GATE Electrical online test paper 3
by Esha Upadhyay · Published · Updated
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Question 1 of 17
1. Question
A cascade of three identical modulo5 counters has an overall modulus of
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Question 2 of 17
2. Question
Let g: [0, ∞]>[0, ∞] be a function defined by g(x) = x [x], where [x] represents the integer part of x. (That is, it is the largest integer which is less than or equal to x). The value of the constant term in the Fourier series expansion of g(x) is
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Question 3 of 17
3. Question
A fair coin is tossed n times. The probability that the difference between the number of heads and tails is (n3) is
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Question 4 of 17
4. Question
The line integral of function F = yzi, in the counterclockwise direction, along the circle x2+y2 = 1 at z = 1 is (where number after x and y denote power like x2 is square of x, pi is constant 3.14)
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Question 5 of 17
5. Question
An incandescent lamp is marked 40 W, 240V. If resistance at room temperature (26°C) is 120 Ω, and temperature coefficient of resistance is .0045/°C, then its ‘ON’ state filament temperature in °C is approximately
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Question 6 of 17
6. Question
In an unbalanced three phase system, phase current Ia = 1<(90 degree)pu, negative sequence current Ib2 = 4<(150 degree)pu, zero sequence current Ic0 = 3<(90 degree)pu. The magnitude of phase current Ib in pu is
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Question 7 of 17
7. Question
Let X(z) = z*z*z / (z*z*z – 1) be the Z transform of a casual signal x[n] then the values of x[2] and x[3] are
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Question 8 of 17
8. Question
The core loss of a single phase, 230/115 V, 50 Hz power transformer is measured from 230 V side by feeding the primary (230 V side) from a variable voltage variable frequency source while keeping the secondary open circuited. The core loss is measured to be 1050 W for 230 V, 50 Hz input. The core loss is again measured to be 500 W for 138 V, 30 Hz input. The hysteresis and eddy current losses of the transformer for 230 V, 50 Hz input are respectively
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Question 9 of 17
9. Question
A 15 kW, 230 V dc shunt motor has armature circuit resistance of 0.4 Ω and field circuit resistance of 230 Ω. At no load and rated voltage, the motor runs at 1400 rpm and the line current drawn by the motor is 5 A. At full load, the motor draws a line current of 70 A. Neglect armature reaction. The full load speed of the motor in rpm is
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Question 10 of 17
10. Question
A 3 phase, 50 Hz, six pole induction motor has a rotor resistance of 0.1 Ω and reactance of 0.92 Ω. Neglect the voltage drop in stator and assume that the rotor resistance is constant. Given that the full load slip is 3%, the ratio of maximum torque to full load torque is
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Question 11 of 17
11. Question
The dc current flowing in a circuit is measured by two ammeters, one PMMC and another electrodynamometer type, connected in series. The PMMC meter contains 100 turns in the coil, the flux density in the air gap is 0.2 Wb/m2, and the area of the coil is 80 mm2. The electrodynamometer ammeter has a change in mutual inductance with respect to deflection of 0.5 mH/deg. The spring constants of both the meters are equal. The value of current, at which the deflections of the two meters are same, is (where m2 and mm2 are m sqaure and mm square)
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Question 12 of 17
12. Question
The maximum value attained by the function f(x) = x(x − 1)(x − 2) in the interval [1, 2] is
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Question 13 of 17
13. Question
Consider a 3 × 3 matrix with every element being equal to 1. Its only nonzero eigenvalue is
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Question 14 of 17
14. Question
The Laplace Transform of f(t) = e to the power 2t sin(5t) u(t) is
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Question 15 of 17
15. Question
The phase crossover frequency of the transfer function G(s) = 100/ (s+1)3 where (s+1)3 means cube of s+1 in rad/s is
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Question 16 of 17
16. Question
Consider a continuoustime system with input x(t) and output y(t) given by y(t) = x(t) cos(t).This system is
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Question 17 of 17
17. Question
A temperature in the range of −40˚ C to 55˚ C is to be measured with a resolution of 0.1˚ C. The minimum number of ADC bits required to get a matching dynamic range of the temperature sensor is
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