GATE Instrumentation engineering test paper 1
by Esha Upadhyay · Published · Updated
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Question 1 of 15
1. Question
With initial condition x(1) = 0.5 , the solution of the differential equation,
t (dx/dt) + x = t is
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Question 2 of 15
2. Question
Two independent random variables X and Y are uniformly distributed in the interval [–1, 1]. The probability that max[X, Y] is less than 1 2 is
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Question 3 of 15
3. Question
The unilateral Laplace transform of f(t) is 1/(s*s+s+1) The unilateral transform of t f(t) is
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Question 4 of 15
4. Question
The average power delivered to an impedance (4 – j3) ohm by a current 5cos(100 pi t +100) A is
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Question 5 of 15
5. Question
A system with transfer function
G(s) = [(s*s +9)(s+2)] / [(s+1)(s+3)(s+4)]
is excited by sin(wt).The steady state output of the system is zero at
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Question 6 of 15
6. Question
The output Y of a 2bit comparator is logic 1 whenever the 2bit input A is greater than the 2bit input B. The number of combinations for which the output is logic 1, is
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Question 7 of 15
7. Question
A psychrometric chart is used to determine
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Question 8 of 15
8. Question
An LED emitting at 1 um with a spectral width of 50 nm is used in a Michelson interferometer. To obtain a sustained interference, the maximum optical path difference between the two arms of the interferometer is
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Question 9 of 15
9. Question
Light of wavelength 630 nm in vacuum, falling normally on a biological specimen of thickness 10 um, splits into two beams that are polarized at right angles. The refractive index of the tissue for the two polarizations are 1.32 and 1.333. When the two beams emerge, they are out of phase by
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Question 10 of 15
10. Question
The bridge method commonly used for finding mutual inductance is
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Question 11 of 15
11. Question
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is
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Question 12 of 15
12. Question
The maximum value of f(x) = x39×2+24x+5 in the interval [1, 6] is (where number after x denote power like x3 is x cube)
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Question 13 of 15
13. Question
The Fourier transform of a signal h(t) is H( jw) = (2cosw)(sin2w) /w . The value of h(0) is
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Question 14 of 15
14. Question
Let y[n] denote the convolution of h[n] and g[n], where h[n] (1/2) (to the power n) u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals
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Question 15 of 15
15. Question
A double convex lens is used to couple a laser beam of diameter 5 mm into an optical fiber with a numerical aperture of 0.5. The minimum focal length of the lens that should be used in order to focus the entire beam into the fiber is
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