GATE ECE 2015 Set 1 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

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Suppose $$A$$ & $$B$$ are two independent events with probabilities $$P\left( A \right) \ne 0$$ and $$P\left( B \right) \ne 0.$$ Let $$\overrightarrow A $$ & $$\overrightarrow B $$ be their complements. Which of the following statements is FALSE?

$$P\left( {A \cap B} \right) = P\left( A \right)P\left( B \right)$$

$$P\left( {A/B} \right) = P\left( A \right)$$

$$P\left( {A \cup B} \right) = P\left( A \right) + P\left( B \right)$$

$$P\left( {\overrightarrow A \cap \overrightarrow B } \right) = P\left( {\overrightarrow A } \right).P\left( {\overrightarrow B } \right)$$

GATE ECE 2015 Set 1

Numerical

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The input $$X$$ to the Binary Symmetric Channel (BSC) shown in the figure is $$'1'$$ with probability $$0.8.$$ The cross-over probability is $$1/7$$. If the received bit $$Y=0,$$ the conditional probability that $$'1'$$ was transmitted is _______. GATE ECE 2015 Set 1 Engineering Mathematics - Probability and Statistics Question 15 English

Your input ____

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

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The Solution of the differential equation $$\,{{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0\,\,$$ with $$\,y\left( 0 \right) = {y^1}\left( 0 \right) = 1\,\,$$ is

$$\left( {2 - t} \right){e^t}$$

$$\left( {1 + 2t} \right){e^{ - t}}$$

$$\left( {2 + t} \right){e^{ - t}}$$

$$\left( {1 - 2t} \right){e^t}$$

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

-0.6

Let $$z=x+iy$$ be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction . Which one of the following statement is NOT TRUE?

The residue of $${z \over {{z^2} - 1}}$$ at $$z=1$$ is $${1 \over 2}$$

$$\oint\limits_C {{z^2}\,\,dz = 0} $$

$${1 \over {2\pi i}}\oint\limits_c {{1 \over z}} dz = 1$$

$$\overline z $$ (complex conjugate of $$z$$ ) is an analytical function.

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