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Q. No. 1 – 5 Carry One Mark Each
Choose the grammatically CORRECT sentence:
Statement: You can always give me a ring whenever you need.
Which one of the following is the best inference from the above statement?
In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41ºC and of Tuesday to Thursday was 43ºC. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in ºC on Thursday was
Let the temperature of Monday be T_{M}
Sum of temperatures of Tuesday and Wednesday = T and
Temperature of Thursday =T_{Th}
Complete the sentence:
Dare ____________ mistakes.
They were requested not to quarrel with others.
Which one of the following options is the closest in meaning to the word quarrel?
Q. No. 6 – 10 Carry Two Marks Each
A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16km in the third quarter. The average speed of the car in km per hour over the entire journey is
Average speed = Total distance/Total time
If the current changes from 3A to 5A in 2s and the emf is 10V. Calculate the inductance.
Statement: There were different streams of freedom movements in colonial India carried out by the moderates, liberals, radicals, socialists, and so on. Which one of the following is the best inference from the above statement?
The set of values of p for which the roots of the equation 3x^{2} + 2x + p (p − 1) = 0 are of opposite sign is
What is the chance that a leap year, selected at random, will contain 53 Sundays?
There are 52 complete weeks in a calendar year 852 × 7 = 364 days
Q. No. 11 – 35 Carry One Mark Each
Given a vector field the line integral evaluated along a segment on the xaxis from x=1 to x=2 is
Square roots of −i, where are
Three moving iron type voltmeters are connected as shown below. Voltmeter readings are V, V_{1} and V_{2} as indicated. The correct relation among the voltmeter readings is
Leakage flux in an induction motor is
The angle δ in the swing equation of a synchronous generator is the
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 elements of the corresponding star equivalent will be scaled by a factor of
A bandlimited 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
For a periodic signal v(t)=30sin 100t + 10cos 300t + 6 sin(500t+π/4), the fundamental frequency in radians/s is
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 Bode plot of a transfer function G(s) is shown in the figure below.
The gain (20logG(s)) is 32 dB and 8 dB at 1 radians/s and 10 radians/s respectively. The phase is negative for all ω. Then G(s) is
In the feedback network shown below, if the feedback factor k is increased, then the
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
The curl of the gradient of the scalar field defined by V = 2x^{2}y+3y^{2}z+4z^{2}x is=
A continuous random variable X has a probability density function f(x) = e^{x }, 0 < x < ∞, Then P{X > 1 } is
The flux density at a point in space is given by B = 4xa_{x }+ 2kya_{y} + 8a_{z} Wb / m^{2} The value of constant k must be equal to^{ }
A singlephase transformer has noload loss of 64 W, as obtained from an opencircuit test. When a shortcircuit test is performed on it with 90% of the rated currents flowing in its both LV and HV windings, he measured loss is 81 W. The transformer has maximum efficiency when operated at
A singlephase load is supplied by a singlephase voltage source. If the current flowing from the load to the source is 10∠  150° A and if the voltage at the load terminals is 100∠60°V , then the
A source V_{s}(t) = V cos100π t has an internal impedance of( 4+ j3). If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in should be
Two systems with impulse responses h_{1} (t) and h_{2} (t) are connected in cascade. Then the overall impulse response of the cascaded system is given by
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
The impulse response of a system is h(t) = tu(t). For an input u(t 1),the output is
Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is
The transfer function V_{2}(s) / V_{1}(s) of the circuit shown below is
In the circuit shown below what is the output voltage (V_{out} ) in Volts if a silicon transistor Q and an ideal opamp are used?
Q. No. 36 – 65 Carry Two Marks Each
When the NewtonRaphson method is applied to solve the equation f(x) = x^{3} + 2x 1 = 0 , the solution at the end of the first iteration with the initial guess value as x_{0 }= 1.2 is
A function y= 5x^{2} +10x is defined over an open interval x = (1,2). Atleast at one point in this interval, dy/dx is exactly
A 4pole induction motor, supplied by a slightly unbalanced threephase 50Hz source, is rotating at 1440 rpm. The electrical frequency in Hz of the induced negative sequence current in the rotor is
Thyristor T in the figure below is initially off and is triggered with a single pulse of width 10 sµ . It is given that L = (100/π)µH and C = (100/π)µF. Assuming latching and holding currents of the thyristor are both zero and the initial charge on C is zero, T conducts for
The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage V_{wx1} = 100V is applied across WX to get an open circuit voltage across YZ. Next, an ac voltage V_{yz2} = 100V is applied across YZ to get an open circuit voltage V_{wx2 }across WX. Then, are respectively,
Two magnetically uncoupled inductive coils have Q factors q_{1} and q_{2} at the chosen operating frequency. Their respective resistances are R_{1} and R_{1}. When connected in series, their effective Q factor at the same operating frequency is
The impulse response of a continuous time system is given by h(t)= δ(t1) + δ (t3). The value of the step response at t = 2 is
The signal flow graph for a system is given below. The Transfer function, Y(s)/U(s) for the system is
In the circuit shown below the opamps are ideal. Then V_{out} in Volts is
In the circuit shown below, Q_{1 }has negligible collectortoemitter saturation voltage and the diode drops negligible voltage across it under forward bias. If V_{cc }is +5V, X and Y are digital signals with 0V as logic 0 and V_{oc} as logic 1, then the Boolean expression for Z is
The clock frequency applied to the digital circuit shown in the figure below is 1kHz. If the initial state of the output of the flipflop is 0, then the frequency of the output waveform Q in kHz is
evaluated anticlockwise around the circle z  i =2, where is
A Matrix has eigenvalues 1 and 2. The corresponding eigenvectors are and respectively. The matrix is
A dielectric slab with 500mm x 500mm crosssection is 0.4m long. The slab is subjected to a uniform electric field of E = 6a_{x} + 8a_{y} kV / mm. The relative permittivity of the dielectric material is equal to 2. The value of constant ε_{0} is 8.85x10^{12} F/m. The energy stored in the dielectric in Joules is
For a power system network with n nodes, Z_{33} 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 separately excited dc motor in the figure below has a rated armature current of 20A and a rated armature voltage of 150V. An ideal chopper switching at 5 kHz is used to control the armature voltage. If L_{a} = 0.1mH, R_{a} = 1, neglecting armature reaction, the duty ratio of the chopper to obtain 50% of the rated a a torque at the rated speed and the rated field current is
A voltage 1000 sin ωt Volts is applied across YZ. Assuming ideal diodes, the voltage measured across WX in Volts is
Three capacitors C_{1} , C_{2} , and C_{3} whose values are 10 µF, 5 µF and 2 µF 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
In the circuit shown below, if the source voltage then the Thevenin’s equivalent voltage in volts as seen by the load resistance R_{L} is
The open loop transfer function of a dc motor is given as When connected in feedback as shown below, the approximate value of K_{a }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
In the circuit shown below, the knee current of the ideal Zener diode is 10mA. To maintain 5V across R_{L}, the minimum value of R_{L} in and the minimum power rating of the Zener diode in mW respectively are
A strain gauge forms one arm of the bridge shown in the figure below and has a nominal resistance without any load as R_{s} = 300 . Other bridge resistances are R_{1} = R_{2} = R_{3} = 300. 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 V_{0} in mV is
Common Data Question: 58 & 59
The state variable formulation of a system is given as:
The response y(t) to the unit step input is
The state variable formulation of a system is given as
The system is
Common Data Questions: 60 & 61
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
Statement for Linked Answer Questions: 62 & 63
In the following network, the voltage magnitudes at all buses are equal to 1 pu, the voltage phase angles are very small, and the line resistances are negligible. All the line reactances are equal to j1
The voltage phase angles in rad at buses 2 and 3 are
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 steadystate is
In the following network, the voltage magnitudes at all buses are equal to 1 pu, the voltage phase angles are very small, and the line resistances are negligible. All the line reactances are equal to j1
If the base impedance and the lineto line base voltage are 100 ohms and 100kV respectively, then the real power in MW delivered by the generator connected at the slack bus is
Statement for Linked Answer Questions: 64 & 65
The Voltage Source Inverter (VSI) shown in the figure below is switched to provide a 50Hz, square wave ac output voltage v_{o} across an RL load. Reference polarity of v_{o} and reference direction of the output current i_{o} are indicated in the figure. It is given that R = 3 ohms, L = 9.55mH.
In the interval when v_{o} < 0 and i_{o} > 0 the pair of devices which conducts the load current is
We consider the following two cases :
Case I : When Q Q1 2 , ON
In this case the +ve terminal of V0 will be at higher voltage. i.e. V0 > 0 and so
i0 > 0 (i.e., it will be +ve). Now, when the Q1, Q2 goes to OFF condition we
consider the second case.
Case II : When Q3, Q4 ON and Q, Q2 OFF :
In this condition, ve terminal of applied voltage V0 will be at higher potential
i.e., V0 < 0 and since, inductor opposes the change in current so, although the
polarity of voltage V0 is inversed, current remains same in inductor i.e. I0 > 0.
This is the condition when conduction have been asked.
In this condition (V_{0} > 0, I_{0} > 0) since, IGBT’s can’t conduct reverse currents therefore current will flow through D D3 4 , until ID becomes negative. Thus, D3 and D4 conducts.
The Voltage Source Inverter (VSI) shown in the figure below is switched to provide a 50Hz, square wave ac output voltage v_{o} across an RL load. Reference polarity of v_{o} and reference direction of the output current i_{o} are indicated in the figure. It is given that R = 3 ohms, L = 9.55mH.
Appropriate transition i.e., Zero Voltage Switching (ZVS) / Zero Current Switching (ZCS) of the IGBTs during turnon / turnoff is
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