# GATE previous question on LTI System and its properties for GATE/IES/PSU

In this post we are providing multiple choice questions on topic linear time invariant, that asked in previous year GATE paper. 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 1990

(1) The impulse response and the excitation of a linear time invariant causal system are shown in figure (A) and (B) respectively. The output of the system at t=2 sec is equal to

1.  0
2.  1/2
3.  3/2
4.  2

GATE 1995

(2) Let h(t) be the impulse response of a linear time invariant system, then the response of the system for any input u(t) is

1.  $$\int _{ 0 }^{ t }{ h(\tau )u(t-\tau )d(\tau )}$$
2.  $$\frac { d }{ dt } \int _{ 0 }^{ t }{ h(\tau )u(t-\tau )d(\tau )}$$
3.  $$\int _{ 0 }^{ \tau }{ h(\tau )u(t-\tau )d(\tau )}$$
4.  $$\int _{ 0 }^{ t }{ { h }^{ 2 }(\tau )u(t-\tau )d(\tau )}$$

GATE 1996

(3) The auto correlation function of an energy signal has

1.  no symmetry
2.  conjugate symmetry
3.  odd symmetry
4.  even symmetry

GATE 1998

(4) The unit impulse response of a linear time invariant system is the unit step function u(t), For t > 0, the response of the system to an excitation $${ e }^{ -at }u(t)$$, a>0 will be

1.  $${ a.e }^{ -at }$$
2.  $${ \frac { 1 }{ a } .(1-e }^{ -at })$$
3.  $${ a.(1-e }^{ -at })$$
4.  $${ (1-e }^{ -at })$$

GATE 2000

(5) A linear time invariant system has an impulse response $${ e }^{ 2t }$$, t>0. if the initial condition are zero and the input is $${ e }^{ 3t }$$, the output for t>0 is

1.  $${ e }^{ 3t }-{ e }^{ 2t }$$
2.  $${ e }^{ 5t }$$
3.  $${ e }^{ 3t }+{ e }^{ 2t }$$
4.  None of these

GATE 2000

(6) Let u(t) be the step function. which of the waveform in the figure corresponds to the convolution of u(t)-u(t-1) with u(t)-u(t-2)?

GATE 2001

(7) The transfer function of a system is given by  $$H(s)=\frac { 1 }{ { s }^{ 2 }(s-2) }$$

The impulse response of the system is

1.  $${ (t }^{ 2 }*{ e }^{ -2t })u(t)$$
2.  $${ (t }*{ e }^{ 2t })u(t)$$\
3.  $${ (t }{ e }^{ -2t })u(t)$$
4.  $${ (t }{ e }^{ 2t })u(t)$$

GATE 2001

(8) Let δ(t) denote the delta function. the value of integral $$\int _{ -\infty }^{ \infty }{ \delta (t)cos(\frac { 3t }{ 2 } )dt }$$ is

1.  1
2.  -1
3.  0
4.  π/2

GATE 2001

(9) The impulse response functions of four linear systems S1, S2, S3, S4 are given respectively by $${ h }_{ 1 }(t)=1$$, $${ h }_{ 2 }(t)=u(t)$$, $${ h }_{ 3 }(t)=\frac { u(t) }{ (t+1) }$$ and $${ h }_{ 4 }(t)={ e }^{ -3(t) }u(t)$$ where u(t) is the unit step function. which of these system is time invariant, causal and stable?

1.  S1
2.  S2
3.  S3
4.  S4

GATE 2002

(10) If the signal f(t) has energy E, the energy of the signal f(2t) is equal to

1.  E
2.  E/2
3.  2E
4.  4E

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

All books mentioned above is very good books for signal and system, we would recommend schoums outline for gate preparation, it is wonderful book to clear basic concepts