GATE EC 2024 Question Paper (11-Feb-2024) (Shift 1)

The free electron concentration profile $n(x)$ in a doped semiconductor at equilibrium is shown in the figure, where the points A, B, and C mark three different positions. Which of the following statements is/are true?

A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set of size 40. Each instruction has five distinct fields, namely opcode, two source register identifiers, one destination register identifier, and an immediate value. Assuming that the immediate operand is an unsigned integer, its maximum value is ____________

An amplitude modulator has output (in Volts)
$s(t)=A\cos (400\pi t)+B\cos (360\pi t)+B\cos (440\pi t)$ .
The carrier power normalized to $1\Omega$ resistance is 50 Watts. The ratio of the total sideband power to the total power is 1/9. The value of $B$ (in Volts, rounded off to two decimal places) is _________.

In a number system of base $r$, the equation $x^2\text{–}12x+37=0$ has $x=8$ as one of its solutions. The value of $r$ is _________

Let $\mathbb{R}$ and ${\mathbb{R}}^3$ denote the set of real numbers and the three dimensional vector space over it, respectively. The value of $\alpha$ for which the set of vectors
$\{[2-3\alpha ],[3-13],[1-57]\}$
does not form a basis of ${\mathbb{R}}^3$ is ____________