1
GATE ECE 2025
Numerical
+2
-0
An ideal p-n junction germanium diode has a reverse saturation current of $10 \mu \mathrm{~A}$ at 300 K . The voltage (in Volts, rounded off to two decimal places) to be applied across the junction to get a forward bias current of 100 mA at 300 K is __________. (Consider the Boltzmann constant $k_B=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$ and the charge of an electron $e=1.6 \times 10^{-19} \mathrm{C}$.)
Your input ____
2
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

Consider the matrix $A$ below:

$$ A=\left[\begin{array}{llll} 2 & 3 & 4 & 5 \\ 0 & 6 & 7 & 8 \\ 0 & 0 & \alpha & \beta \\ 0 & 0 & 0 & \gamma \end{array}\right] $$

For which of the following combinations of $\alpha, \beta$ and $\gamma$, is the rank of $A$ at least three?

(i) $\alpha=0$ and $\beta=\gamma \neq 0$

(ii) $\alpha=\beta=\gamma=0$

(iii) $\beta=\gamma=0$ and $\alpha \neq 0$

(iv) $\alpha=\beta=\gamma \neq 0$

A
Only (i), (iii), and (iv)
B
Only (iv)
C
Only (ii)
D
Only (i) and (iii)
3
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

Consider the following series:

(i) $\sum\limits_{n=1}^{\infty} \frac{1}{\sqrt{n}}$

(ii) $ \sum\limits_{n=1}^{\infty} \frac{1}{n(n+1)}$

(iii) $\sum\limits_{n=1}^{\infty} \frac{1}{n!}$

A
Only (ii) converges
B
Only (ii) and (iii) converge
C
Only (iii) converges
D
All three converge
4
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement.

What is the probability that the two balls drawn have different colours?

A
$\frac{2}{3}$
B
$\frac{1}{3}$
C
$\frac{1}{2}$
D
1
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