1
GATE ECE 2024
Numerical
+2
-1.33

A non-degenerate n-type semiconductor has 5 % neutral dopant atoms. Its Fermi level is located at 0.25 eV below the conduction band ($E_C$) and the donor energy level ($E_D$) has a degeneracy of 2. Assuming the thermal voltage to be 20 mV, the difference between $E_C$ and $E_D$ (in eV, rounded off to two decimal places) is _______.

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2
GATE ECE 2024
Numerical
+2
-1.33

The photocurrent of a PN junction diode solar cell is 1 mA. The voltage corresponding to its maximum power point is 0.3 V. If the thermal voltage is 30 mV, the reverse saturation current of the diode (in nA, rounded off to two decimal places) is _____.

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3
GATE ECE 2024
MCQ (Single Correct Answer)
+1
-0.33

The general form of the complementary function of a differential equation is given by $y(t) = (At + B)e^{-2t}$, where $A$ and $B$ are real constants determined by the initial condition. The corresponding differential equation is ____.

A

$\dfrac{d^2 y}{d t^2} + 4 \dfrac{d y}{d t} + 4 y = f(t)$

B

$\dfrac{d^2 y}{d t^2} + 4 y = f(t)$

C

$\dfrac{d^2 y}{d t^2} + 3 \dfrac{d y}{d t} + 2 y = f(t)$

D

$\dfrac{d^2 y}{d t^2} + 5 \dfrac{d y}{d t} + 6 y = f(t)$

4
GATE ECE 2024
MCQ (More than One Correct Answer)
+1
-0.33

Let $\rho(x, y, z, t)$ and $u(x, y, z, t)$ represent density and velocity, respectively, at a point $(x, y, z)$ and time $t$. Assume $\frac{\partial \rho }{\partial t}$ is continuous. Let $V$ be an arbitrary volume in space enclosed by the closed surface $S$ and $\hat{n}$ be the outward unit normal of $S$. Which of the following equations is/are equivalent to $\frac{\partial \rho }{\partial t} + \nabla \cdot(\rho u) = 0$?

A
GATE ECE 2024 Engineering Mathematics - Vector Calculus Question 2 English Option 1
B
GATE ECE 2024 Engineering Mathematics - Vector Calculus Question 2 English Option 2
C

$\int\limits_{V} \frac{\partial \rho}{\partial t} \, dv = - \int\limits_{V} \nabla \cdot(\rho u) \, dv$

D

$\int\limits_{V} \frac{\partial \rho}{\partial t} \, dv = \int\limits_{V} \nabla \cdot(\rho u) \, dv$

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