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Solve the linear homogeneous equation \[ D^2y - 5Dy + 6y = 0 \]
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Solve the following using Taylor’s Series Method (up to 3 terms): \[ \frac{dy}{dx} = x^2 + y, \quad y(0) = 1 \] Find \( y(0.2) \).

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Solve the first-order PDE using Lagrange’s method \[ p + q = x + y \] where \( p = \frac{\partial z}{\partial x} \) and \( q = \frac{\partial z}{\partial y} \).

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Is the superposition theorem applicable only to networks that are a linear b nonlinear c time invariant d passive?

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What is the equation for the relation between electric displacement vector D and polarization P?

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Convert the following Boolean equation to standard SOP form and implement using NAND-NAND logic: (i) y = A'B'C' + ABC'D' + A'C'D' (ii) y = PQ + P'QR + PQR.

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Why do you solve differential equation?
Answer : We solve differential equations because they help us model and understand how things change over time or space. In many fields like physics, engineering, biology, and economics, systems are constantly ... a tool to understand, predict, and control the dynamic processes in the world around us....

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How to apply Laplace's equation to solve differential equations?
Answer : Laplace's equation is a second-order partial differential equation that plays a crucial role in fields like physics, engineering, and mathematics, particularly for problems involving potential theory, heat flow, and ... you'd like help with? I can walk you through an example if you'd like....

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How to solve a differential equation?
Answer : Solving a differential equation involves finding a function (or set of functions) that satisfies the equation. There are different types of differential equations, and the methods vary depending on their form ... with practice, it becomes easier to recognize which method to use for a given problem....

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Is 0 a yes or no?
Answer : In many contexts, **0** is typically used to represent **no**, and **1** is used to represent **yes**. This is common in binary systems, where 0 and 1 are used to represent two possible states (off/on, ... So, in general, **0** is often associated with **no**, but it depends on how it's being used!...

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Can a photon have 0 spin?
Answer : No, a photon cannot have zero spin. A photon is a particle of light, and it always has a spin of 1. However, its spin can only take certain values depending on the direction it's moving. Photons are **massless** ... motion. So, in summary, a photon always has spin 1, but it can't have a spin of 0....

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Does a circle have 0 or 1 side?
Answer : A circle is often said to have **1 side**. This is because it's a continuous curve with no breaks or angles. So, while it doesn't have sides in the same way a polygon (like a triangle ... circle has 0 sides because it doesn't have straight edges, but mathematically, it's considered to have 1 side....

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Why is a diode 0.7 V?
Answer : The 0.7V you're referring to is typically the **forward voltage drop** of a **silicon diode**. It's the minimum voltage required for the diode to allow current to flow through it ... for the silicon material to overcome its internal barrier and allow current to flow in the forward direction....

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Why most of analog o/p devices having o/p range 4 to 20 mA and not 0 to 20 mA?
Answer : The main reason most analog output devices use a 4 to 20 mA range instead of 0 to 20 mA is to ensure reliable operation and easier detection of faults. Here's a breakdown of why 4- ... fault detection, and stability in signal transmission, which is why it's widely adopted in analog output devices....

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What is the current in the RL circuit at a time t=0?

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Is there an instantaneous change in the voltage across the capacitor at t 0?
Answer : No, there is no instantaneous change in the voltage across a capacitor at \( t = 0 \). The voltage across a capacitor cannot change instantaneously due to the capacitor's inherent ... switch being turned on or off), the voltage across the capacitor will change gradually, not instantaneously....

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What does 0 hg mean on a battery?
Answer : The "0 hg" label on a battery typically refers to "0 inches of mercury" (Hg), which is a way of measuring pressure in a vacuum or sealed environment. In the context of a battery, ... on a typical battery, it might be best to check the manufacturer's manual or datasheet for further clarification....

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Why is voltage always 0?
Answer : Voltage is not always 0. However, if you're asking why voltage sometimes seems to be zero in certain situations, it could be due to a few reasons: 1. **Reference Point**: Voltage is always ... appear to be 0 in certain scenarios depending on where you're measuring and the condition of the circuit....

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Is a power factor of 0.8 good?
Answer : A power factor of 0.8 means that 80% of the power is being used effectively, and 20% is wasted. In many industrial or commercial settings, a power factor of 0.8 is considered okay but not ... not optimal. Aiming for a power factor closer to 1 is usually preferred for efficiency and cost savings....

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Which meter has a greater sensitivity and why? Meter A having a range of 0-10 V and a multiplier resistance of 18 kΩ and meter B with a range of 0-300 V and multiplier resistance of 298 kΩ? Both meter movements have a resistance of 2 kΩ.

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A 500kVA distribution transformer having copper and iron losses of 5kW and 3kW respectively on full load. The transformer is loaded as shown below: Loading (kW) Power Factor (Lag) No. of hours 400 0.8 06 300 0.75 12 100 0.8 03 No load - 03 Calculate the all-day efficiency.
Answer : To calculate the all-day efficiency of the transformer, we need to consider the total energy output, the total energy input, and the losses over a 24-hour period. The transformer experiences two types of ... \] ### Final Answer: The all-day efficiency of the transformer is approximately **98.39%**....

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A 3 phase line of 4 km length delivers 4000 kW at a p.f of 0.8 lagging to a load the resistance and reactance per km of each conductor are 0.2 Ω and 0.5 Ω respectively if the voltage at the supply end is maintained at 11 kV. Calculate the received end voltage and efficiency of line.
Answer : Let's break down the problem step by step and calculate the received end voltage and the efficiency of the line. ### Given Data: - Power delivered to the load, \( P = 4000 \, \text{kW} \) - Power factor, \( \text{p. ... voltage**: \( 10.43 \, \text{kV} \) - **Efficiency of the line**: \( 98.61\% \)...

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An industrial consumer charged with the scheduled tariff of Rs.250 /kVA per month for maximum demand and 150 paisa per unit consumed for load factor of 60% and 80%. Find overall cost per unit at i) unity P.F. ii) 0.9 P.F. consider maximum demand of 50 kVA.
Answer : To solve this, we need to calculate the total cost of electricity consumption for an industrial consumer, considering the maximum demand (MD), load factor (LF), and power factor (PF) at ... tariff is based on kVA, and the load factor and total consumption determine the cost more significantly....

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A three-phase transformer having a line voltage ratio of 0.4 kV/11kV is connected Star/Delta and protective transformers on the 0.4 kV side have a current ratio of 500/5. Calculate the ratio of ... on the 11 kV side. Draw a neat circuit diagram and indicate the given values at appropriate places.

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A workshop measures 10m × 25m. The shop is illuminated by 24 lamps of 200 watts each. The lumen efficiency of each lamp is 15 lumens per watt. Depreciation factor is assumed to be 0.8 and a coefficient of utilization 0.5. Determine the illumination on the working plane.

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