GATE EE 2016 Set 1 | GATE EE Year Wise Previous Years Questions

GATE EE 2016 Set 1

MCQ (Single Correct Answer)

-0.6

The output of a continuous-time, linear time-invariant system is denoted by T{x(t)} where x(t) is the input signal. A signal z(t) is called eigen-signal of the system T, when T{z(t)}= yz(t), where $$\gamma$$ is a complex number, in general, and is called an eigen value of T. suppose the impulse response of the system T is real and even. Which of the following statements is TRUE?

cos(t) is and eigen-signal but sin(t) is not

cos(t) is and sin(t) are both eigen-signal but with different eigen values

sin(t) is an eigen-signal but cos(t) is not

cos(t) and sin(t) are both eigen-signal with identical eigen values

GATE EE 2016 Set 1

MCQ (Single Correct Answer)

-0.3

The value of $$\int_{-\infty}^{+\infty}e^{-t}\partial\left(2t-2\right)dt$$. where $$\partial\left(t\right)$$ is the Dirac delta function, is

$$\frac1{2e}$$

$$\frac2e$$

$$\frac1{e^2}$$

$$\frac1{2e^2}$$

GATE EE 2016 Set 1

MCQ (Single Correct Answer)

-0.3

Consider a continuous-time system with input x(t) and output y(t) given by $$y\left(t\right)=x\left(t\right)\cos\left(t\right)$$. This system is

linear and time-invariant

Non-linear and time-invariant

linear and time-varying

Non-linear and time-varying

GATE EE 2016 Set 1

MCQ (Single Correct Answer)

-0.6

Suppose x₁(t) and x₂(t) have the Fourier transforms as shown below. GATE EE 2016 Set 1 Signals and Systems - Continuous Time Signal Fourier Transform Question 9 English

GATE EE 2016 Set 1 Signals and Systems - Continuous Time Signal Fourier Transform Question 9 English

Which one of the following statements is TRUE?

x₁(t) and x₂(t) are complex and x₁(t)x₂(t) is also complex with nonzero imaginary part

x₁(t) and x₂(t) are real and x₁(t)x₂(t) is also real

x₁(t) and x₂(t) are complex but x₁(t)x₂(t) is real

x₁(t) and x₂(t) are imaginary but x₁(t)x₂(t) is real

GATE EE Papers

2024