A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid is

Square roots of –i, where            

 Evaluated anticlockwise around the circle, where i =, is

In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode drops negligible voltage across it under forward bias. If Vcc. is +5 V, X and Y are digital signals with 0 V as logic 0 and Vcc. as logic 1, then the Boolean expression for Z is

When the Newton-Raphson method is applied to solve the equation, the solution at the end of the first iteration with the initial guess value as is

A continuous random variable  has a probability density function. Then P is

In the feedback network shown below, if the feedback factor k is increased, then the

A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles        

The impulse response of a system is h(t)=t u(t) . for an input u(t-1), the output is

The impulse response of a continuous time system is given by h(t)=δ(t-1)+δ(t-3). The value of the step response at t=2 is

A strain gauge forms one arm of the bridge shown in the figure below and has a nominal resistance without any load as  Other bridge resistances are. The maximum permissible current through the strain gauge is 20mA. During certain measurement when the bridge is excited by maximum permissible voltage and the strain gauge resistance is increased by 1% over the nominal value, the output voltage V₀ in mV is

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?        

For a periodic signal

, the fundamental frequency in rad/s is

Two systems with impulse responses and  are connected in cascade. Then the overall impulse response of the cascaded system is given by

The transfer function of the circuit shown below is

The signal flow graph for a system is given below. The transfer function  for this system is

The clock frequency applied to the digital circuit shown in the figure below is 1 kHz. If the initial state of the output Q of the flip-flop is 0, then the frequency of the output waveform Q in kHz is

A source  has an internal impedance of . If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in Ω should beA source  has an internal impedance of . If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in Ω should be

For a power system network with n nodes,  of its bus impedance matrix is j0.5 per unit. The voltage at node 3 is  per unit. If a capacitor having reactance of –j3.5 per unit is now added to the network between node 3 and the reference node, the current drawn by the capacitor per unit is

The curl of the gradient of the scalar field defined by  is

In the following network, the voltage magnitudes at all buses are equal to 1 p.u., the voltage phase angles are very small, and the line resistances are negligible. All the line reactances are equal to j1 Ω.

The voltage phase angles in rad at buses 2 and 3 are

The Voltage Source Inverter (VSI) shown in the figure below is switched to provide a 50 Hz, square-wave ac output voltage (V₀) across an R-L load. Reference polarity of V₀ and reference direction of the output current i₀ are indicated in the figure. It is given that R=3Ω, L=9.55mH.

In the interval when V₀<0 and i₀>0 the pair of devices which conducts the load current is

Given a vector field , the line integral ∫F.dl evaluated along a segment on the x-axis from x=1 to x=2 is

In the circuit shown below, the knee current of the ideal Zener diode is 10mA. To maintain 5 V across , in Ω and the minimum power rating of the Zener diode in mW respectively are         

In the following network, the voltage magnitudes at all buses are equal to 1 p.u., the voltage phase angles are very small, and the line resistances are negligible. All the line reactances are equal to j1 Ω.

If the base impedance and the line-to-line base voltage are 100 Ω and 100kV, respectively, then the real power in MW delivered by the generator connected at the slack bus is

A function is defined over an open interval x= (1, 2). At least at one point in this interval,  is exactly

The Voltage Source Inverter (VSI) shown in the figure below is switched to provide a 50 Hz, square-wave ac output voltage (V₀) across an R-L load. Reference polarity of V₀ and reference direction of the output current i₀ are indicated in the figure. It is given that R=3Ω, L=9.55mH.

Appropriate transition i.e., Zero Voltage Switching (ZVS) /Zero Current Switching (ZCS) of the IGBTs during turn-on/turn-off is  

The flux density at a point in space is given by. The value of constant k must be equal to        

The angle δ in the swing equation of a synchronous generator is the

The state variable formulation of a system is given as

, , and

The system is

The separately excited dc motor in the figure below has a rated armature current of 20A and a rated armature voltage of 150 V. An ideal chopper switching at 5 kHz is used to control the armature voltage. If , , neglecting armature reaction, the duty ratio of the chopper to obtain 50% of the rated torque at the rated speed and the rated field current is

The state variable formulation of a system is given as

, , and

The response y (t) to a unit step input is

In the figure shown below, the chopper feeds a resistive load from a battery source. MOSFET Q is switched at 250 kHz, with a duty ratio of 0.4. All elements of the circuit are assumed to be ideal.

The average source current in Amps in steady-state is  

In the figure shown below, the chopper feeds a resistive load from a battery source. MOSFET Q is switched at 250 kHz, with a duty ratio of 0.4. All elements of the circuit are assumed to be ideal.

The PEAK-TO-PEAK source current ripple in Amps is  

Three capacitors , , and , whose values are 10μF, 5μF, and 2μF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown, the maximum safe voltage in volts that can be applied across the combination and the corresponding total charge in μC stored in the effective capacitance across the terminals are respectively         

A dielectric slab with 500mm × 500mm cross –section is 0.4m long. The slab is subjected to a uniform electric field of. is equal to 2. The value of constant  is . The energy stored n the dielectric in joules is

The Bode plot of a transfer function G(s) is shown in the figure below.

The gain (20log|G(s)|) is 32 dB and -8 dB at 1rad/s and 10rad/s respectively. The phase is negative for all ω. Then G(s) is

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k>0, the element of the corresponding star equivalent will be scaled by a factor of

The equation has        

A voltage  Volts is applied across YZ. Assuming ideal diodes, the voltage measured across WX in Volts, is

A matrix has Eigen values –1 and -2. The corresponding eigenvectors are  and respectively. The matrix is

Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is         

The open-loop transfer function of a dc motor is given as. When connected in feedback as shown below, the approximate value of  that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

Thyristor T in the figure below is initially off and is triggered with a single pulse of width 10μs. It is given that and. Assuming latching and holding currents of the thyristor are both zero and the initial charge on C is zero, T conducts for

A single-phase load is supplied by a single –phase voltage source. If the current flowing from the Load to the source is  and if the voltage at the load terminals is , then the

In the circuit shown below, if the source voltage  then the Thevenin’s equivalent voltage in volts as seen by the load resistance  is

In the circuit shown below what is the output voltage  in Volts if a silicon transistor Q and an ideal op-amp are used?        

Two magnetically uncoupled inductive coils have Q factors  and  at the chosen operating frequency. Their respective resistances are  and . When connected in series, their effective Q factor at the same operating frequency is

In the circuit shown below the op-amps are ideal. Then  in Volts is

The input impedance of the permanent magnet moving coil (PMMC) voltmeter is infinite. Assuming that the diode shown in the figure below is ideal, the reading of the voltmeter in volts is          

Three moving iron type voltmeters are connected as shown below. Voltmeter readings are V,  and , as indicated. The correct relation among the voltmeter readings is  

A single-phase transformer has no-load loss of 64W, as obtained from an open-circuit test. When a short-circuit test is performed on it with 90% of the rated currents flowing in its both LV and HV windings, the measured loss is 81W. The transformer has maximum efficiency when operated at  

The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage is applied across WX to get an open circuit voltage across YZ. Next, an ac voltage is applied across YZ to get an open circuit voltage across WX. Then,  are respectively,

Leakage flux in an induction motor is  

A 4-pole induction motor, supplied by a slightly unbalanced three-phase 50Hz source, is rotating at 1440rpm. The electrical frequency in Hz of the induced negative sequence current in the rotor is