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# GATE EC 2021: Engineering Mathematics Quiz 13 (App update required to attempt this test)

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Question 1

A bolt is manufactured by 3 machines A, B and C. Machine A turn out twice as many items as B, and machines B and C produce equal number of items. 2% of bolts produced by A and B are defective and 4% of bolts produced by C are defective. All bolts put into 1 stock pile and 1 is chosen from this pile. The probability that it is defective is __________ x 10-1.

Question 2

Let f(z) = . If f(z ­1) = f(z2) for all z1 z2, a = 2, b = 4 and c = 5, then d should be equal to _______

Question 3

Evaluate

Question 4

Consider the state space realization
=+ u(t), with the initial condition where u(t) denotes the unit step function. The value of is _____.

Question 5

The solution of is

Question 6

A vector field D = exists inside a cylindrical region enclosed by the surfaces r = 1, z = 0 and z = 5. Let S be the surface bounding this cylindrical region. The surface integral of this field on S is _____.
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