# GATE Ec Scholarship Test

25 Questions  Settings  .

Related Topics
• 1.
The root-locus diagram for a closed loop feedback system is shown in Figure The system is overdamped.
• A.

Only if zero < K < 1

• B.

Only if 1 < K < 5

• C.

Only if K > 5

• D.

If zero < K < 1 or K > 5

• 2.
The Nyquist plot for the open-loop transfer function G(s) of a unity negative feedback system is shown in figure. if G(s) has no pole in the right half of splane, the number of roots of the system characteristic equation in the right half of s-plane is
• A.

Zero

• B.

1

• C.

2

• D.

3

• 3.
The feedback control system in Figure is stable
• A.

for all K > Zero

• B.

Only if K > 1

• C.

Only if Zero < K < 1

• D.

None

• 4.
Consider a system with the transfer function, G(s) = (s + 6) / {ks^2 + s + 6}. Its damping ratio will be 0.5 when the value of k is
• A.

2/6

• B.

3

• C.

1/6

• D.

6

• 5.
A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has
• A.

A higher type number

• B.

Reduced damping

• C.

Higher noise amplification

• D.

Larger transient overshoot

• 6.
The signal flow graph of a system is shown in figure. The transfer function C(S)/R(S) of the system is
• A.

A

• B.

B

• C.

C

• D.

D

• 7.

• A.

A

• B.

B

• C.

C

• D.

D

• 8.

• A.

A

• B.

B

• C.

C

• D.

D

• 9.

• A.

A

• B.

B

• C.

C

• D.

D

• 10.

• A.

A

• B.

B

• C.

C

• D.

D

• 11.

• A.

A

• B.

B

• C.

C

• D.

D

• 12.
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is
• A.

0.067

• B.

0.073

• C.

0.082

• D.

0.091

• 13.

• A.

A

• B.

B

• C.

C

• D.

D

• 14.

• A.

A

• B.

B

• C.

C

• D.

D

• 15.

• A.

A

• B.

B

• C.

C

• D.

D

• 16.

• A.

A

• B.

B

• C.

C

• D.

D

• 17.

• A.

A

• B.

B

• C.

C

• D.

D

• 18.

• A.

A

• B.

B

• C.

C

• D.

D

• 19.

• A.

A

• B.

B

• C.

C

• D.

D

• 20.

• A.

A

• B.

B

• C.

C

• D.

D

• 21.
If z = xyln(xy), then
• A.

A

• B.

B

• C.

C

• D.

D

• 22.

• A.

A

• B.

B

• C.

C

• D.

D

• 23.

• A.

A

• B.

B

• C.

C

• D.

D

• 24.

• A.

1

• B.

Zero

• C.

-1

• D.

3.14

• 25.

• A.

A

• B.

B

• C.

C

• D.

D

• 26.

• A.

A

• B.

B

• C.

C

• D.

D

• 27.

• A.

A

• B.

B

• C.

C

• D.

D

• 28.
The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions correspond to a casual system?
• A.

Y(t) = x(t − 2) + x(t + 4)

• B.

Y(t) = (t − 4) x(t + 1)

• C.

Y(t) = (t + 4) x(t − 1)

• D.

Y(t) = (t + 5) x(t + 5)

• 29.

• A.

A

• B.

B

• C.

C

• D.

D

• 30.

• A.

A

• B.

B

• C.

C

• D.

D

• 31.
In the circuit of figure, the equivalent impedance seen across terminals A, B is
• A.

(16/3) Ω

• B.

(8/3) Ω

• C.

(8/3 + 12j) Ω

• D.

None of the above

• 32.
If 24 V is applied across 4 Ω resistor then the current flowing through the resistor is
• A.

6 A

• B.

24 A

• C.

48 A

• D.

96 A

• 33.
Superposition theorem is based on the concept of
• A.

Duality

• B.

Reciprocity

• C.

Linearity

• D.

Non linearity

• 34.
The value of the resistance, R, connected across the terminals, A and B, (ref. Fig.) which will absorb the maximum power is
• A.

4 kΩ

• B.

5 kΩ

• C.

8 kΩ

• D.

10 kΩ

• 35.
Which of the following statement(s) about passive elements is / are correct? (i) These elements generate or produce electrical energy. (ii) These elements consume (receive) energy or store energy.
• A.

Only (i)

• B.

Only (ii)

• C.

Both (i) and (ii)

• D.

None

• 36.
Which of the following is linear element?
• A.

Voltage Source

• B.

Current Source

• C.

Resistor

• D.

None

• 37.
The superposition theorem is valid for
• A.

All linear networks

• B.

Non-linear networks

• C.

Only linear networks having no dependent sources

• D.

Both (A) & (B)

• 38.
In a practical voltage source, the terminal voltage
• A.

Cannot be less than source voltage

• B.

Cannot be higher than source voltage

• C.

Is always equal to source voltage

• D.

None

• 39.
The capacitance values of three capacitors C1, C2 & C3 are 1 F, 2 F & 3F respectively. If these capacitors are connected in parallel then the equivalent capacitance value is
• A.

(6 / 11) F

• B.

(11 / 6) F

• C.

6 F

• D.

2 F

• 40.
Nodal method of solving the network is based on
• A.

Ohm’s law

• B.

Kirchhoff’s Current Law (KCL)

• C.

Kirchhoff’s Voltage Law (KVL)

• D.

Both (A) & (B)

• 41.
When determining Thevenin’s resistance of a circuit
• A.

All sources must be open circuited

• B.

All sources must be short circuited

• C.

All voltage sources must be open circuited and all current sources must be short circuited

• D.

All sources must be replaced by their internal resistances

• 42.
If 4 Ω resistor & 2 H inductor are connected in parallel then time constant of the circuit is
• A.

0.25 sec

• B.

0.5 sec

• C.

5 sec

• D.

8 sec

• 43.
The resistance values of three resistors R1, R2 & R3 are 1 Ω, 2 Ω & 4 Ω respectively. If these resistors are connected in series then the equivalent resistance value is
• A.

7/4 Ω

• B.

4/7 Ω

• C.

5/4 Ω

• D.

4/5 Ω

• 44.
A 12V DC source with an internal resistance of 2 Ω can supply maximum power to the resistive load when the value of load resistor is
• A.

8 Ω

• B.

4 Ω

• C.

2 Ω

• D.

1 Ω

• 45.
In steady state, the inductor behaves as
• A.

Open Circuit

• B.

Short Circuit

• C.

Both (A) & (B)

• D.

None

• 46.
_______ is defined as the time rate of flow of charge.
• A.

Voltage

• B.

Current

• C.

Energy

• D.

Power

• 47.
At resonant frequency, the current flowing through series R-L-C circuit is
• A.

Zero

• B.

Minimum

• C.

Maximum

• D.

None

• 48.
Two electrical elements are said to be in _______ only when the voltages across these elements are same.
• A.

Series

• B.

Parallel

• C.

Both (A) & (B)

• D.

None

• 49.
Which of the following is not an electrical quantity?
• A.

Voltage

• B.

Current

• C.

Distance

• D.

Power

• 50.
The value of voltage source for a circuit carrying 4 A of current through 5Ω resistor
• A.

2.5 V

• B.

5 V

• C.

10 V

• D.

20 V

• 51.
The energy stored in a capacitor charged to 10 volts is 0.01 J. The capacitor value is
• A.

2 mF

• B.

1mF

• C.

200 µF

• D.

100 µF

• 52.
_______ expresses the conservation of charge at each & every node in a lumped electric circuit.
• A.

Ohm’s Law

• B.

Kirchhoff’s Current Law (KCL)

• C.

Kirchhoff’s Voltage Law (KVL)

• D.

None

• 53.
Which of the following statement(s) is/ are correct? S1: The network theory is valid for all frequencies. S2: Bilateral elements are always linear.
• A.

Only S1

• B.

Only S2

• C.

Both S1 & S2

• D.

Neither S1 nor S2

• 54.
If the network has an impedance of (1-j) Ω at a specific frequency, the circuit would consists of series combination of
• A.

Resistor & Inductor

• B.

Resistor & Capacitor

• C.

Resistors

• D.

None

• 55.
Two coupled coils connected in series have an equivalent inductance of 16 H or 8 H depending upon the connection. The value of mutual inductance is
• A.

24 H

• B.

16 H

• C.

8 H

• D.

2 H

• 56.
Which of the following statement(s) is/ are correct? S1: Ohm’s law is valid for both active and passive elements. S2: Linear elements are always Bilateral.
• A.

Only S1

• B.

Only S2

• C.

Both S1 & S2

• D.

Neither S1 nor S2

• 57.
For a given network, the relationship between the number of independent mesh equations (m) and the number of independent nodal equations (n) is
• A.

M > n always

• B.

M < n always

• C.

M = n always

• D.

M ≥ n or m < n depends upon the form of the network

• 58.
A linear circuit consists of two sources & other elements. When one source acting alone produces 10 mA through a given branch (B1). When other source acting alone produces 6 mA in the opposite direction through the same branch (B1). The current (in mA) through the branch (B1) when two sources are acting simultaneously is equal to
• A.

10

• B.

16

• C.

6

• D.

4

• 59.
If I = 2 V^2 (Where V^2 is the square of V) , then the characteristics of current (I) & voltage (V) are
• A.

Linear

• B.

Non- Linear

• C.

Passive

• D.

Bilateral

• 60.
_______ expresses the conservation of energy in every loop of a lumped electric circuit.
• A.

Ohm’s Law

• B.

Kirchhoff’s Current Law (KCL)

• C.

Kirchhoff’s Voltage Law (KVL)

• D.

None

• 61.
A network contains only independent current sources & resistors. If the values of all resistors are doubled then the values of node voltages
• A.

Will become half

• B.

Will remain unchanged

• C.

Will become double

• D.

Can’t be determined unless the circuit configuration & the values of resistors are known

• 62.
Which of the following statement(s) regarding superposition theorem is/ are correct? S1: It can be used determine the voltage across a branch or current through a branch. S2: It is applicable to networks consisting more than one source. S3: It is applicable to DC circuits only.
• A.

Only S1

• B.

Only S2

• C.

Both S1 & S2

• D.

Both S2 & S3

• 63.
A delta connection contains 3 equal impedances of 60 Ω. The impedances of the equivalent star connection will be
• A.

15 Ω each

• B.

20 Ω each

• C.

30 Ω each

• D.

40 Ω each

• 64.
Twelve 1 Ω resistances are used as edges to form a cube. The resistance between two diagonally opposite corners of the cube is
• A.

(5 / 6) Ω

• B.

(6 / 5) Ω

• C.

1 Ω

• D.

(3 / 2) Ω

• 65.
The ideal voltage & current sources are in parallel. This combination will have
• A.

Thevenin’s equivalent

• B.

Norton’s equivalent

• C.

Both (A) & (B)

• D.

None

• 66.
How many symbols are used in the octal number system?
• A.

4

• B.

8

• C.

10

• D.

16

• 67.
In a digital computer binary subtraction is performed
• A.

In the same way we perform subtraction in decimal number system

• B.

Using 2’s complement method

• C.

Using 9’s complement method

• D.

Using 10’s complement method

• 68.
_______ bit represents the sign bit of a signed binary number
• A.

Right most

• B.

Middle

• C.

Left most

• D.

None

• 69.
The logic expression f = ∑m (0, 6, 7) is equivalent to
• A.

F = π M (0, 3, 6, 7)

• B.

F = π M (1, 2, 3, 4, 5)

• C.

F = ∑m (0, 1, 2, 3)

• D.

F = ∑m (1, 2, 6, 7)

• 70.
Sum of all the min terms of any Boolean function is equal to
• A.

Zero

• B.

1

• C.

2

• D.

Complement of the function

• 71.
The minimum number of NAND gates required to implement the Boolean function A + AB' + AB'C is equal to
• A.

Zero

• B.

1

• C.

3

• D.

5

• 72.
_________ is an example for sequential circuit.
• A.

• B.

Magnitude comparator

• C.

D Flip flop

• D.

Mux

• 73.
What is the binary equivalent of the decimal number 368
• A.

101110000

• B.

110110000

• C.

111010000

• D.

111100000

• 74.
Which of the following statement(s) is / are correct? (i) The NAND and NOR gates are called as the universal gates. (ii) All the basic gates can be implemented by using these gates.
• A.

Only (i)

• B.

Only (ii)

• C.

Both (i) and (ii)

• D.

None

• 75.
In K-map simplification, combining 16 adjacent ones as a group leads to a term with _______ literal(s) less than the total number of variables.
• A.

1

• B.

2

• C.

3

• D.

4

• 76.
• A.

Two Half adders & an AND gate

• B.

Two Half adders & an Ex-OR gate

• C.

One Half adder & Ex-NOR gate

• D.

Two Half adders & an OR gate

• 77.
00111 is the two's complement representation of
• A.

-7

• B.

7

• C.

24

• D.

-24

• 78.
If f (A, B) = A’ + B then the simplified expression for the function f ( f (p + q, q’), q)
• A.

P’

• B.

P

• C.

Q

• D.

Q'

• 79.
If the input signal frequency of a 3-bit binary up counter is 16 K Hz, then the output signal frequency is
• A.

16 K Hz

• B.

32 K Hz

• C.

5 K Hz

• D.

2 K Hz

• 80.
For the equation, s^3 − 4s^2+ s + 6 = 0 the number of roots in the left half of s -plane will be(where y^x means y raised to x)
• A.

Zero

• B.

1

• C.

2

• D.

3

• 81.
A system has its two poles on the negative real axis and one pair of poles lies on jω axis. The system is
• A.

Unstable

• B.

Marginally Stable

• C.

Stable

• D.

None

• 82.
The zero-input response of a system given by the state-space equation
• A.

A

• B.

B

• C.

C

• D.

D

• 83.
Consider the Bode magnitude plot shown in Fig. The transfer function H(s) is
• A.

A

• B.

B

• C.

C

• D.

D

• 84.
In the formation of Routh–Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of
• A.

Only one root at the origin

• B.

Imaginary roots

• C.

Only positive real roots

• D.

Only negative real roots

• 85.
The transfer function of a plant is T(s) = 5/ {(s+5)(s^2 + s + 1)}. The second-order approximation of T (s) using dominant pole concept is:
• A.

1 / {(s+5)(s + 1)}

• B.

5 / {(s+5)(s + 1)}

• C.

5 / (s^2 + s + 1)

• D.

1 / (s^2 + s + 1)

• 86.
A unity negative feedback system has the open-loop transfer function G(s) = k/{s(s+1)(s+3)}. The value of the gain K (>0) at which the root locus crosses the imaginary axis is _________________.
• A.

12

• B.

8

• C.

20

• D.

5

• 87.
A unity negative feedback system has an open–loop transfer function G(s) = k/{s(s+10)}. The gain K for the system to have a damping ratio of 0.25 is
• A.

100

• B.

200

• C.

400

• D.

500

• 88.
The centroid for the open loop transfer function {K(s+6)} / {(s+3)(s+5)(s+10)}
• A.

6

• B.

-6

• C.

-10

• D.

-16

• 89.
The open-loop transfer function of a plant is given as G(s) = 1 / (s^2 - 1). If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is:
• A.

10 (s-1) / (s + 2)

• B.

10 (s+4) / (s + 2)

• C.

10 (s + 2) / (s + 10)

• D.

2 (s+2) / (s + 10)

• 90.
The relationship between gain cross over frequency (Wgc) & phase cross over frequency (Wpc) for marginal stable system is
• A.

Wgc > Wpc

• B.

Wgc < Wpc

• C.

Wgc = Wpc

• D.

None

• 91.
The open loop transfer function of a system is k / {s(s+4)}. If the damping ratio is 0.5 then the value of ‘k’ is
• A.

2

• B.

4

• C.

8

• D.

16

• 92.
The asymptotic Bode plot of a transfer function is as shown in the figure. The transfer function G (s) corresponding to this Bode plot is:
• A.

A

• B.

B

• C.

C

• D.

D

• 93.
The relationship between gain cross over frequency (Wgc) & phase cross over frequency (Wpc) for an unstable system is
• A.

Wgc > Wpc

• B.

Wgc < Wpc

• C.

Wgc = Wpc

• D.

None

• 94.
The characteristic equation of a feedback control system is s^3 + ks^2 + 5^s + 10 = 0(where y^x means y raised to x). The value of k for sustained oscillations & the corresponding frequency of oscillations (in rad/sec) are respectively given by
• A.

1, √2

• B.

2, √5

• C.

3, √7

• D.

04-05-15

• 95.
The relationship between gain cross over frequency (Wgc) & phase cross over frequency (Wpc) for a stable system is
• A.

Wgc > Wpc

• B.

Wgc < Wpc

• C.

Wgc = Wpc

• D.

None

• 96.
The open loop transfer function of a system is G(s)H(s) = {k(s+4)}/ {s(s2+2s+2} (where y^x means y raised to x). The root locus will intersect the imaginary axis at
• A.

2j, -2j

• B.

0.7j, -0.7j

• C.

3j,-3j

• D.

10j,-10j

• 97.
The gain margin for the open loop transfer function of a system G(s) = 1 / {s(s+16)}
• A.

Zero

• B.

1

• C.

16

• D.

• 98.
Negative feedback in a closed-loop control system does not
• A.

Reduce the overall gain

• B.

Reduce bandwidth

• C.

Improve disturbance rejection

• D.

Reduce sensitivity to parameter variation

• 99.
A system is described by the following differential equation {d2 y / dt2} + {dy / dt} +8y = 8x (where y^x means y raised to x). The natural frequency (in rad/sec) is
• A.

2.93

• B.

2.63

• C.

2.83

• D.

3.23

• 100.
The impulse response h[n] of a linear time-invariant system is given by h[n] = u[n + 3] + u[n − 2] − 2u[n − 7] where u[n] is the unit step sequence. The above system is
• A.

Stable but not causal

• B.

Stable and causal

• C.

Causal but unstable

• D.

Unstable and not causal

• 101.
If a system is characterized by the equation y(t) = 5x(t) + 10 then the system is
• A.

Linear

• B.

Non-linear

• C.

Both (A) & (B)

• D.

None

• 102.
The Fourier series expansion of a real periodic signal with fundamental frequency f0 is given byIt is given that C3 = 3 + j5, then C−3 is (NoteC suffix -3)
• A.

5 + 3j

• B.

-3 + 3j

• C.

5 - 3j

• D.

3 - 5j

• 103.
Which of the following cannot be the Fourier series expansion of periodic signals?
• A.

X(t) = 2 cos t + 3 cos 3t

• B.

X(t) = 2 cos πt + 7 cos t

• C.

X(t) = cos t + 0.5

• D.

X(t) = 2 cos 1.5πt + sin 3.5πt

• 104.
The trigonometric Fourier series of an even function of time does not have
• A.

The dc term

• B.

Cosine terms

• C.

Sine terms

• D.

Odd harmonic terms

• 105.
The period of the signal x(t) = 5cos12πt + 3 sin18πt is
• A.

6 π

• B.

9 π

• C.

1/6

• D.

1/3

• 106.
Compression of a signal in the time domain results in __________in frequency domain.
• A.

Compression

• B.

Expansion

• C.

Both (A) & (B)

• D.

None

• 107.
Two sequences x1 (n) and x2 (n) are related by x2 (n) = x1 (- n). In the z- domain, their ROC’s are
• A.

Same

• B.

Reciprocal to each other

• C.

Negative of each other

• D.

Complements of each other

• 108.
The waveform of a periodic signal x(t) is shown in the figure.A signal g(t) is defined as g(t) = x{0.5(t-1)}. The average power of g(t) is _____
• A.

Zero

• B.

1

• C.

2

• D.

3

• 109.
If a signal f(t) has energy E, then energy of the signal f(2t) is equal to
• A.

E/2

• B.

E

• C.

2E

• D.

4E

• 110.
The power in the signal
• A.

40

• B.

41

• C.

50

• D.

51

• 111.
The Fourier transform of the exponential signal e^(jW0t) (where y^x means y raised to x)is
• A.

A constant

• B.

A rectangular pulse

• C.

An impulse

• D.

A series of impulses

• 112.
A continuous, linear time has an impulse response h(t) described by when a constant input of value 5 is applied to this filter, the steady state output is--------
• A.

25

• B.

35

• C.

40

• D.

45

• 113.
Nyquist Frequency for the signal x(t) =3 sin 50πt +10 cos 300πt is
• A.

25 Hz

• B.

50 Hz

• C.

150 Hz

• D.

300 Hz

• 114.
Autocorrelation of a sinusoid is
• A.

Sinc function

• B.

Another sinusoid

• C.

Rectangular pulse

• D.

Triangular pulse

• 115.
X(n)=a^|n|, |a|
• A.

An energy signal

• B.

A power signal

• C.

Neither an energy nor a power signal

• D.

An energy as well as a power signal

• 116.
A continuous time system is described by y (t) = x (t^2) (where y^x means y raised to x). The system is
• A.

Causal, linear

• B.

Causal, non-linear

• C.

Non causal, non-linear

• D.

Non causal, linear

• 117.
The impulse response of a system is h(n) = (a^n) . u(n) (where y^x means y raised to x). The condition for the system to be BIBO stable is
• A.

A is real and positive

• B.

A is real and negative

• C.

│a│ > 1

• D.

│a│ < 1

• 118.
The Fourier transform of a rectangular pulse existing between t = − T /2 to t = T / 2 is a
• A.

Sinc squared function

• B.

Sinc function

• C.

Sine squared function

• D.

Cos function

• 119.
The unit impulse response of a linear time invariant system is the unit step function u(t). For t > 0, the response of the system to an excitation e^(-at) u(t) (where y^x means y raised to x) will be (Assume a > 0)
• A.

A.e^(-at)

• B.

{1- e^(-at)} / a

• C.

A{1- e^(-at)}

• D.

1- e^(-at)

• 120.
The auto-correlation function of a rectangular pulse of duration T is
• A.

A rectangular pulse of duration T

• B.

A rectangular pulse of duration 2T

• C.

A triangular pulse of duration T

• D.

A triangular pulse of duration 2T

• 121.
If X(f) represents the Fourier Transform of a signal x (t) which is real and odd symmetric in time, then X (f) is
• A.

Complex

• B.

Imaginary

• C.

Real

• D.

None

• 122.
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
• A.

Product of h1(t) and h2(t)

• B.

Sum of h1(t) and h2(t)

• C.

Convolution of h1(t) and h2(t)

• D.

Subtraction of h2(t) from h1(t)

• 123.
The magnitude of the gradient for the function f(x,y,z)=x^2+3y^2+z^3 at the point (1,1,1) is _________
• A.

3

• B.

4

• C.

5

• D.

7

• 124.
The determinant of matrix A is 5 and the determinant of matrix B is 40 .The determinant of the matrix AB is ______.
• A.

8

• B.

4

• C.

35

• D.

200

• 125.
The real part of an analytic function f(z) where z=x+jy is given by e^(iy) . cosx. The imaginary part of f(z) is
• A.

E^y . cosx

• B.

E^-y . sinx

• C.

-e^y . sinx

• D.

-e^-y . sinx

• 126.
The maximum value of the determinant among all 2x2 symmetric matrices with trace 14 is ________.
• A.

Zero

• B.

14

• C.

49

• D.

64

• 127.
The Newton-Raphson method is used to solve the equation f(x)=x^3-5x^2+6x-8=0. Taking the initial guess as x=5, the solution obtained at the end of the first iteration is ________.
• A.

4.2903

• B.

3.2903

• C.

0.2903

• D.

7.5213

• 128.
The minimum number of 2-input NOR gates required to implement the Boolean function f(A, B, C, D) = ∑m (0, 1, 2, 3, 8, 9, 10, 11) is equal to
• A.

1

• B.

2

• C.

4

• 129.
The phase cross over frequency for the open loop transfer function of a system G(s) = 1 / {s(s+16)}
• A.

1

• B.

16

• C.

• 130.
The maximum value of f(x)=2x^(3)-9x^(2)+12x-3 in the interval 0
• A.

2

• B.

6

• C.

36