Home / GATE 2017-2018 / GATE Instrumentation :: Practice Test Paper 1

### GATE 2017-2018 :: GATE Instrumentation

1. If x = √-1, then the value of xx is
2.  A. e-Ï€/2 B. eÏ€/2 C. x D. 1

3. With initial condition x(1) ï€½ 0.5 , the solution of the differential equation, t dx/dt + x = t is
4.  A. x = t - 1/2 B. x = t2 - 1/2 C. x = t2/2 D. x = t/2

5. 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
6.  A. 3/4 B. 9/16 C. 1/4 D. 2/3

7. The unilateral Laplace transform of f (t) is 1/(s2 + s + 1). The unilateral Laplace transform of t f (t) is
8.  A. - s/(s2 + s + 1)2 B. - (2s + 1)/(s2 + s + 1)2 C. s/(s2 + s + 1)2 D. (2s + 1)/(s2 + s + 1)2

9. Given f(z) = 1(z + 1) - 2/(z + 3). If C is a counterclockwise path in the z-plane such that |z + 1|, the value of  is
10.  A. -2 B. -1 C. 1 D. 2

11. The average power delivered to an impedance (4 - j3)â„¦ by a current 5cos(100 Ï€t + 100) A is
12.  A. 44.2 W B. 50 W C. 62.5 W D. 125 W

13. In the circuit shown below, the current through the inductor is

14.  A. 2/(1 + j) A B. -1/(1 + j) A C. 1/(1 + j) A D. 0 A

15. In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is

16.  A. zero B. a step function C. an exponentially decaying function D. an impulse function

17. The impedance looking into nodes 1 and 2 in the given circuit is

18.  A. 50 â„¦ B. 100 â„¦ C. 5 kâ„¦ D. 10.1 kâ„¦

19. The i-v characteristics of the diode in the circuit given below are

The current in the circuit is
20.  A. 10 mA B. 9.3 mA C. 6.67 mA D. 6.2 mA