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

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

-0.3

A vector $$\overrightarrow P $$ is given by $$\,\,\overrightarrow P = {x^3}y\overrightarrow a {}_x - {x^2}{y^2}\overrightarrow a {}_y - {x^2}yz\overrightarrow a {}_z.\,\,\,$$ Which one of the following statements is TRUE?

$$\overrightarrow P $$ is solenoidal, but not irrotational

$$\overrightarrow P $$ is irrotational, but not solenoidal

$$\overrightarrow P $$ is neither solenoidal nor irrotational

$$\overrightarrow P $$ is both solenoidal and irrotational

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

-0.3

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

-0

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 14 English

Your input ____

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

-0.6

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

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

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

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

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

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