parallel and the equivalent resistance is \( X \). If one of the resistances is removed the equivalent resistance is \( Y \). What is the conductance value of removed resistance?
A signal of \( v = 5 + 10 \sin \omega t \) is applied across a \( 2\, \Omega \) resistor. The power dissipated in the resistor is
Three impedances \( 6 + j(10/3)\, \Omega \) each are connected in delta. The per-phase impedance of equivalent star circuit will be
The integrating factor of \[ \frac{dy}{dx} + y \cot x = 2x + x^2 \cot x \] is
Particular integral of \[ \frac{dy}{dx} + y = e^{x} \] is
If \[ f(x) = \begin{cases} -\pi, & -\pi<x<0 \\ x, & 0<x<\pi \end{cases} \] then the constant term of the Fourier series is
The mean and variance of a random variable \( X \) having a Binomial distribution are 4 and 2 respectively, then \( P(X=1) \) is
A 1-$\phi$, RC series circuit has \( R = 5\, \Omega \) and \( C = 10\, \mu F \). If the angular frequency of current is 20000 rad/sec, then the applied voltage
If the function \( u = \sin^{-1} \left( \frac{x^3 + y^3}{x + y} \right) \), then \[ x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} \] is
A particle of mass \( 2 \) kg is on a smooth horizontal table and moves in a circular path of radius \( 0.6 \) m. The height of the table from the ground is \( 0.8 \) m. If the angular speed of the particle is \( 12 \) rad/s, the magnitude of its angular momentum about a point on the ground right under the center of the circle is:
The minimum deviation produced by a hollow prism filled with a certain liquid is found to be 30\(^\circ\). The light ray is also found to be refracted at an angle of 30\(^\circ\). Then the refractive index of the liquid is
What is the minimum age required to become a member of the Legislative Assembly (Vidhan Sabha) in India?
There are 2 bags each containing 3 white and 5 black balls and 4 bags each containing 6 white and 4 black balls. If a ball drawn randomly from a bag is found to be black, then the probability that this ball is from the first set of bags is:
A solid cylinder rolls down an inclined plane without slipping. If the translational kinetic energy of the cylinder is 140 J, the total kinetic energy of the cylinder is
When I look at my past, I often regret of my past decisions?
Find the sum of the first 10 terms of the sequence \( 2.5 + 5.9 + 8.13 + 11.17 + \cdots \ to \ 10 \ terms =\):
If \[ \cos \alpha + 4 \cos \beta + 9 \cos \gamma = 0 \quad \text{and} \quad \sin \alpha + 4 \sin \beta + 9 \sin \gamma = 0, \] then \[ 81 \cos (2\gamma - 2\alpha) - 16 \cos (2\beta - 2\alpha) = ? \]
If the position of the electron was measured with an accuracy of \( \pm 0.002 \) nm, the uncertainty in the momentum of it would be (in kg ms\(^{-1}\)) (\( h = 6.626 \times 10^{-34} \) Js):