List of practice Questions

Consider a distribution feeder, with $ R/X $ ratio of 5. At the receiving end, a 350 kVA load is connected. The maximum voltage drop will occur from the sending end to the receiving end, when the power factor of the load is: \[ {(round off to three decimal places).} \]

In the circuit with ideal devices, the power MOSFET is operated with a duty cycle of 0.4 in a switching cycle with $ I = 10 \, {A} $ and $ V = 15 \, {V} $. The power delivered by the current source, in W, is: \[ {(round off to the nearest integer).} \]

The induced emf in a 3.3 kV, 4-pole, 3-phase star-connected synchronous motor is considered to be equal and in phase with the terminal voltage under no-load condition. On application of a mechanical load, the induced emf phasor is deflected by an angle of $ 2^\circ $ mechanical with respect to the terminal voltage phasor. If the synchronous reactance is $ 2 \, \Omega $, and stator resistance is negligible, then the motor armature current magnitude, in amperes, during loaded condition is closest to: \[ {(round off to two decimal places).} \]

Let $ (x, y) \in \mathbb{R}^2 $. The rate of change of the real-valued function
\[ V(x, y) = x^2 + x + y^2 + 1 \] at the origin in the direction of the point $ (1, 2) $ is _____________ (round off to the nearest integer).

Consider ordinary differential equations given by \[ \frac{dx_1(t)}{dt} = 2x_2(t), \quad \frac{dx_2(t)}{dt} = r(t) \] with initial conditions $ x_1(0) = 1 $ and $ x_2(0) = 0 $. If

Let $ C $ be a clockwise oriented closed curve in the complex plane defined by $ |z| = 1 $. Further, let $ f(z) = jz $ be a complex function, where $ j = \sqrt{-1} $. Then, \[ \oint_C f(z)\, dz = \underline{{2cm}} \quad {(round off to the nearest integer)}. \]

The op-amps in the following circuit are ideal. The voltage gain of the circuit is __________ (round off to the nearest integer).

The switch (S) closes at $ t = 0 $ sec. The time, in sec, the capacitor takes to charge to 50 V is ___________ (round off to one decimal place).

In an experiment to measure the active power drawn by a single-phase RL Load connected to an AC source through a $2\,\Omega$ resistor, three voltmeters are connected as shown in the figure below. The voltmeter readings are as follows: $ V_{{Source}} = 200\,{V}, \quad V_R = 9\,{V}, \quad V_{{Load}} = 199\,{V}. $ Assuming perfect resistors and ideal voltmeters, the Load-active power measured in this experiment, in W, is ___________ (round off to one decimal place).

In the Wheatstone bridge shown below, the sensitivity of the bridge in terms of change in balancing voltage $ E $ for unit change in the resistance $ R $, in mV/$\Omega$, is _____________ (round off to two decimal places).

The steady-state capacitor current of a conventional DC–DC buck converter operating in continuous conduction mode (CCM) is shown over one switching cycle. If the input voltage is $30\,\text{V}$, the value of the inductor used (in mH) is ____________ (rounded off to one decimal place).

An ideal low pass filter has frequency response given by
\[ H(j\omega) = \begin{cases} 1, & |\omega| \leq 200\pi \\ 0, & \text{otherwise} \end{cases} \] Let $ h(t) $ be its time domain representation. Then $ h(0) = \underline{\hspace{2cm}} $ (round off to the nearest integer).

Which one of the following immunoglobulin is responsible for atopic allergy?

Typhoid Vi antigen type of vaccine is:

There is a circular park of diameter 65 m as shown in the following figure, where AB is a diameter. An entry gate is to be constructed at a point P on the boundary of the park such that distance of P from A is 35 m more than the distance of P from B. Find distance of point P from A and B respectively.

From the following information, calculate opening and closing inventory :

Gross Profit Ratio – 25%
Revenue from operations – ₹ 8,00,000
Inventory turnover ratio – 4 times
Opening inventory was 2 times of the closing inventory.

The graph shows the variation of current with voltage for a p-n junction diode. Estimate the dynamic resistance of the diode at $ V = -0.6 $ V.

Define electric flux through a surface. Give the significance of a Gaussian surface. A charge outside a Gaussian surface does not contribute to total electric flux through the surface. Why?

Four resistors, each of resistance R and a key K are connected as shown in the figure. The equivalent resistance between points A and B when key K is open will be:

If $ x = a \left( \cos \theta + \log \tan \frac{\theta}{2} \right) $ and $ y = \sin \theta $, then find $ \frac{d^2y}{dx^2} $ at $ \theta = \frac{\pi}{4} $.

A bank offers loans to its customers on different types of interest rates namely, fixed rate, floating rate, and variable rate. From the past data with the bank, it is known that a customer avails loan on fixed rate, floating rate, or variable rate with probabilities 10%, 20%, and 70% respectively. A customer after availing a loan can pay the loan or default on loan repayment. The bank data suggests that the probability that a person defaults on loan after availing it at fixed rate, floating rate, and variable rate is 5%, 3%, and 1% respectively. Based on the above information, answer the following:
(i) What is the probability that a customer after availing the loan will default on the loan repayment?
(ii) A customer after availing the loan, defaults on loan repayment. What is the probability that he availed the loan at a variable rate of interest?

The integrating factor of the differential equation $ (x + 2y^3) \frac{dy}{dx} = 2y $ is:

A battery of emf $ E $ and internal resistance $ r $ is connected to a rheostat. When a current of 2A is drawn from the battery, the potential difference across the rheostat is 5V. The potential difference becomes 4V when a current of 4A is drawn from the battery. Calculate the value of $ E $ and $ r $.

$ \int \frac{e^{-x}}{16 + 9e^{-2x}} \, dx$ is equal to :

The company's profits dropped significantly this quarter; _________, it plans to expand into three new markets.