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GATE EXAMINATION2010

ELECTRONICS & COMMUNICATION

Q.1 to Q.25 Carry one mark each

Q.1 The eigen values of a skew-symmetric matrix are

• Always zero
• Always pure imaginary 
• Either zero or pure imaginary
• Always real

Q.2 The trigonometric Fourier series for the waveform f(t) shown below contains
 

• Only cosine terms and zero value for the dc component 
• Only cosine terms and a positive value for the dc component
• Only cosine terms and a negative value for the dc component 
• Only sine terms and a negative value for the dc component  

Q.3.A function n(x) satisfies the differential equation where L is a constant. The boundary conditions are : n(0) = K and n(∞) = 0 . The solution to this equation is

• n( x) = K exp(x / L)
• n(x) = K exp(−x / L^1/2 ) 
• n( x) = K^2 exp(−x / L)
• n( x) = K exp(−x / L)

Q.4.For the two-port network shown below, the short-circuit admittance parameter matrix is

 

 

Q.5.For a parallel RLC circuit, which one of the following statements is NOT correct ?

• The bandwidth of the circuit decreases if R is increased 
• The bandwidth of the circuit remains same if L is increased
• At resonance, input impedance is a real quantity
• At resonance, the magnitude of input impedance attains its minimum value

Q.6 At room temperature, a possible value for the mobility of electrons in the inversion layer of a silicon n-channel MOSFET is

• 450cm2/V-s
• 1350cm2/V-s
• 1800cm2/V-s 
•  3600cm2/V-s

Q.7 Thin gate oxide in CMOS process is preferably grown using

• Wet oxidation
• Dry oxidation
• Epitaxial deposition
• Ion implantation

Q.8 In the silicon BJT circuit shown below, assume that the emitter area of transistor Q1 is half that of transistor Q2. 

The value of current Io is approximately

• 0.5 mA
• 2 mA
• 9.3 mA
• 15 mA

Q.9 The amplifier circuit shown below uses a silicon transistor.The capacitors CC and CE can be assumed to be short at signal frequency and the effect of output resistance Ro can be ignored. If CE is disconnected from the circuit, which one of the following statements is TRUE?

• The input resistance Ri increases and the magnitude of voltage gain AV decreases 
• The input resistance Ri decreases and the magnitude of voltage gain AV increases
• Both input resistance Ri and the magnitude of voltage gain AV decrease
• Both input resistance Ri and the magnitude of voltage gain AV increase

Q.10 Assuming the OP-AMP to be ideal, the voltage gain of the amplifier shown below is

• -R2/R1
• -R3/R1
• -[R2||R3]/R1
• -[R2+R3]/R1

Q.11.For the output F to be 1 in the logic circuit shown, the input combination should be

 

• A = 1, B = 1, C = 0
• A = 1, B = 0, C = 0
• A = 0, B = 1, C = 0 
• A = 0, B = 0, C = 1

Q.12.Match the logic gates in Column A with their equivalents in Column B

• P - 2, Q - 4, R - 1, S - 3
• P - 4, Q - 2, R - 1, S - 3
• P - 2, Q - 4, R - 3, S - 1
• P - 4, Q - 2, R - 3, S - 1

Q.13.In the circuit shown, the device connected to Y 5 can have address in the range

 

• 2000 - 20FF
• 2D00 - 2DFF
• 2E00 - 2EFF
• FD00 - FDFF

Q.14.Consider the z-transform X ( z) = 5z^2 + 4z−1 + 3;0 <| z |∞ . The inverse z-transform x[n] is

• 5δ [n + 2] + 3 δ [n] + 4δ [n −1]
• 5δ [n − 2] + 3 δ [n] + 4δ [n +1]
• 5u[n + 2] + 3 u[n] + 4u[n +1]
• 5u[n − 2] + 3 u[n] + 4u[n +1]

Q.15 Two discrete time systems with impulse responses h1 [n] =δ [n −1] and h2 [n] =δ [n − 2] are connected in cascade. The overall impulse response of the cascaded system the cascaded system is

• δ [n −1] +δ [n − 2]
• δ [n − 4]
• δ [n − 3]
• δ [n −1]δ [n − 2]

Q.16 For an N-point FFT algorithm with N = 2m, which one of the following statements is TRUE?

• It is not possible to construct a signal flow graph with both input and output in normal order
• The number of butterflies in the mth stage is N/m
• In-place computation requires storage of only 2N node data
• Computation of a butterfly requires only one complex multiplication

Q.17 The transfer function Y(s)/R(s) of the system shown is

 

• 0
• 1/(s +1)
• 2/(s +1)
• 2/(s +3)

Q.18.A system with the transfer function Y(S)/X(S)= s/(s=p) has an output y(t) = cos [2t-π/3] for the input signal x(t)=pcos[2t-π/3] Then, the system parameter ‘p’ is

• (3)^1/2
• 2/(3)^1/2
• 1
• (3)^1/2/2

Q.19.