GATE ECE 2024 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2024

Numerical

-0.33

Suppose $X$ and $Y$ are independent and identically distributed random variables that are distributed uniformly in the interval $[0,1]$. The probability that $X \geq Y$ is _______ .

Your input ____

GATE ECE 2024

MCQ (Single Correct Answer)

-1.33

Consider the Earth to be a perfect sphere of radius $R$. Then the surface area of the region, enclosed by the 60°N latitude circle, that contains the north pole in its interior is _______.

$\left( 2 - \sqrt{3} \right) \pi R^2$

$\frac{\left( \sqrt{2} - 1 \right) \pi R^2}{2}$

$\frac{2 \pi R^2}{3}$

$\frac{\left( 2 + \sqrt{3} \right) \pi R^2}{8 \sqrt{2}}$

GATE ECE 2024

MCQ (Single Correct Answer)

-1.33

Let $z$ be a complex variable. If $f(z)=\frac{\sin(\pi z)}{z^{7}(z-2)}$ and $C$ is the circle in the complex plane with $|z|=3$ then $\oint\limits_{C} f(z)dz$ is _______.

$ \pi^2 j $

$ j\pi\left(\frac{1}{2}-\pi\right) $

$ j\pi\left(\frac{1}{2}+\pi\right) $

$-\pi^2 j$

GATE ECE 2024

MCQ (More than One Correct Answer)

-1.33

Let $F_1$, $F_2$, and $F_3$ be functions of $(x, y, z)$. Suppose that for every given pair of points A and B in space, the line integral $\int\limits_C (F_1 dx + F_2 dy + F_3 dz)$ evaluates to the same value along any path C that starts at A and ends at B. Then which of the following is/are true?

For every closed path Γ, we have $\oint\limits_Γ (F_1 dx + F_2 dy + F_3 dz) = 0$.

There exists a differentiable scalar function $f(x, y, z)$ such that $F_1 = \frac{\partial f}{\partial x}$, $F_2 = \frac{\partial f}{\partial y}$, $F_3 = \frac{\partial f}{\partial z}$.

$\frac{\partial F_1}{\partial x} + \frac{\partial F_2}{\partial y} + \frac{\partial F_3}{\partial z} = 0$.

$\frac{\partial F_3}{\partial y} = \frac{\partial F_2}{\partial z}$, $\frac{\partial F_1}{\partial z} = \frac{\partial F_3}{\partial x}$, $\frac{\partial F_2}{\partial x} = \frac{\partial F_1}{\partial y}$.

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