Previous GATE Instrumentation Engineering Paper with answer

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2. If the A- matrix of the state space model of a SISO linear time invariant system
is rank deficient, the transfer function of the system must have
(A) a pole with positive real part (B) a pole with negative real part
(C) a pole with positive imaginary part (D) a pole at the origin
Answer: (D)

3. Two systems with impulse responses ( ) 1 h t and ( ) 2 h t are connected in cascade.
Then the overall impulse response of the cascaded system is given by
(A) a product of ( ) 1 h t and ( ) 2 h t (B) sum of ( ) 1 h t and ( ) 2 h t
(C) convolution of ( ) 1 h t and ( ) 2 h t (D) subtraction of ( ) 2 h t from ( ) 1 h t
Answer: (C)

9. Which of the following statements is NOT TRUE for a continuous time causal and
stable LTI system?
(A) All the poles of the system must lie on the left side of the jw-axis
(B) Zeroes of the system can lie anywhere in the s-plane
(C) All the poles must lie within s 1 =
(D) All the roots of the characteristic equation must be located on the left side of
the jw-axis.
Answer: (C)

17. 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
(A) 5 (B) 12 (C) 15 (D) 20
Answer: (A)

19. 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) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
Answer: (C)

22. An accelerometer has input range of 0-10g, natural frequency 30Hz and mass
0.001kg. The range of the secondary displacement transducer in mm required to
cover the input range is
(A) 0 to 2.76 (B) 0 to 9.81 (C) 0 to 11.20 (D) 0 to 52.10
Answer: (A)

35. Signals from fifteen thermocouples are multiplexed and each one is sampled once
per second with a16–bit ADC. The digital samples are converted by a parallel to
serial converter to generate a serial PCM signal. This PCM signal is frequency
modulated with FSK modulator with 1200 Hz as 1 and 960 Hz as 0. The minimum
band allocation required for faithful reproduction of the signal by the FSK receiver
without considering noise is
(A) 840Hz to 1320Hz (B) 960Hz to 1200Hz
(C) 1080Hz to 1320Hz (D) 720Hz to 1440Hz
Answer: (A)