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

A 220V/12V single-phase transformer is designed for use in India and rated 100 VA at 50 Hz. Later, this unit is shipped to the USA where it is used as a 110V/6V transformer at 60 Hz.

Which of the following statements is/are correct?

Given that $\vec{F}(x,y,z)=\sin (y)\hat{x}+\cos (x)\hat{y}+5\hat{z}$, the integral ${\iint }_S\vec{F}(x,y,z)\cdot \overrightarrow{ds}$ over the unit sphere $S$ centered at the origin evaluates to ________

(Round off to one decimal place)

In the linear regulator circuit shown, the base to emitter voltage $V_{BE}$ of the BJT is 0.6 V. The Zener diode clamps the base voltage to 5.4 V. Ignore the biasing current of the Zener diode and BJT.

The maximum possible efficiency of the regulator circuit is ___________ %

(Round off to one decimal place)

Consider the circuit shown. Assume that the diode $D$ is ideal. The supply voltage $v_s=325\sin (2\pi 50t)\text{ V}$, $L=500\mu H$, and $R=10\Omega$. The peak diode current (in amperes) is ______________

(Round off to one decimal place)

A $m\times m$ skew-symmetric matrix with real-valued entries, and $x$ is an $m$ -dimensional column vector with real-valued entries such that $x^{T}x=1$. The quantity $x^{T}Ax$ evaluates to _________

(Answer in integer)