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The column vector (aba) is a simultaneous Eigen vector of  and​
  • a)
    b = 0 or a = 0
  • b)
    b = a or b = -2a
  • c)
    b = 2a or b = -a
  • d)
    b = a/2 or b = -a/2
Correct answer is option 'B'. Can you explain this answer?

Gate Gurus answered
Given that, X =  is an Eigen vector of A.
⇒ AX = λ1X
 
For all values of a and b,  is an Eigen vector of A.
 
Given that,   is an Eigen vector of B
⇒ BX = λ2X
being an eigen vector of matrix B
a + b = λ2 a      ----(1)
2a = λ2 b      ----(2)
From (1) and (2)
⇒ ab + b2 = 2a2
⇒ 2a2 - ab - b2 = 0
⇒ 2a2 - 2ab + ab - b2 = 0
⇒ 2a (a - b) + b (a - b) = 0
⇒ b = a, b = -2a
For b = a, (or) b = -2a, X is an eigen vector of matrix B.

A 50 Hz, 11 kV, 3 phase alternator with earthed neutral having a reactance of 3 ohms per phase and is connected to a bus bar through a circuit breaker, if the distributed capacitance upto CB between the phase and neutral is 0.01 μ F.
What is the peak re striking voltage?
  • a)
    18.36 kV
  • b)
    17.96 kV
  • c)
    15.96 kV
  • d)
    12.65 kV
Correct answer is option 'B'. Can you explain this answer?

Pankaj Mehta answered
Microfarad per phase, then determine the short circuit current available at the bus bar if a fault occurs at the CB.

To find the short circuit current, we need to first calculate the total impedance of the system. The reactance of the alternator per phase is given as 3 ohms, and the distributed capacitance per phase up to the CB is 0.01 microfarad.

The reactance of the distributed capacitance can be calculated as:

Xc = 1 / (2πfC) = 1 / (2π x 50 x 0.01 x 10^-6) = 318.3 ohms

The total impedance per phase is then given by:

Z = √(R^2 + Xl^2 + Xc^2) = √(3^2 + 318.3^2 + 3^2) = 318.9 ohms

Since we have a 3 phase system, the total impedance will be 3 times this value, which is 956.7 ohms.

The short circuit current can be calculated using Ohm's law:

I = V / Z

Where V is the voltage of the system, which is 11 kV or 11,000 volts.

I = 11,000 / 956.7 = 11.5 kA

Therefore, the short circuit current available at the bus bar is 11.5 kA.

Determine the peak inverse voltage that appear across the diode in the given circuit.
  • a)
    0 V
  • b)
    10 V
  • c)
    20 V
  • d)
    14.14 V
Correct answer is option 'C'. Can you explain this answer?

Ravi Singh answered
 
During positive half cycle capacitor get charge and during negative half cycle the equivalent circuit is shown as
    so,    VD    =    VmSinωt
    so,     P1V    =    2Vm
    here,     Vm    =    10 volt,
    so,    P1V    =    20 volt

Frequency compensation is used in op-amp to increase its
  • a)
    Voltage gain
  • b)
    Input impedance
  • c)
    Stability
  • d)
    None
Correct answer is option 'C'. Can you explain this answer?

Nikhil Ghoshal answered
Frequency compensation is used in operational amplifiers to improve the stability of the op-amp over the input signal frequency range.

Which of the following Boolean expression represents the given logic circuit?
  • a)
    B + AC
  • b)
    A + BC
  • c)
    C + AB
  • d)
    AB + BC
Correct answer is option 'A'. Can you explain this answer?

Telecom Tuners answered

 
Y = AB + A(B + C) + B(B + C)
= AB + AB + AC + BB + BC
= AB + AC + B + BC
= AB + AC + B(1 + C)
= AB + AC + B
= B(A + 1) + AC
= B + AC

The power supplied by the 40 V source in the circuit shown in the figure is _____(in W)
    Correct answer is '20'. Can you explain this answer?

    Constructing Careers answered
    By applying Delta to star conversion as shown below:


    Now the given circuit becomes,



    Power supplied by 40 V source = 40 × 0.5 = 20 W

    The Headmaster ___________ to speak to you.
    Which of the following options is correct to complete the above sentence?
    • a)
      is wanting
    • b)
      wants
    • c)
      want
    • d)
      was wanting
    Correct answer is option 'B'. Can you explain this answer?

    Niti Desai answered
    The correct tense that fits here is simple present and the subject being singular, the verb should be in the correct form too. Thus 'wants' is the correct answer. The other options are incorrect as:
    Is wanting ⇒ it is in present continuous tense which is used to denote an activity which is continuing
    Want ⇒ subject is singular thus the verb cannot be in plural form
    Was wanting ⇒ it is in past continuous tense which is used to denote an activity which was continuing in the past
    Thus option 2 is the correct answer.

    Latching current for an SCR, inserted in between a dc voltage source of 300 V and the load, is 150 mA. Compute the minimum width of gate pulse current required to turn-on this SCR in case the load of L = 0.3 H in series with R = 30 Ω
    • a)
      171.42 μsec
    • b)
      135.48 μsec
    • c)
      142.53 μsec
    • d)
      151.13 μsec
    Correct answer is option 'D'. Can you explain this answer?

    Anshul Shah answered
    Given data:

    DC voltage source = 300 V

    Latching current for SCR = 150 mA

    Load, L = 0.3 H

    Load, R = 30 Ω

    We know that SCR needs a gate pulse to turn on. The minimum width of the gate pulse is given by:

    $t_{on} = \frac{\pi}{2 \omega_{r}}$

    Where,

    $\omega_{r} = \frac{1}{\sqrt{LC}}$

    L and C are the inductance and capacitance of the load respectively. In this case, we have only given the value of L, so we need to calculate the value of C first.

    $Z = R + j\omega L$

    $Z = \sqrt{R^{2} + (\omega L)^{2}} \angle \tan^{-1}(\frac{\omega L}{R})$

    At resonance, Z is minimum and the phase angle is zero. Hence,

    $\omega L = R$

    $\omega = \frac{R}{L}$

    $\omega_{r} = \frac{R}{L} = \frac{30}{0.3} = 100 \text{ rad/s}$

    $C = \frac{1}{\omega_{r}^{2} L} = \frac{1}{(100)^{2} \times 0.3} = 3.33 \times 10^{-6} \text{ F}$

    Now, we can calculate the minimum width of the gate pulse as:

    $t_{on} = \frac{\pi}{2 \omega_{r}} = \frac{\pi}{2 \times 100} = 0.0159 \text{ s}$

    The gate pulse current required to turn on the SCR can be calculated using the formula:

    $I_{g} = \frac{I_{L}}{\beta}$

    Where,

    $I_{L}$ is the load current

    $\beta$ is the current gain of the SCR

    We know that the latching current of the SCR is 150 mA. So, we can assume that the current gain is at least 50.

    $I_{L} = \frac{V_{dc}}{R + j \omega L} = \frac{300}{30 + j 100 \times 0.3} = 7.5 \text{ A}$

    $I_{g} = \frac{7.5}{50} = 0.15 \text{ A}$

    Therefore, the minimum width of gate pulse current required to turn-on this SCR is 0.0159 s and its value is 0.15 A.

    Consider the following synchronous counter made up of JK, D and T Flip-Flops.  The modulus value of the counter is
    Correct answer is '5'. Can you explain this answer?

    Sarita Yadav answered
    Consider characteristic equation of here
    Consider characteristic equation of D− Flip-Flop.
    (ii) Consider characteristic equation of T - Flip-Flop Consider charactrisic
    Using equations (i), (ii) and (iii)
    The number of used states = 5
    ∴ Modulus value = 5

    In the given figure, a V volt Battery is connected across the capacitor, galvanometer shows the deflection of found. The switch is closed at t = 0. If distance between the plate of capacitor is increased after which the switch is removed from the circuit. What will be effect on Vc capacitor voltage & electric field .
    • a)
      Vc increased, remain same
    • b)
      Vc decreased, remain same
    • c)
      Vc & Both are increased
    • d)
      Vc & Both are decreased
    Correct answer is option 'A'. Can you explain this answer?

    Pie Academy answered
    When the switch is closed for a long line then capacitor will charges up to Vc = V volt.
    Now as the switch is removed as shown in figure.
    The charge Q across the plate of capacitor are trapped.
    After removing the switch distance between the plate of capacitor to increased.
    therefore C w ill decrease.
    as the charge are trapped i.e; constant.
    So where VC is decreased therefore Vc will increases.
    So, E remain constant.

    Consider a function f(x, y, z) = x2yz + 3xy2. The greatest rate of increase of function f at point (2, 1, -1) is
      Correct answer is '9'. Can you explain this answer?

      Krithika Tiwari answered
      Greatest rate of increase of function f is directional derivative at that point.
      ∇f = (2xyz + 3y2) i + (x2yz + 6xy) j + x2y k
      At the given point (2, 1, -1), ∇f = -i + 8 j + 4 k
      Greatest rate of increase 

      “Nobody praised her ________ nature, so she decided to mend her ways to become ________.”
      The words that best fill the blanks in the above sentence are
      • a)
        Complacent, complaisant
      • b)
        Complaisant, complaisant
      • c)
        Complaisant, complacent
      • d)
        Complacent, complacent
      Correct answer is option 'C'. Can you explain this answer?

      Upasana Tiwari answered
      There are several ways to make money online, such as:

      1. Freelancing: Offer your skills and services on freelancing platforms like Upwork, Fiverr, or Freelancer. You can find work in various fields like writing, graphic design, programming, and more.

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      3. Affiliate marketing: Promote products or services on your website or social media platforms and earn a commission for every sale made through your referral.

      4. Online tutoring or teaching: If you have expertise in a particular subject, you can offer online tutoring or teaching services through platforms like VIPKid or Teachable.

      5. Creating and selling online courses: Share your knowledge and skills by creating online courses and selling them on platforms like Udemy, Coursera, or Teachable.

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      7. Blogging: Start a blog and monetize it through advertising, sponsored content, or selling products or services.

      8. Social media influencing: Build a large following on platforms like Instagram, YouTube, or TikTok and collaborate with brands for sponsored posts or endorsements.

      9. Stock market trading: Learn about stock market trading and invest in stocks, either through a brokerage account or trading platforms.

      10. Virtual assistant: Offer administrative or technical support to businesses or individuals remotely.

      Remember that making money online requires hard work, dedication, and consistent effort. It may take time to generate a significant income, so be patient and persistent.

      A (0-300)V Voltmeter has a guaranteed accuracy of 2% of full scale reading if the voltage measured by this instrument is 180V then the limiting error will be
      • a)
        Less than 2%
      • b)
        Less than 3% but greater than 2%
      • c)
        Less than 4% but greater than 3%
      • d)
        4%
      Correct answer is option 'C'. Can you explain this answer?

      Yashvi Shah answered
                                     Error    = 2% of F.S.D.
                                                = 2% of 300 V
                                                = 2/100 x 300 = 6 V
                  Measured Value    =     180 V
                                     Error   =     6 V
                      Absolute error   =    Measured value – True value
                                           6   =    180 - True value
                             Tue Value   =    174 Volt
                  Limiting error or % error
                         = 6/174 x 100 =   3.44%

      Let x[n] = e-2n u[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?
      • a)
         h[n] = n
      • b)
         h[n] = 1/n
      • c)
         h[n] = 1/n2
      • d)
         Both 2 & 3
      Correct answer is option 'C'. Can you explain this answer?

      Gitanjali Datta answered
      A system is said to be BIBO stable if it’s impulse response is absolutely summable,

      Out of all the responses only  is absolutely summable.

      Is not absolutely summable it is divergent.

      The integrating factor of equation y log y dx + (x – log y) dy = 0 is
      • a)
        log x
      • b)
        log y
      • c)
        log (log x)
      • d)
        log (log y)
      Correct answer is option 'B'. Can you explain this answer?

      Mainak Pillai answered
      Understanding the Given Differential Equation
      The equation provided is:
      y log y dx + (x – log y) dy = 0
      This is a first-order differential equation that can be analyzed for an integrating factor.
      Identifying the Components
      To find the integrating factor, we rewrite the equation in the standard form:
      M(x, y) = y log y,
      N(x, y) = x - log y.
      Here, M and N are functions of x and y.
      Calculating the Partial Derivatives
      Next, we calculate the partial derivatives:
      - ∂M/∂y = log y + 1
      - ∂N/∂x = 1
      We check for exactness:
      - If ∂M/∂y ≠ ∂N/∂x, the equation is not exact.
      Since log y + 1 ≠ 1, the equation is not exact.
      Finding the Integrating Factor
      For the equation to become exact, we seek an integrating factor that depends solely on y. The integrating factor is typically of the form µ(y).
      The ratio of the differences of the partial derivatives gives us a clue:
      µ(y) = (∂N/∂x) / (∂M/∂y - ∂N/∂x)
      Substituting the values:
      µ(y) = 1 / (log y + 1 - 1) = 1 / log y
      Thus, the integrating factor simplifies to:
      µ(y) = log y
      Conclusion
      The integrating factor for the given differential equation is indeed log y, confirming that option 'B' is the correct answer. This factor can be used to multiply the entire equation, making it exact and solvable.

      Chapter doubts & questions for Practice Tests - GATE Electrical Engineering (EE) Mock Test Series 2026 2025 is part of Electrical Engineering (EE) exam preparation. The chapters have been prepared according to the Electrical Engineering (EE) exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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