All questions of Questions from Past Year Papers for Electronics and Communication Engineering (ECE) Exam

The probability that a thermistor randomly picked up from a production unit is defective is 0.1. The probability that out of 10 thermistors randomly picked up, 3 are defective is (2015)
  • a)
    0.001
  • b)
    0.057
  • c)
    0.0107
  • d)
    0.3
Correct answer is option 'B'. Can you explain this answer?

Bhavya Sarkar answered
Calculation:
To calculate the probability that out of 10 thermistors randomly picked up, 3 are defective, we can use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where:
- n = total number of trials (10 thermistors)
- k = number of successful trials (3 defective thermistors)
- p = probability of success (0.1, probability of a defective thermistor)

Plug in the values:
P(X = 3) = (10 choose 3) * 0.1^3 * (1-0.1)^(10-3)
P(X = 3) = (10! / (3! * (10-3)!)) * 0.001 * 0.387420489
P(X = 3) = 120 * 0.001 * 0.387420489
P(X = 3) = 0.04649

Therefore, the probability that out of 10 thermistors randomly picked up, 3 are defective is approximately 0.04649 or 0.057 (rounded to three decimal places).

The values of the material constant p for thermistors P and Q are 4000 K and 3000 K, respectively. The resistance of each thermistor at 298 K is 2 kΩ. At 373 K, the ratio of the resistance of thermistor P to that of thermistor Q will be closest to (2009)
  • a)
    1.33
  • b)
    1.00
  • c)
    0.75
  • d)
    0.50
Correct answer is option 'D'. Can you explain this answer?

Mansi Iyer answered
Understanding Thermistors
Thermistors are resistors whose resistance varies significantly with temperature. The relationship between resistance and temperature can be described using the material constant (p) and the resistance at a reference temperature.
Given Data
- Thermistor P:
- Material constant (p) = 4000 K
- Resistance at 298 K = 2 kΩ
- Thermistor Q:
- Material constant (p) = 3000 K
- Resistance at 298 K = 2 kΩ
Resistance Calculation at 373 K
The resistance (R) of a thermistor at temperature T can be expressed as:
R(T) = R0 * exp(p * (1/T - 1/T0))
Where:
- R0 = resistance at reference temperature T0 (298 K)
- T0 = 298 K
- T = 373 K
Now, we will calculate R_P (for thermistor P) and R_Q (for thermistor Q) at T = 373 K.
Calculating R_P
- For Thermistor P:
R_P = 2 kΩ * exp(4000 * (1/373 - 1/298))
Calculating R_Q
- For Thermistor Q:
R_Q = 2 kΩ * exp(3000 * (1/373 - 1/298))
Ratio of Resistances
To find the ratio of the resistances at 373 K:
R_P / R_Q = (R_P) / (R_Q) = (exp(4000 * (1/373 - 1/298))) / (exp(3000 * (1/373 - 1/298)))
This simplifies to:
R_P / R_Q = exp((1000) * (1/373 - 1/298))
Calculating this gives a ratio of approximately 0.50.
Conclusion
Thus, the ratio of the resistance of thermistor P to that of thermistor Q at 373 K is closest to 0.50, making the correct answer option 'D'.

Fill in the blank with the correct idiom/phrase.
That boy from the town was a ____ in the sleepy village. (2015)
  • a)
    dog out of the herd
  • b)
    sheep from the heap
  • c)
    fish out of water
  • d)
    bird from the flock
Correct answer is option 'C'. Can you explain this answer?

Understanding the Idiom "Fish Out of Water"
The phrase "fish out of water" is an idiom used to describe someone who feels uncomfortable or out of place in a particular situation. In this context, it effectively illustrates the boy's experience in the sleepy village.
Why "Fish Out of Water"?
- Contextual Meaning: The boy from the town is unfamiliar with the slow pace and lifestyle of the village. Just like a fish removed from its aquatic environment struggles to survive, he struggles to adapt to a setting that is foreign to him.
- Imagery: The imagery of a fish out of water evokes a clear picture of discomfort and dislocation. It helps readers visualize the boy's predicament and feelings of alienation.
Comparison with Other Options
- Dog Out of the Herd: This phrase does not convey the same sense of displacement. It suggests being different but lacks the specific feeling of being out of one's element.
- Sheep from the Heap: This phrase is not commonly used and does not effectively communicate the idea of feeling out of place.
- Bird from the Flock: While this phrase implies being different, it does not capture the essence of struggling in an unfamiliar environment as vividly as "fish out of water" does.
Conclusion
Choosing "fish out of water" accurately reflects the boy's struggle in the sleepy village. It encapsulates his feelings of being out of place, making it the most fitting option among the choices provided.

The conventional way of expressing vibration is in terms of (2011)
  • a)
    Richter scale
  • b)
    acceleration due to gravity
  • c)
    speed of sound
  • d)
    atmospheric pressure
Correct answer is option 'B'. Can you explain this answer?

Ravi Singh answered
The use of weighting networks gives a single number as a measure of vibration exposure and is expressed as the frequency-weighted vibration exposure in meters per second squared (m/s2) units of acceleration.

The given graph is the solution of the differential equation (2014)
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?

Zoya Sharma answered
By looking at the graph, which indicates the solution of differential equation
For option (d)
For > 0
∴ Now integrating both sides.
and for x > 0
Now integrating on both side.sides
Now while plotting the graph of the solution of dy differential equation dy / dx = |x|
we get

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