GATE EE 2026 | GATE EE Year Wise Previous Years Questions

GATE EE 2026

MCQ (Single Correct Answer)

-0

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

(u: input, $x$ : state vector, $y$ : output)

$$ \begin{aligned} & \dot{x}=\left[\begin{array}{cc} 1 & 2 \\ -3 & 0 \end{array}\right] x+\left[\begin{array}{l} 1 \\ 2 \end{array}\right] u \\ & y=\left[\begin{array}{ll} 1 & 2 \end{array}\right] x \end{aligned} $$

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

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

$$ \begin{aligned} & \dot{z}=\left[\begin{array}{cc} -1 & 4 \\ -1 & -2 \end{array}\right] z+\left[\frac{4}{-1}\right] u \\ & y=\left[\begin{array}{ll} 2 & 3 \end{array}\right] z \end{aligned} $$

$$ \begin{aligned} & \dot{z}=\left[\begin{array}{ll} 2 & 3 \\ 0 & 3 \end{array}\right] z+\left[\frac{3}{5}\right] u \\ & y=\left[\begin{array}{ll} 2 & 3 \end{array}\right] z \end{aligned} $$

$$ \begin{aligned} & \dot{z}=\left[\begin{array}{cc} 4 & 9 \\ -2 & -3 \end{array}\right] z+\left[\frac{4}{-1}\right] u \\ & y=\left[\begin{array}{ll} 2 & 3 \end{array}\right] z \end{aligned} $$

$$ \begin{aligned} & \dot{z}=\left[\begin{array}{cc} 2 & 1 \\ -4 & 1 \end{array}\right] z+\left[\frac{4}{-1}\right] u \\ & y=\left[\begin{array}{cc} 4 & -1 \end{array}\right] z \end{aligned} $$

GATE EE 2026

MCQ (Single Correct Answer)

-0

The digital circuit shown has 3 inputs $(x, y$ and $z)$.

GATE EE 2026 Digital Electronics - Boolean Algebra Question 1 English

The simplified logical expression for the output (OUT) is:

$\bar{x} \bar{y} \bar{z}$

$\bar{x}(y+z)$

GATE EE 2026

MCQ (Single Correct Answer)

-0

The MOSFET switches shown in the circuit are ideal.

Which of the following is the correct option for Boolean logical expression of the output (OUT), and the maximum possible power (P) consumed by the circuit?

$\mathrm{OUT}=\overline{A B+\bar{C}}, P=5 \mathrm{~mW}$

$\mathrm{OUT}=\overline{(A+B) \bar{C}}, P=5 \mathrm{~mW}$

$\mathrm{OUT}=\overline{A B \bar{C}}, P=7.5 \mathrm{~mW}$

$\mathrm{OUT}=\overline{A B} C, P=7.5 \mathrm{~mW}$

GATE EE 2026

MCQ (Single Correct Answer)

-0

A circuit with ideal elements is shown.

GATE EE 2026 Electric Circuits - Network Elements Question 2 English

Which one of the following options correctly identifies all the linear elements in the circuit?

R only

R, L, and C only

D only

L, C and D only

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