In this post we are providing multiple choice questions on topic linear time invariant, that asked in previous year GATE paper(2002-2007). if you want video solution for this questions then comment below if we get more comments then we will provide video solutions for all this questions on our you tube channel ENGINEER TREE. if you have any GATE related queries then ask on our Facebook group, all links of our other social platforms are given below, you can follow us by them.

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**Signal and System (Linear Time Invariant System MCQ’s ) GATE (2002-2007)**

**GATE 2002**

(1) Convolution of x(t+5) with impulse function δ(t-7) is equal to\

- x(t-12)
- x(t+12)
- x(t-2)
- x(t+2)

**GATE 2003**

(2) Let x(t) be the input to a linear time invariant system. the required output is 4x(t-2). the transfer function of the system should be

- \({ 4e }^{ j4\pi f }\)
- \({ 2e }^{ -j8\pi f }\)
- \({ 4e }^{ -j4\pi f }\)
- \({ 2e }^{ j8\pi f }\)

**GATE 2004**

(3) The impulse response h[n] of a linear time invariant system is given by h[n] = u[n+3] + u[n-2] – 2u[n-7] where u[n] is the unit step sequence. the above system is

- stable nut not causal
- stable and causal
- causal but unstable
- unstable and not causal

**GATE 2004**

(4) A causal LTI system is described by the difference equation

2y(n) = αy(n-2) – 2x(n) + βx(n-1) The system is stable only if

- lαl = 2, lβl < 2
- lαl > 2, lβl > 2
- lαl < 2, any value of β
- lβl < 2, any value of α

**GATE 2005**

(5) Which of the following can be impulse response of a causal system?

**GATE 2005**

(6) The sequence

**GATE 2006**

(7) In the system shown below x(t) = (sint)u(t) In steady state, the response y(t) will be

- \(\frac { 1 }{ \sqrt { 2 } } sin(t-\frac { \pi }{ 4 } )\)
- \(\frac { 1 }{ \sqrt { 2 } } sin(t+\frac { \pi }{ 4 } )\)
- \(\frac { 1 }{ \sqrt { 2 } } { e }^{ -t }sin(t)\)
- \(sin(t)-cos(t)\)

**GATE 2006**

(8) The unit step response of a system starting from rest is given by \(c(t)=1-{ e }^{ -2t }\) for t ≥ 0. The transfer function of the system is

- \(\frac { 1 }{ 1+2s } \)
- \(\frac { 2 }{ 2+s } \)
- \(\frac { 1 }{ 2+s } \)
- \(\frac { 2s }{ 1+2s } \)

**GATE 2007**

(9) A Hilbert transform is a

- non-linear system
- non-causal system
- time-varying system
- low-pass system

**GATE 2007**

(10) The frequency response of a linear, time-invariant system is given by

\(\frac { 5 }{ 1+j10\pi f } \)

The step response of the system is

- \(5(1-{ e }^{ -5t })u(t)\)
- \(5(1-{ e }^{ -\frac { t }{ 5 } })u(t)\)
- \(\frac { 1 }{ 2 } (1-{ e }^{ -5t })u(t)\)
- \(\frac { 1 }{ 5 } (1-{ e }^{ -\frac { t }{ 5 } })u(t)\)

#### Answer key will be provided within 48 hours of this post

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