If $f\left(x\right)=x^3-3x-1$ is continuous in the closed interval $\left[\frac{13}{7},-\frac{11}{7}\right]$ and f’(x) exists in the open interval $\left(\frac{13}{7},-\frac{11}{7}\right)$ then find the value of c such that it lies in $\left(\frac{13}{7},-\frac{11}{7}\right)?$

The vector $\overrightarrow{u}$ is defined as $\overrightarrow{u}=y{\hat{e}}_x-x{\hat{e}}_y$, where ê_x and ê_y are the unit vectors along x and y directions, respectively. If the vector $\overrightarrow{\omega }$ is defined as $\overrightarrow{\omega }=\overrightarrow{\mathrm{\nabla }}\times \overrightarrow{u}$, then $\left|\left(\overrightarrow{\omega }.\overrightarrow{\mathrm{\nabla }}\right)\overrightarrow{u}\right|$ = ________.

There are two identical locks, with two identical keys and the keys are among the six different ones which a person carries in his pocket. In a hurry he drops one key somewhere. Then the probability that locks can still be opened by drawing one key at random is equal to

A 200 / 440 V, 1 kVA transformer has impedance of Z = (0.1 + j X) pu. The voltage regulation of the transformer at full load 0.8 p.f lagging is 32%. Then the voltage regulation at half load 0.8 p.f leading is ____%

Match List I (Power factor) and List II (Armature reaction in Alternator) and select the correct answer according to the codes given below:

A three phase, 6 pole 50 Hz induction motor takes 40 A at full load speed of 960 rpm and develops a torque of 100 N-m. The staring current at rated voltage is 200 A. The starting torque and starting current respectively if a star delta starter is used?

Match List-I (Test's) with List-II (Machines) and List-III (To find) and select the correct answer using the codes given below

A 2 pole, 50 Hz single phase induction motor running at 2600 rpm has an effective rotor resistance and reactance each of 0.5 Ω. The stator impedance and magnetizing current are to be neglected. The frequencies of rotor current in forward branch and in backward branch are to be respectively

For a power system network with 10 nodes, Z₄₄ of its bus impedance matrix is j0.5 pu. The voltage at node-4 is 1.5∠2° pu. If a capacitor having a reactance of -j3.5 pu is now added to the network between node-4 and the reference node, the current drawn by the capacitor in pu is _______.

The conductors of a three – phase 50 Hz, 125 km long transmission line are shown in the figure. The diameter of each conductor is 0.6 cm. What is the value of inductance per phase?

Figure-1 shows a 3-phase inverter fed by a constant voltage source V_DC and connected to a balanced resistive load at the output. Each switching device may conduct for 120° (or) 180°. The wave form shown in the figure- II is the

In the voltage regulator shown in the figure, the load current can vary from 100 mA to 500 mA. Assuming that the Zener diode is ideal (i.e. The Zener knee current is negligibly small and Zener resistance is Zero in the breakdown region), the value of R is

For a silicon BJT shown in figure find R_B that establish V_CE = 2 V. Assume V_BE = 0.7 V

The minimum number of gates required to design the logic system shown in figure, to satisfy the given truth table are ________ (complements to variables are not available)

Assume that you can use all the gates i.e. AND, OR, NOT, NAND, NOR, XOR, XNOR.

The ratio of maximum conversion time of an 8-bit digital ramp ADC, successive approximation ADC to flash type ADC respectively with same clock frequency is

The current and potential coil of a dynamometer type wattmeter were accidentally interchanged while connecting. After energizing the circuit, it was observed that the wattmeter did not show the reading. This could be due to the 

The figure shown below is the pole zero plot for the z-transform X(z) of a sequence x[n].

The ROC (region of convergence) for x[n] to be a right signal and ROC for x[n] to be a left sided signal are respectively

In the system shown in the figure, r(t) = sin ωt

The steady-state response c(t) will exhibit a resonance peak at a frequency of:

Consider the transfer functions of the following systems

System 1: $TF=\frac{10}{\left(s+4\right)}$

System 2: $TF=\frac{10}{\left(s+10\right)}$

Then the ratio of the bandwidth of system 1 to the bandwidth of system 2 is ______

A parallel plate air capacitor as shown below has a total charge Q and a breakdown voltage V. A slab of a dielectric constant 6 is inserted as shown. The maximum breakdown voltage and the charge at this voltage respectively would be

The potential at the centroid of an equilateral triangle of side r√3 due to three equal positive point charges each of value q and placed at the vertices of the triangle would be:

Two electric dipoles aligned parallel to each other and having the same axis exert a force F on each other, when a distance d apart, If the dipoles are a distance 2d a part, then the mutual force between them would be

For static electric and magnetic fields in an inhomogeneous source - free medium, which of the following represents the correct form of two of Maxwell’s equations?

A rectangular loop carrying a current I is situated near a long straight wire such that the wire is parallel to one of the sides of the loop and is in the plane of the loop. If a steady current I is established in the wire as shown in the figure, then the loop will

For the signal x(t) = 5 sin 2πat + 7e^jbt to be a power signal the numbers ‘a’ and ‘b’ must be 

In the circuit shown, the voltage V_X (in Volts) is _________.

For the linear network shown above, the following results are obtained.

If I₁ = 6 A and I₂ = 10 A, V is 74 V

If I₁ = -4 A and I₂ = 6 A, V is 14 V

The value of V for I₁ = 7 A and I₂ = 6 A is ________

The device Q in the circuit shown above has i – v relation

i_Q = V_Q² + 2V_Q      V_Q > 0

i_Q = 0                      V_Q ≤ 0

The value of V_Q in the circuit is __________ volts.

In the following circuit the switch is closed at t = 0. The total energy lost in the resistor R = 20Ω is found to be 400 J. If the value of R is reduced to 15 Ω, the energy lost in the resistor in Joules would be

The transmission line parameters of the two port network shown are:

A = 5 × 10^-4, B = 10 Ω, C = 10^-6 S, D = -3 × 10^-2

The network is driven by a sinusoidal voltage source having a maximum amplitude of 50 mV and an internal impedance of (100 + j0) Ω. It is terminated in a resistive load of 5 kΩ.

The average power delivered to the load resistor is _______ (in mW)

Let $M=\left[\begin{array}{ccc}\alpha & 1& 1\\ 1& \beta & 1\\ 1& 1& \gamma \end{array}\right],\alpha \beta \gamma =1,\propto ,\beta ,\gamma ,ϵ,R$ and $x=\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]\in R^3$.

 The Mx = 0 has infinitely many solutions if trace (M) is ______ 

Let C be the positively oriented square with vertices (0, 0), (1, 0), (1, 1), (0, 1). The value of line integral ${\int }_C\left(4y^{2}xdx+8x^{2}ydy\right)$ is ______

An integrating factor of the differential equation $\left(y+\frac{y^3}{3}+\frac{x^2}{2}\right)dx+\frac{1}{4}\left(x+x{y}^2\right)dy=0$ is:

The contour C given below is on the complex plane z = x + jy, where $\mathrm{j}=\sqrt{-1}$

The value of the integral $\frac{1}{\pi \mathrm{j}}\underset{\mathrm{c}}{\oint }\frac{\mathrm{d}\mathrm{z}}{{\mathrm{z}}^2-1}$ is _______

The mean of a normal distribution is the average of the first ten natural numbers. then what is the probability of variable between 4 and 7, if $\mathrm{P}\left(\mathrm{x}\le 4\right)=\frac{1}{5}$

At 50% of full load the armature current drawn by a dc shunt motor is 40 A when connected to a 200 V supply. By decreasing the field flux its speed is raised by 20%. This also causes a 10% increase in load torque. The armature resistance including the brushes is 1 ohm. Neglecting armature reaction and saturation the percentage change in field current will be

A three-phase, 4 – pole, 600 V, 60 Hz induction motor is modeled by Z_th = 0.6933 + j1.933 Ω, $R_2^1=4.5\mathrm{\Omega }$ and $X_2^1=2\mathrm{\Omega }$. If the motor is absorbing power from the three-phase lines at rated frequency, which of the following is/are true?

A 1 kVA, 200/100 V, 50 Hz, single phase transformer gave the following results on 50 Hz:

OC (LV side): 100 V, 20 watts

SC (HV side): 5 A, 25 watts

It is assumed that no load loss components are equally divided. The above tests were then conducted on the same transformer at 40 Hz. Test results are

OC (HV): 160 V, W_1­ watts

SC (LV): 10 A, W_2­ watts

Neglecting skin effect, W_1­ and W₂ will be

A three-phase transformer is connected to on 11 kV supply and draws 6A current.

Which of the following statements is/are true?

Consider the turns ratio of the transformer is 11.

A 10 kW, 600 V, 3 phase star connected synchronous motor is having an internal reactance of 15 Ω. Initially it is operating at 60% load at 0.8 lagging power factor. Now, if the excitation is decreased by 3% with power factor remaining the same, what will be the new load in percent ?

A 60 Hz generator connected directly to an infinite bus operating at a voltage of 1 ∠0° pu has a synchronous reactance of 1.35 pu. The generator no-load rated voltage is 1.1 pu. The generator is suddenly loaded to 60% of the maximum power limit. The frequency of the oscillation of the generator rotor is 0.50 Hz. The inertia constant in MJ/MVA will be

Consider the power system shown in the figure below.

T : 50 MVA, X = 10%

A, B, C: Fault level = 1000 MVA

Assume Base = 100 MVA

Assuming 1.0 pu voltage throughout before the fault, the value of the current limiting reactor X to be chosen, such that the feeder breaker rating does not exceed 425 MVA, is 

The generator having a synchronous reactance of x_d = 1.4 pu is connected to a very large system. The terminal voltage is 1∠0° pu and generator is supplying to the system a current of 0.75 pu at 0.8 pf lagging. If the real power output and terminal voltage of the generator remains constant but the excitation of the generator is increased by 25% then the reactive power delivered to the bus is _________.

For a buck-boost converter the waveform of current through the inductor is shown below:

The source and output voltage are related as:

A line commutated inverter transfer energy into 450 V, 50 Hz, 3 phase supply from a battery of 600 V. The battery is linked to converter through a large choke filter having a resistor ‘R’. It is desired to transfer some power into supply. Consider the firing angle ‘α’ 120° and dc load current is 7 A. Calculate the resistor ‘R’ in ohms ______ 

A 12-V battery feeds a single-phase full bridge inverter whose output is connected to an ideal single-phase transformer. Its primary has 10 turns and the load voltage is 230 V. For a load resistance of 100 Ω, the rms value of primary current is____

Consider only the fundamental component of inverter out-put voltage.

In the circuit shown below, all the components are ideal. If V_i is +2 V, the current I₀ sourced by the op-amp is ______ mA

The initial binary sequence of the given counter is 000 where Q₀ is LSB and Q₂ is MSB. The binary sequence at Q₂Q₁Q₀ after four clock pulses is

A rectifier type PMMC voltmeter has a sensitivity of 20 kΩ/V. A reading of 4.5 V is obtained when measuring a voltage source with an internal resistance on it’s 5 V scale. When the scale is changed to 10 V full scale, a reading of 6 V is obtained. The value of the voltage and its internal resistance R are

The signal x(t) is described by

$x\left(t\right)=\{\begin{array}{cc}1for& -1\le t\le 1\\ 0& otherwise\end{array}$

Two of the angular frequencies at which its Fourier transform becomes zero are

The time-domain signal corresponding to the following z-transform is:

$X\left(z\right)=\sum _{k=5}^{10}\frac{1}{k}{z}^{-k},\left|\mathrm{z}\right|>0$

The first two rows in the Routh Hurwitz tabulation of a C.E are given below

Consider the following statements,

1. Number of RHP = 3

2. Number of LHP = 2

3. Number of poles on the imaginary axis is 2.

4.Number of poles on the imaginary axis is 4.

5. Number of left-hand side poles is equal to 1.

Which of these statements are correct?

The asymptotic Bode plot of a system G(s) is shown below.

Which of the following statements is/are true regarding the transfer function G(s)

The open-loop transfer function of a unity feedback system is given by

$G\left(s\right)=\frac{10}{s\left(\frac{s}{5}+1\right)\left(\frac{s}{20}+1\right)}$

In G(s) plane, the Nyquist plot of G(s) passes through the negative real axis at the point:

Consider the electrical network shown in the figure in state space, where i_R(t) is the output.

Which of the following represents the state space for the above circuit.