GATE ECE 2020 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2020

Numerical

-0

The two sides of a fair coin are labelled as 0 and 1 . The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses. For a random variable $X$, defined as $X=\min (M, N)$, the expected value $E[X]$ (rounded off to two decimal places) is $\_\_\_\_$ .

Your input ____

GATE ECE 2020

MCQ (Single Correct Answer)

-0.33

The general solution of $\frac{d^2 y}{d x^2}-6 \frac{d y}{d x}+9 y=0$ is

$y=C_1 e^{3 x}+C_2 e^{-3 x}$

$y=C_1 e^{3 x}$

$y=\left(C_1+C_2 x\right) e^{3 x}$

$y=\left(C_1+C_2 x\right) e^{-3 x}$

GATE ECE 2020

MCQ (Single Correct Answer)

-0.33

The partial derivative of the function

$$ f(x, y, z)=e^{1-x \cos y}+x z e^{\frac{-1}{\left(1+y^2\right)}} $$

with respect to $x$ at the point $(1,0, e)$ is

$\frac{1}{e}$

-1

GATE ECE 2020

MCQ (Single Correct Answer)

-0.33

For a vector field $\vec{A}$, which one of the following is FALSE?

$\vec{A}$ is solenoid if $\nabla \cdot \vec{A}=0$.

$\nabla \times(\nabla \times \vec{A})=\nabla(\nabla \cdot \vec{A})-\nabla^2 \vec{A}$

$\nabla \times \vec{A}$ is another vector field.

$\vec{A}$ is irrotational if $\nabla^2 \vec{A}=0$.

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