GATE IN 2026 Question Paper (07-Feb-2026) (Shift-1)

A 16-bit processor has 16-bit wide instructions and a few internal registers. Every 16-bit instruction is encoded in a fixed format with one operation code of 7 bits and up to three operands. The operand can be an internal register and each operand is encoded by 3 bits. All the internal registers can be specified in an instruction using three bits.

The correct statement(s) for this processor is/are _____.

Let
$$f(t)=\{\begin{array}{ll}1,& t\in [0,2]\\ -t+3,& t\in [2,3]\\ 0,& \text{otherwise}\end{array}$$
Then
$${\int }_{-\infty }^{\infty }f(\tau )d\tau =\_\_\_\_\_.$$
(rounded off to one decimal place)

A single phase transformer has a rating of $10\text{ kVA}$, $50\text{ Hz}$, $1100\text{ V}/220\text{ V}$. In an open circuit test with the high voltage side open, the following are obtained:

$\bullet$ Voltage applied to the low voltage winding = $220\text{ V}$

$\bullet$ Measured power = $363\text{ W}$

$\bullet$ Measured current = $2.75\text{ A}$

Magnetizing reactance $X_m$ referred to the high voltage winding is __________$\Omega$. (rounded off to the nearest integer)

A linear time invariant (LTI) system has a transfer function
$$G(s)=\frac{10(s+1)}{s(s^2+2s+5)}$$
The system is placed in unity negative feedback configuration.

For a unit ramp reference, the steady state error is _______.

(rounded off to two decimal places)

The system $G(s)=\frac{K}{(s+1{)}^4}$ has a gain margin of $20\text{ dB}$. The value of $K$ is ______. (rounded off to two decimal places)