GATE EE 2026 Question Paper (14-Feb-2026) (Shift 1)

The figure shows an arbitrarily shaped planar conducting loop A in the XY plane. Two nonintersecting regions with areas $a_1$ and $a_2$ within the loop are subjected to magnetic fields ${\vec{B}}_1=\frac{m}{\sqrt{2}}\sin (\omega t)(1\hat{x}+0\hat{y}+1\hat{z})$, and

${\vec{B}}_2=-\frac{n}{\sqrt{2}}\cos (2\omega t+\pi /4)(0\hat{x}+1\hat{y}+1\hat{z})$, respectively.



What is the expression for the induced rms voltage in loop A?

A system is characterized by the following state equation and output equation ($u$: input, $\mathbf{x}$: state vector, $y$: output)
$$\dot{\mathbf{x}}=\left[\begin{array}{cc}a& b\\ -a& 0\end{array}\right]\mathbf{x}+\left[\begin{array}{c}1\\ 0\end{array}\right]u$$

$$y=\left[\begin{array}{cc}1& 2\end{array}\right]\mathbf{x}$$
What are the values of $a$ and $b$ for which the poles of the transfer function are at $-2+j3$ and $-2-j3$?

A system is represented in state-space form as follows:

($u$: input, $\mathbf{x}$: state vector, $y$: output)
$$\dot{\mathbf{x}}=\left[\begin{array}{cc}1& 2\\ -3& 0\end{array}\right]\mathbf{x}+\left[\begin{array}{c}1\\ 2\end{array}\right]u$$

$$y=\left[\begin{array}{cc}1& 2\end{array}\right]\mathbf{x}$$
Consider the new state vector $\mathbf{z}=\left[\begin{array}{cc}2& 1\\ -1& 0\end{array}\right]\mathbf{x}$

What is the state-space representation of the system in terms of the new state vector $\mathbf{z}$?

For the balanced 3-phase transmission line shown, consider the following cases:

Case-1: $|V_1|=1.1\text{ p.u.}$, $|V_2|=0.9\text{ p.u.}$, $Z=0.75\angle 0^{\circ }\text{ p.u.}$ and ${\theta }_{12}={\theta }_1-{\theta }_2=0^{\circ }$

Case-2: $|V_1|=1.1\text{ p.u.}$, $|V_2|=0.9\text{ p.u.}$, $Z=0.75\angle 90^{\circ }\text{ p.u.}$ and ${\theta }_{12}={\theta }_1-{\theta }_2=90^{\circ }$



Which of the following statements is/are correct about real power loss and reactive power loss in the line?

Consider an $n\times n$ orthogonal matrix $A$ with real entries and each column having unit Euclidean norm.

Which of the following statements is/are correct?