1
GATE ECE 2023
MCQ (Single Correct Answer)
+2
-0.67

The state equation of a second order system is

$$x(t) = Ax(t),\,\,\,\,x(0)$$ is the initial condition.

Suppose $$\lambda_1$$ and $$\lambda_2$$ are two distinct eigenvalues of A and $$v_1$$ and $$v_2$$ are the corresponding eigenvectors. For constants $$\alpha_1$$ and $$\alpha_2$$, the solution, $$x(t)$$, of the state equation is

A
$$\sum\limits_{i = 1}^2 {{\alpha _i}{e^{{\lambda _i}t}}{v_i}} $$
B
$$\sum\limits_{i = 1}^2 {{\alpha _i}{e^{2{\lambda _i}t}}{v_i}} $$
C
$$\sum\limits_{i = 1}^2 {{\alpha _i}{e^{3{\lambda _i}t}}{v_i}} $$
D
$$\sum\limits_{i = 1}^2 {{\alpha _i}{e^{4{\lambda _i}t}}{v_i}} $$
2
GATE ECE 2023
Numerical
+2
-0

The value of the integral $$\int\limits\!\!\!\int_R {xy\,dx\,dy} $$ over the regioin R, given in the figure, is _________ (rounded off to the nearest integer).

GATE ECE 2023 Engineering Mathematics - Calculus Question 6 English

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3
GATE ECE 2023
MCQ (Single Correct Answer)
+1
-0.33

A series $$RLC$$ circuit has a quality factor Q of 1000 at a center frequency of $$10^6$$ rad/s. The possible values of R, L and C are

A
$$R=1~\Omega,L=1~\mu H$$ and $$C=1~\mu F$$
B
$$R=0.1~\Omega,L=1~\mu H$$ and $$C=1~\mu F$$
C
$$R=0.01~\Omega,L=1~\mu H$$ and $$C=1~\mu F$$
D
$$R=0.001~\Omega,L=1~\mu H$$ and $$C=1~\mu F$$
4
GATE ECE 2023
Numerical
+1
-0

In the circuit shown below, the current i flowing through 200 $$\Omega$$ resistor is __________ mA (rounded off to two decimal places).

GATE ECE 2023 Network Theory - Network Theorems Question 4 English

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