1
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Match the following.

List-$${\rm I}$$
$$P.$$ Stoke's Theorem
$$Q.$$ Gauss's Theorem
$$R.$$ Divergence Theorem
$$S.$$ Cauchy's Integral Theorem

List-$${\rm I}{\rm I}$$
$$1.$$ GATE EE 2015 Set 2 Engineering Mathematics - Vector Calculus Question 6 English 1
$$2.$$ GATE EE 2015 Set 2 Engineering Mathematics - Vector Calculus Question 6 English 2
$$3.$$ GATE EE 2015 Set 2 Engineering Mathematics - Vector Calculus Question 6 English 3
$$4.$$ GATE EE 2015 Set 2 Engineering Mathematics - Vector Calculus Question 6 English 4

A
$$P = 2,Q = 1,R = 4,S = 3$$
B
$$P = 4,Q = 1,R = 3,S = 2$$
C
$$P = 4,Q = 3,R = 1,S = 2$$
D
$$P = 3,Q = 4,R = 2,S = 1$$
2
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Two coins $$R$$ and $$S$$ are tossed. The $$4$$ joint events $$\,\,\,\,\,\,{H_R}{H_S},\,\,\,\,{T_R}{T_S},\,\,\,\,{H_R}{T_S},\,\,\,\,{T_R}{H_S}\,\,\,\,\,\,\,$$ have probabilities $$0.28,$$ $$0.18,$$ $$0.30,$$ $$0.24$$ respectively, where $$H$$ represents head and $$T$$ represents tail. Which one of the following is TRUE?
A
The coin tosses are independent
B
$$R$$ is fair, $$S$$ is not
C
$$S$$ is fair, $$R$$ is not
D
The coin tosses are dependent
3
GATE EE 2015 Set 2
Numerical
+2
-0
A differential equation $$\,\,{{di} \over {dt}} - 0.21 = 0\,\,$$ is applicable over $$\,\, - 10 < t < 10.\,\,$$ If $$i(4)=10,$$ then $$i(-5)$$ is
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4
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Given $$f\left( z \right) = g\left( z \right) + h\left( z \right),$$ where $$f,g,h$$ are complex valued functions of a complex variable $$z.$$ Which ONE of the following statements is TRUE?
A
If $$f(z)$$ is differentiable at $${z_0},$$ then $$g(z)$$ & $$h(z)$$ are also differentiable at $${z_0}.$$
B
If $$g(z)$$ & $$h(z)$$ are differentiable at $${z_0},$$ then $$f(z)$$ is also differentiable at $${z_0}.$$
C
If $$f(z)$$ is continuous at $${z_0},$$ then it is differentiable at $${z_0}.$$
D
If $$f(z)$$ is differentiable at $${z_0},$$ then so are its real and imaginary parts.
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