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

Consider the system of linear equations: $A\mathbf{x}=\mathbf{b}$, where $A$ is an $n\times n$ matrix, and $\mathbf{x}$ and $\mathbf{b}$ are $n$ -dimensional column vectors.

Suppose this system of equations has a unique solution. Which of the following statements is/are correct?

The resistance values of the Wheatstone bridge shown are: $P=2000\Omega$, $Q=500\Omega$, $R=3000\Omega$. The battery voltage $E=50\text{ V}$. The battery has an internal resistance of $1\Omega$ and the Galvanometer (G) has a resistance of $50\Omega$.



The value of the resistance $S$ for balanced condition is _____________

$\Omega$ (Answer in integer)

A system with two generators G1 and G2 (without generator limits) is shown.



The total load on the system is 1184 MW. The expressions for the cost of generation ($C_1$ and $C_2$) and real power loss ($P_{\text{Loss}}$) are as follows:

$C_1(P_{G1})=1000+50P_{G1}+0.01(P_{G1}{)}^2\text{ Rs/MWh}$

$C_2(P_{G2})=2000+50P_{G2}+0.001(P_{G2}{)}^2\text{ Rs/MWh}$

$P_{\text{Loss}}=0.001(P_{G2}-50{)}^2\text{ MW}$

When the generators are operating at their optimal generation, meeting the total load requirement, the real power loss in the system is ________ MW (Round off to one decimal place)

Consider the Lagrange multiplier $\lambda =70.25$ for optimal generation.

A balanced three-phase supply is given to a 30 kW, 4-pole, 400 V, 50 Hz, wound rotor induction motor with Y-connected stator and rotor windings. The motor is driving a constant torque load. With shorted sliprings, the machine runs at 1476 rpm.

When an external non-inductive resistance of 0.27 $\Omega$ per phase is connected in series in the rotor circuit, the steady-state speed drops to 1404 rpm.

Neglecting rotational losses, the actual per phase rotor winding resistance is ____ $\Omega$

(Round off to two decimal places)

Consider the two-port network shown. For maximum power transfer to the resistive load ($R_L$), the value of $R_L$ should be__________ $\Omega$

(Round off to two decimal places)