Olete.in – MCQs, Mock Tests & Government Job Prep | Gate Engineering GATE 2017-2018 EEE

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

1. t2/2 u(t)
2. t(t - 1)/2 u(t - 1)
3. (t - 1)2/2 u(t - 1)
4. (t2 - 1)/2 u(t - 1)

✅ Correct Answer: 3

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

1. All the poles of the system must lie on the left side of the jÏ‰ axis.
2. Zeros of the system can lie anywhere in the s-plane.
3. All the poles must lie within |s| = 1
4. All the roots of the characteristic equation must be located on the left side of the jÏ‰

✅ Correct Answer: 3

Two systems with impulse responses h1 (t) and h2 (t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

1. product of h1 (t) and h2 (t)
2. sum of h1 (t) and h2 (t)
3. convolution of h1 (t) and h2 (t)
4. subtraction of of h2 (t) and h1 (t)

✅ Correct Answer: 3

A source vs (t) = V cos 100 Ï€t has an internal impedance of (4 + j3)â„¦ . If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in â„¦ should be

1. 3
2. 4
3. 5
4. 7

✅ Correct Answer: 3

A single-phase load is supplied by a single-phase voltage source. If the current flowing from the load to the source is 10âˆ -150oA and if the voltage at the load terminals is 100âˆ 60o V, then the

1. load absorbs real power and delivers reactive power.
2. load absorbs real power and absorbs reactive power.
3. load delivers real power and delivers reactive power
4. load delivers real power and absorbs reactive power.

✅ Correct Answer: 2

A single-phase transformer has no-load loss of 64 W, 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 81 W. The transformer has maximum efficiency when operated at

1. 50.0% of the rated current
2. 64.0% of the rated current
3. 80.0% of the rated current
4. 88.8% of the rated current.

✅ Correct Answer: 3

The flux density at a point in space is given by B = 4 xax + 2kyay + 8 az Wb/m2. The value of constant k must be equal to

1. -2
2. -50.
3. +0.5
4. +2

✅ Correct Answer: 1

A continuous random variable X has a probability density function f(x) = e-x , 0 < x < âˆž. Then P{X > 1} is

1. 0.368
2. 0.5
3. 0.632
4. 1.0

✅ Correct Answer: 1

The curl of the gradient of the scalar field defined by V = 2x2y + 3y2z + 4z2x is

1. 4xyax + 6yzay + 8zxaz
2. 4ax + 6ay + 8az
3. (4xy + 4z2)ax + (2x2 + 6yz)ay + (3y2 + 8zx)az
4. 0

✅ Correct Answer: 4

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 A.

1. an AND gate
2. an OR gate
3. an XOR gate
4. a NAND gate

✅ Correct Answer: 3

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 A.

1. an AND gate
2. an OR gate
3. an XOR gate
4. a NAND gate

✅ Correct Answer: 3

For a periodic signal v(t) = 30 sin100t + 10 cos 300t + 6 sin (500t + Ï€ / 4) , the fundamental frequency in rad/s is

1. 100
2. 300
3. 500
4. 1500

✅ Correct Answer: 1

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

1. 5
2. 12
3. 15
4. 20

✅ Correct Answer: 1

The angle Î´ in the swing equation of a synchronous generator is the

1. angle betweeangle between stator voltage and currentn stator voltage and current
2. angular displacement of the rotor with respect to the stator
3. angular displacement of the stator mmf with respect to a synchronously rotating axis
4. angular displacement of an axis fixed to the rotor with respect to a synchronously rotating axis.

✅ Correct Answer: 4

Leakage flux in an induction motor is

1. flux that leaks through the machine
2. flux that links both stator and rotor windings
3. flux that links none of the windings
4. flux that links the stator winding or the rotor winding but not both

✅ Correct Answer: 4

For a power system network with n nodes, Z33 of its bus impedance matrix is j0.5 per unit. The voltage at node 3 is 1.3 âˆ -10o 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

1. 0.325âˆ -100o
2. 0.325âˆ 80o
3. 0.371âˆ -100o
4. 0.433âˆ 80o

✅ Correct Answer: 4

A dielectric slab with 500 mm Ã— 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform electric field of E = 6ax + 8ay kV/mm. The relative permitivity of the dielectric material is equal to 2. The value of constant Îµo is 8.85 * 10-12 F/m. The energy stored in the dielectric in Joules is

1. 8.85 * 10-11
2. 8.85 * 10-5
3. 88.5
4. 885

✅ Correct Answer: 3

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

1. 0
2. 1
3. 2
4. 3

✅ Correct Answer: 2

Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating frequency. Their respective resistances are R1 and R2. When connected in series, their effective Q factor at the same operating frequency is

1. q1 R1 + q2 R2
2. q1/R1 + q2/R2
3. (q1 R1 + q2 R2)/(R1 + R2)
4. q1 R2 + q2 R1

✅ Correct Answer: 3

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

1. 100
2. 98
3. 52
4. 48

✅ Correct Answer: 2

A function y = 5x2 +10 x is defined over an open interval x = (1, 2) . At least at one point in this interval, dy/dx is exactly

1. 20
2. 25
3. 30
4. 35

✅ Correct Answer: 2

When the Newton-Raphson method is applied to solve the equation f (x) = x3 + 2x -1= 0, the solution at the end of the first iteration with the initial guess value as x0 = 1.2 is

1. "“0.82
2. 0.49
3. 0.705
4. 1.69

✅ Correct Answer: 3

They were requested not to quarrel with others. Which one of the following options is the closest in meaning to the word quarrel?

1. make out
2. call out
3. dig out
4. fall out

✅ Correct Answer: 4

In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in °C on Thursday was

1. 40
2. 43
3. 46
4. 49

✅ Correct Answer: 3

Complete the sentence: Dare _______________ mistakes.

1. commitB. to commit
2. to commit
3. committed
4. committing

✅ Correct Answer: 1

Choose the grammatically CORRECT sentence:

1. Two and two add four.
2. Two and two become four
3. Two and two are four
4. Two and two make four.

✅ Correct Answer: 4

Choose the grammatically CORRECT sentence:

1. Two and two add four.
2. Two and two become four
3. Two and two are four
4. Two and two make four.

✅ Correct Answer: 4

Statement: You can always give me a ring whenever you need. Which one of the following is the best inference from the above statement?

1. Because I have a nice caller tune.
2. Because I have a better telephone facility.
3. Because a friend in need is a friend indeed
4. Because you need not pay towards the telephone bills when you give me a ring.

✅ Correct Answer: 3

What is the chance that a leap year, selected at random, will contain 53 Saturdays?

1. 2/7
2. 3/7
3. 1/7
4. 5/7

✅ Correct Answer: 1

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?

1. The emergence of nationalism in colonial India led to our Independence.
2. Nationalism in India emerged in the context of colonialism.
3. Nationalism in India is homogeneous.
4. Nationalism in India is heterogeneous.

✅ Correct Answer: 4

The set of values of p for which the roots of the equation 3x2+2x+p(p“1) = 0 are of opposite sign is

1. ("“âˆž, 0)
2. (0, 1)
3. (0, âˆž)
4. (0, âˆž)

✅ Correct Answer: 2

A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey is A. 30B. 36C. 40D.

1. 64
2. 36
3. 40
4. 24

✅ Correct Answer: 3

Find the sum to n terms of the series 10+84+ 734 + .....

1. [9(9n + 1)]/10 + 1
2. [9(9n - 1)]/8 + 1
3. [9(9n - 1)]/8 + n
4. [9(9n - 1)]/8 + n2

✅ Correct Answer: 4