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The differential equation $$\frac{{{\text{dx}}}}{{{\text{dt}}}} = \frac{{4 - {\text{x}}}}{\tau },$$   with x(0) = 0 and the constant $$\tau $$ > 0, is to be numerically integrated using the forward Euler method with a constant integration time step T. The maximum value of T such that the numerical solution of x converges is

The differential equation $$\frac{{{\text{dx}}}}{{{\text{dt}}}} = \frac{{4 - {\text{x}}}}{\tau },$$   with x(0) = 0 and the constant $$\tau $$ > 0, is to be numerically integrated using the forward Euler method with a constant integration time step T. The maximum value of T such that the numerical solution of x converges is Correct Answer $$2\tau $$

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While numerically solving the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + 2{\text{x}}{{\text{y}}^2} = 0,\,{\text{y}}\left( 0 \right) = 1$$     using Euler's predictor-corrector (improved Euler-Cauchy) with a step size of 0.2, the value of y after the first step is
An electronic device rearranges numbers step-by-step in a particular order according to set of rules. The device stops when the final result is obtained.
Input: 84 15 35 04 18 96 62 08
Step 1: 96 84 15 35 04 18 62 08
Step 2: 96 84 62 15 35 04 18 08
Step 3: 96 84 62 35 15 04 18 08
Step 4: 96 84 62 35 18 15 04 08
Step 5: 96 84 62 35 18 15 08 04
And Step 5 is the last step for this input. Now, find out an appropriate step in the following question following the above rule. Question:
Input: 16 09 24 28 15 04
What will be the third step for this input ?
An electronic device when fed with the numbers, rearranges them in a particular order following certain rules. The following is a step-by-step process of rearrangement for the given input of numbers. Input :- 85 16 36 04 19 97 63 09 Step I :- 97 85 16 36 04 19 63 09 Step II :- 97 85 63 16 36 04 19 09 Step III :- 97 85 63 36 16 04 19 09 Step IV :- 97 85 63 36 19 16 04 09 Step V :- 97 85 63 36 19 16 09 04 (for the given input step V is the last step). Which of the following will be the last step for the given input ? Input :- 03 31 43 22 11 09
A 60% spirit solution is mixed with r% spirit solution in the ratio 1 : 3 such that a s% spirit solution is obtained. When a (s/3)% spirit solution is mixed with 55% spirit solution in equal ratio, an (r/2)% spirit solution is obtained. Which of the following can be determined? (A) Value of ‘r’ (B) Value of ‘s’ (C) Volume of the 60% spirit solution mixed initially (D) If 9 liters of r% spirit solution was mixed initially, what was the volume of the s% spirit solution thus obtained?
Consider a system whose input r and output y are related by the equation $$y\left( t \right) = \int\limits_{ - \infty }^\infty {x\left( {t - \tau } \right)} h\left( {2\tau } \right)d\tau $$
Signal Processing mcq question image
Where h(t) is shown in the graph
Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output
Causal: The system is causal.
LP : The system is low pass.
LTI: The system is linear and time-invariant.
A word arrangement machine, When given an input line of words, rearranges it in every step following a certain rule. Following is an illustration of an input line of words and various steps of rearrangement.
Input: gone are take enough brought station
Step 1: take gone are enough brought station
Step 2: take are gone enough brought station
Step 3: take are station gone enough brought
Step 4: take are station brought gone enough
And Step 4 is the last step for this input. Now, find out an appropriate step in the following question following the above rule. Question:
Input: car on star quick demand fat
What will be the third step for this input ?
A device rearranges numbers step by step in a particular order according to a set of rules. The device stops when the final result is obtained. Step V is the final for this device. Input: 86 17 35 03 20 99 64 08 Step I: 99 86 17 35 03 20 64 08 Step II: 99 86 64 17 35 03 20 08 Step III: 99 86 64 35 17 03 20 08 Step IV: 99 86 64 35 20 17 03 08 Step V: 99 86 64 35 20 17 08 03 Study the above arrangement carefully and answer this question. Which one of the following would be the last step for the input below? Input: 02 30 40 20 11 08 
A word arranging device rearranges words step-by-step in a particular order according to set of rules. The device stops when the final result is obtained.
Input: but going for crept te light sir
Step 1: crept but going for te light sir
Step 2: crept going light but for te sir
Step 3: crept going light but for sir te
And Step 3 is the last step for this input. Now, find out an appropriate step in the following question following the above rules. Question:
Input: more fight cats cough sough acts idea
What will be the last step for this input ?
During the numerical solution of a first order differential equation using Euler method with step size h, the local truncation error is of order of
The velocity v (in m/s) of a moving mass, starting from rest, given as $$\frac{{{\text{dv}}}}{{{\text{dt}}}} = {\text{v}} + {\text{t}}{\text{.}}$$   Using Euler forward difference method (also known as Cauchy-Euler method) with a step size of 0.1 s, the velocity at 0.2 s evaluate to