GATE In Scholarship Test

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

• (16/3) Ω

• (8/3) Ω

• (8/3 + 12j) Ω

• None of the above

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.

• Only (i)

• Only (ii)

• Both (i) and (ii)

• None

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

• Resistor & Inductor

• Resistor & Capacitor

• Resistors

• None

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

• 15 Ω each

• 20 Ω each

• 30 Ω each

• 40 Ω each

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

• Unstable

• Marginally Stable

• Stable

• None

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

• Compression

• Expansion

• Both (A) & (B)

• None

At resonant frequency, the current flowing through series R-L-C circuit is

• Zero

• Minimum

• Maximum

• None

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

• Series

• Parallel

• Both (A) & (B)

• None

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

• Ohm’s Law

• Kirchhoff’s Current Law (KCL)

• Kirchhoff’s Voltage Law (KVL)

• None

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.

• Only S1

• Only S2

• Both S1 & S2

• Both S2 & S3

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.

• Only (i)

• Only (ii)

• Both (i) and (ii)

• None

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

• Sinc squared function

• Sinc function

• Sine squared function

• Cos function

• A

• B

• C

• D

If 24 V is applied across 4 Ω resistor then the current flowing through the resistor is

• 6 A

• 24 A

• 48 A

• 96 A

In a practical voltage source, the terminal voltage

• Cannot be less than source voltage

• Cannot be higher than source voltage

• Is always equal to source voltage

• None

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

• Complex

• Imaginary

• Real

• None

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

• 8

• 4

• 35

• 200

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

• Ohm’s Law

• Kirchhoff’s Current Law (KCL)

• Kirchhoff’s Voltage Law (KVL)

• None

In a digital computer binary subtraction is performed

• In the same way we perform subtraction in decimal number system

• Using 2’s complement method

• Using 9’s complement method

• Using 10’s complement method

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

• Same

• Reciprocal to each other

• Negative of each other

• Complements of each other

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

• 1

• 16

• ∞

Which of the following is not an electrical quantity?

• Voltage

• Current

• Distance

• Power

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

• (5 / 6) Ω

• (6 / 5) Ω

• 1 Ω

• (3 / 2) Ω

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

• F = π M (0, 3, 6, 7)

• F = π M (1, 2, 3, 4, 5)

• F = ∑m (0, 1, 2, 3)

• F = ∑m (1, 2, 6, 7)

What is the binary equivalent of the decimal number 368

• 101110000

• 110110000

• 111010000

• 111100000

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)

• Zero

• 1

• 2

• 3

The power in the signal

• 40

• 41

• 50

• 51

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.e^(-at)

• {1- e^(-at)} / a

• A{1- e^(-at)}

• 1- e^(-at)

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 ________.

• 4.2903

• 3.2903

• 0.2903

• 7.5213

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

• 1

• 2

• 4

• A

• B

• C

• D

• A

• B

• C

• D

• A

• B

• C

• D

The superposition theorem is valid for

• All linear networks

• Non-linear networks

• Only linear networks having no dependent sources

• Both (A) & (B)

Sum of all the min terms of any Boolean function is equal to

• Zero

• 1

• 2

• Complement of the function

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

• Only one root at the origin

• Imaginary roots

• Only positive real roots

• Only negative real roots

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

• 2j, -2j

• 0.7j, -0.7j

• 3j,-3j

• 10j,-10j

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

• Zero

• 1

• 16

• ∞

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

• Stable but not causal

• Stable and causal

• Causal but unstable

• Unstable and not causal

Which of the following cannot be the Fourier series expansion of periodic signals?

• X(t) = 2 cos t + 3 cos 3t

• X(t) = 2 cos πt + 7 cos t

• X(t) = cos t + 0.5

• X(t) = 2 cos 1.5πt + sin 3.5πt

Autocorrelation of a sinusoid is

• Sinc function

• Another sinusoid

• Rectangular pulse

• Triangular pulse

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

• 6

• -6

• -10

• -16

Superposition theorem is based on the concept of

• Duality

• Reciprocity

• Linearity

• Non linearity

_______ bit represents the sign bit of a signed binary number

• Right most

• Middle

• Left most

• None

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

• 2

• 4

• 8

• 16

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

• B

• C

• D

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

• 2.93

• 2.63

• 2.83

• 3.23

X(n)=a^|n|, |a|

• An energy signal

• A power signal

• Neither an energy nor a power signal

• An energy as well as a power signal