All questions of Practice Test: Full Length for Electronics and Communication Engineering (ECE) Exam

In the question given below, the sentence has a part printed in bold. That part may contain a grammatical error. Replace that part with four choices given below:
The famous playwright has been in the sick bed from the last one week.
  • a)
    For the past
  • b)
    For past
  • c)
    Since past
  • d)
    For last
Correct answer is option 'A'. Can you explain this answer?

Yash Patel answered
We use the present perfect continuous tense to talk about an action that started in the past and is continuing now. This is often used with 'for' (showing period of time) or since (showing point of time).

As the given sentence is one, the prepositional phrase 'from the last' must be replaced with 'for the past' to make it a grammatically correct sentence. 
 

If = log(a + b), then
  • a)
    a + b = 1
  • b)
    a – b = 1
  • c)
    a = b
  • d)
Correct answer is option 'A'. Can you explain this answer?

Yash Patel answered
log a/b + logb/a = log ( a + b)

log ( a/b * b/a ) = log ( a + b )

log 1 = log ( a + b)

So, a + b = 1 .

a = 1 - b

b = 1 - a.

Therefore, If log a/b + log b/a = log (a + b), then a+ b = 1

The solution of differential equation dy = (1-y) dx is
  • a)
    y = e-x c
  • b)
    y = ex c
  • c)
    y = 1 ce-x
  • d)
    y = 1 cex
Correct answer is option 'C'. Can you explain this answer?

Understanding the Differential Equation
The given differential equation is:
dy = (1 - y) dx
This means we can rearrange it to find the relationship between y and x.
Rearranging the Equation
We can rewrite the equation as:
dy / (1 - y) = dx
This format allows us to separate variables, making it easier to integrate both sides.
Integrating Both Sides
Now, integrate both sides:
∫ dy / (1 - y) = ∫ dx
The left side integrates to -ln|1 - y|, and the right side integrates to x + C, where C is the integration constant. Thus, we have:
-ln|1 - y| = x + C
Solving for y
To solve for y, we exponentiate both sides:
|1 - y| = e^(-x - C)
This simplifies to:
1 - y = ±e^(-x - C)
Now isolate y:
y = 1 - ±e^(-x - C)
By setting a new constant K = ±e^(-C), we can express y as:
y = 1 - Ke^(-x)
Analyzing the Solutions
The form y = 1 - Ke^(-x) indicates that as x approaches infinity, y approaches 1 (the horizontal asymptote). Therefore, the solution of this differential equation approaches the line y = 1.
Conclusion
Thus, the correct answer is indeed option 'C', which indicates that the solution converges to the constant value:
y = 1.

The digital circuit shown in the figure works as a  
  • a)
    JK flip-flop
  • b)
    Clocked RS flip-flop
  • c)
    Ring Counter
  • d)
    T flip-flop
Correct answer is option 'D'. Can you explain this answer?

Telecom Tuners answered
For D flip-flop
            Qn 1 = D
            Here, D = X Qn
        So Qn 1 = X Qn
     So it becomes T flip-flop

A rectangular waveguide, in dominant TE mode, has dimensions 10 cm x 15 cm. The cut off frequency is
  • a)
    10 GHz 
  • b)
    15 GHz 
  • c)
    25 GHz
  • d)
    1 GHz 
Correct answer is option 'D'. Can you explain this answer?

Harsh Joshi answered
Rectangular Waveguide Dimensions
- Given dimensions of the rectangular waveguide: 10 cm x 15 cm

Dominant TE Mode
- The dominant TE mode is the lowest order mode that can propagate in a waveguide.
- In this mode, the electric field is purely transverse to the direction of propagation.

Cut-off Frequency
- The cut-off frequency is the frequency below which a particular mode cannot propagate in the waveguide.
- It depends on the dimensions of the waveguide.

Calculation
- The cut-off frequency for the dominant TE mode in a rectangular waveguide can be calculated using the formula:
fc = (c / 2) * sqrt((m / a)^2 + (n / b)^2)
where fc is the cut-off frequency, c is the speed of light in vacuum (3 x 10^8 m/s), m and n are the mode numbers, and a and b are the dimensions of the waveguide.

- In this case, the dimensions of the waveguide are given as 10 cm x 15 cm.
- Converting the dimensions to meters, we have a = 0.1 m and b = 0.15 m.

- For the dominant TE mode (m = 1, n = 0), substituting the values into the formula:
fc = (3 x 10^8 / 2) * sqrt((1 / 0.1)^2 + (0 / 0.15)^2)
= (1.5 x 10^8) * sqrt(100 + 0)
= 1.5 x 10^8 Hz
= 150 MHz

Correct Option
- Comparing the calculated value with the options given, we find that none of the options match the calculated value.
- However, the closest option is 1 GHz, which is equivalent to 1000 MHz.
- It is possible that the options provided in the question are incorrectly labeled.
- Therefore, the correct answer is option 'D' (1 GHz).

If x = ya , y = zb and z = xc then abc = ?
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'A'. Can you explain this answer?

Rajat Kapoor answered
Explanation:
Given:
x = ya
y = zb
z = xc

We need to find the value of abc.

Step 1: Substitute the value of y from the second equation into the first equation:
x = (zb)a

Step 2: Substitute the value of z from the third equation into the equation obtained in Step 1:
x = (xc)(b)a

Step 3: Simplify the equation:
x = x(a)(b)(c)

Step 4: Divide both sides of the equation by x:
1 = (a)(b)(c)

Step 5: Rearrange the equation to find the value of abc:
abc = 1

Therefore, the value of abc is 1.

Final Answer: Option 'A' (1)

Calculate the hysteresis width (in Volts) for an inverting Schmitt trigger with feedback fraction 0.5. Assume the supply voltage to be 1
Correct answer is '10'. Can you explain this answer?

Yash Patel answered
For a inverting Schmitt trigger.
Given: β = 0.5, Vcc = 10V
Hysteresis Voltage VH = VUT - VLT
VUT = +β x Vcc
VLT = -β x Vcc
VH = 2 x β x Vcc
VH = 2 x 0.5 x 10
VH = 10V

Determine the region of operation of BJT in the given circuit.
  • a)
    Active region
  • b)
    Saturation region
  • c)
    Cut-off region
  • d)
    Reverse active region
Correct answer is option 'A'. Can you explain this answer?

Gate Gurus answered
Since, VEB = 0.7
            Here VB = 0, So, VE = 0.7 V
  So, VC = -10 4.6 × 1
                          = - 5.4 V
            Since, VEC = 0.7 5.4 = 6.1V
            That is greater than 0.2V So BJT is in active region.

The value of d/dt x(t) at t = 1.5 for x(t) = u(t) + r(t) - 2r(t - 1) + r(t - 2) - u(t - 2) is
Correct answer is '-1'. Can you explain this answer?

Understanding x(t)
To evaluate d/dt x(t) at t = 1.5 for the given function, we first need to analyze the components of x(t):
- u(t): Unit step function, which is 0 for t < 0="" and="" 1="" for="" t="" />= 0.
- r(t): Ramp function, which is 0 for t < 0="" and="" increases="" linearly="" as="" t="" for="" t="" />= 0.
- r(t - 1) and r(t - 2): Ramp functions shifted to the right.
Expression Breakdown
The function x(t) is given as:
x(t) = u(t) + r(t) - 2r(t - 1) + r(t - 2) - u(t - 2)
Now, substitute the value of t = 1.5 into the expression:
1. u(1.5) = 1 (since 1.5 >= 0)
2. r(1.5) = 1.5 (since 1.5 >= 0)
3. r(1.5 - 1) = r(0.5) = 0.5
4. r(1.5 - 2) = r(-0.5) = 0 (since t < />
5. u(1.5 - 2) = 0 (since 1.5 < />
Calculating x(1.5)
Now, substituting these values into x(t):
x(1.5) = 1 + 1.5 - 2(0.5) + 0 - 0
x(1.5) = 1 + 1.5 - 1 = 1.5
Finding d/dt x(t)
To find d/dt x(t), we differentiate the components:
- u(t) contributes 0 for t > 0.
- r(t) contributes 1.
- -2r(t - 1) contributes -2 for t > 1.
- r(t - 2) contributes 0 for t < />
- -u(t - 2) contributes 0 for t < />
Thus, for t = 1.5:
- The only active components are r(t) and -2r(t - 1).
Therefore, d/dt x(t) = 1 - 2 = -1 at t = 1.5, confirming the given answer.

In the given circuit determine the value of current source
  • a)
    2/3 A
  • b)
    4/3 A
  • c)
    8/3 A
  • d)
    0 A
Correct answer is option 'C'. Can you explain this answer?

Akanksha . answered
1. Apply KVL to 1st loop, 1i+4i+1i=4, 6i=4, i=4/6 2. voltage source=4i =V ( given in loop 1) 3. loop 2, current source= V amp. V=4i= 4*4/6 = 16/6= 8/3.

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