A binomial distribution has a mean of 5 and variance 4. The number of trials is

Find the electric field across each dielectric in the capacitor shown in fig when the applied voltage is 200 V.

The value of integral ${\int }_C\frac{\cos \pi z^2}{\left(z-1\right)\left(z-2\right)}dz$ where C : |z| = 3 (Positively oriented) is equal to

A metallic sphere with charge -Q is placed inside a hollow conducting sphere with radius R carrying charge +Q. The potential at a point outside the hollow sphere

A generating station has a maximum demand of 25 MW, a load factor of 60%, a plant capacity factor of 50% and a plant use factor of 72%.

The maximum energy that could be produced daily if the plant while running as per schedule, were full loaded is ______

Spherical cloud of charged particles of radius R₀ = 1 m produces a known electric field intensity inside the cloud (r ≤ R₀), given as E̅ = R² a_r (N/C). The total charge in the cloud is:

(Assume the spherical cloud to approximate a solid sphere)

For the clocked flip-flop circuit shown below, what is the correct characteristic equation?

A signal x(t) having a frequency component up to 20 kHz is sampled at a rate of 38 kHz and reconstructed through an LPF with unity gain and a cutoff frequency of 25 kHz. Which of the following statement is true?

The current I₀ in the circuit

The root locus plot of a system having open-loop transfer function $G\left(s\right)H\left(s\right)=\frac{K}{s\left(s+1\right)\left(s+3\right)}$ has:

The circuit shown is:

The reactance relay is essentially

The toroidal core has a mean radius of 10 cm and a circular cross-sectional radius 'a' of 1 cm. If the core is made of steel (μ = 1000 μ₀) and has a coil will 200 turns, then the amount of current that will produce a flux of 0.5 mWb in the core is ________ A.

When a time-varying signal has to be digitized using an ADC, which of the following is necessary to use before digitization?

The electric field at point P due to dipole as shown in below diagram is proportional to

Which of the following has a problem in convergence for a system with long radial lines?

6 alternators, each having a rating of 9 MVA, 33 kV with 30% reactance are working in parallel. The short circuit level at bus bar is

Consider the following statements with regard to a GTO:

1. The turn-off gain of the GTO is large.

2. Large negative gate current pulses are required to turn off the GTO.

3. GTO has a large reverse blocking capability.

Which of the above statements is/are correct?

In a DC motor, the input is measured as 2 kW ± 4% and the losses are 200 ± 5 W.

The percentage limiting error of the output power is 

If a square matrix $A=\left[\begin{array}{ccc}1& 2& 2\\ 0& 2& 1\\ -1& 2& 2\end{array}\right]$ then which of the following will be eigenvalue of adj (A)?

What is the inverse Fourier transform of $X\left(\omega \right)=e^{-\frac{\left|\omega \right|}{2}}$

A DC machine has hysteresis loss 600 W and eddy current loss 400 W. If it is running at 1000 rpm then what speed will the total losses be one fourth keeping flux constant.

Consider the following statements regarding the no-load test of the transformer when the test is conducted at rated voltage and reduced frequency (V₁ = V_rated and f < f_rated)

1. The magnetizing current increases

2. The core loss component of no-load current remains the same.

3. No-load power factor increases.

4. Iron losses of the transformer increases.

Which of the above statements are correct?

The figure shows the plot of current i(t) through a series R – L circuit when a constant forcing function of magnitude V_s = 50 V is applied to it. The values of Resistance R and inductance L are

The block diagram is shown in the figure.

The expression for c(t) if r(t) = u(t) and n(t) = δ(t) is ______

A dc series motor drives a fan at 600 rpm and takes 15 A. When fed from rated voltage of 220 V. The armature resistance is 0.5 Ω. The motor speed is to be raised to 900 rpm by voltage control. The new voltage when the magnetic circuit unsaturated is _________ (in V)

Two 50 Hz generating units operate in parallel within the same plant with the following ratings:

Unit 1 : 500 MVA, 0.8 pf, 13.2 kV, 3600 rpm, H = 4 mJ/MVA

Unit 2 : 1000 MVA, 0.8 pf, 13.8 kV, 1800 rpm, H = 5 MJ/MVA

For a base of 100 MVA, which of the following statements is/are true if two machines swing coherently?

For r(t) = 0.9 t, it is required that the steady state error should be less than 0.05. The value of gain K of proportional controller for the system shown above is ____.

The complementary function of the differential equation $x^2\frac{d^{2}y}{d{x}^2}+3x\frac{dy}{dx}+y=\frac{1}{{\left(1-x\right)}^2}$ is

If $\overrightarrow{F}\left(x,y,z\right)=\left(2x+3yz\right)\hat{i}+\left(3xz+2y\right)\hat{j}+\left(3xy+2z\right)\hat{k}$ for (x, y, z) ∈ R³, then which among the following is (are) TRUE?

Consider the function $y=\frac{x^3}{3}+\frac{x^2}{2}-2x+4$ in the interval x ∈ [-5, 5]

Which of the following statement is / are true?

The switch has been in position 1 for a long time and abruptly changes to position 2 at t = 0.

.

If time $\mathrm{t}$ is in seconds, the capacitor voltage ${\mathrm{V}}_{\mathrm{C}}$ (in volts) for $\mathrm{t}>0$ is given by

A step-up chopper has an input voltage of 10 V and the average output voltage of 18 V. The average load current is 1.5 A at a switching of 16 kHz. If the value of inductor is 200 μH, the maximum value of current flows through it is _________ (in A) 

A 3 by 3 matrix B is known to have eigenvalues 0, 1, 2.

Which of the following can be inferred from the above information?

The rotor of three phase 6 pole 50 Hz slip ring induction motor has resistance of 0.2 Ω per phase and runs at 960 rpm on full load. The resistance to be inserted in the rotor circuit so that speed reduces to 800 rpm. With torque remain constant is ________

The following test results are obtained from a 3-phase, 6000 kVA, 6600 V, star connected, 2-pole, 50-Hz turbo alternator.

With a field current of 125 A, the open circuit voltage is 8,000 V at the rated speed. With the same field current and rated speed, the short circuit current is 800 A. At the rated full load, the resistance drop is 3 percent.

The percentage regulation of the alternator on full-load and at a power factor of 0.8 lagging is _____

For the operational amplifier circuit shown, the output saturation voltages are ± 15V. The upper and lower threshold voltages for the circuit are, respectively.

A system with impulse response h(t) = e^tu(t) is connected as a feedback system shown in the figure:

The above system is BIBO stable for a > _______

Choose the correct transfer function of the bode plot shown below.

Let X be a continuous random variable with PDF

$f_x\left(x\right)=\{\begin{array}{c}4x^{3}0<x\le 1\\ 0otherwise\end{array}$

The value of $P\left(X\le \frac{2}{3}|X>\frac{1}{3}\right)$is

Consider the transfer function $G\left(s\right)=\frac{10\left(s+2\right)}{\left(s+20\right)}$

Which of the following is/are true?

A single-phase full-bridge inverter has RLC load of R = 4Ω, L = 35 mH, C = 155 μF. The DC input voltage is 230 V and the output frequency is 50 Hz. The third harmonic component in load current is:

A connection is made consisting of resistance A in series with a parallel combination of resistances B and C. Three resistors of value 10 Ω, 5 Ω, 2 Ω, are provided. Consider all possible permutations of the given resistors into the positions A, B, C, and identify the configurations with maximum possible overall resistance, and also the ones with minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is __________.

An 8 : 1 multiplexer has inputs A, B and C connected to the selection inputs S₂, S₁ and S₀ respectively. The data input P₀, P₁, ….. P_r (associated with selection S₂ S₁ S₀ = 000, 001, ….. 111 respectively) are as follows. P₁ = P₂ = P₇ = 0; P₃ = P₅ = 1; P₀ = P₄ = D; and P₆ = D̅.

Which of the Boolean function this multiplexer implements (m represents min term)?

Consider the circuit shown in the figure:

Which of the following results is/are correct?

The admittance parameters matrix for the two port network shown below is

The efficiency of a 1000 kVA, 110/220 V, 50 Hz, single-phase transformer is 98.5 % at half load at 0.8 leading and 98.8% at full load upf.

A synchronous generator is connected to infinite bus through a loss – less line. It is delivering initially 0.5 pu power to infinite bus. The infinite bus voltage is 1.0. the maximum power transfer before fault is 1.0 pu. The inertia constant is 6 MJ/MVA. the critical clearing angle is 75°, then the critical clear time is _______(in sec)

A certain linear time invariant system has the state and the output equations given below

$\left[\begin{array}{c}{\dot{x}}_1\\ {\dot{x}}_2\end{array}\right]=\left[\begin{array}{cc}1& -1\\ 0& 1\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}0\\ 1\end{array}\right]u$

$y=\left[11\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]$

If $\left[\begin{array}{c}{x}_1\left(0\right)\\ x_2\left(0\right)\end{array}\right]=\left[\begin{array}{c}1\\ -1\end{array}\right]$and u(0) = -1, then $\frac{dy}{dt}att=0$ is ______

The reading of the wattmeter shown in the figure is

A load of 15 MW at a power factor of 0.8 lagging can be delivered by a three-phase transmission line having conductors each of resistance 1 Ω per kilometer. The voltage at the receiving end is to be 132 kV and the loss in the transmission is to be 5%. The length of the transmission line is _____ (in km)

In the figure shown below, V_r = 0.7 for the diode. The output voltage V₀ in (V) is _______

A second order discrete system is characterized by the difference equation.

y(n) – 3y(n – 1) + 2y(n – 2) = x(n) – 2x(n – 1)

The initial conditions are given as y(-1) = y(-2) = 1.

The value of y(3) and x(n) = u(n)  when n ≥ 0 is ______

If x (t) is a continuous time periodic signal given as

$x\left(t\right)=\sum _{k=\left(-100\right)}^{100}j\sin \left(\frac{k\pi }{2}\right)e^{j\frac{k2\pi }{50}t}$

Then which of the following options is correct.

The single-phase half wave controlled rectifier supplies a resistive load draws an average current of 1.62 A. If the converter is operated from a 240 V, 50 Hz supply and the average value of the output voltage is 81 V, the ripple factor is __________