1
GATE EE 2022
MCQ (Single Correct Answer)
+1
-0.33

Let an input x(t) = 2 sin(10$$\pi$$t) + 5 cos(15$$\pi$$t) + 7 sin(42$$\pi$$t) + 4 cos(45$$\pi$$t) is passed through an LTI system having an impulse response,

$$h(t) = 2\left( {{{\sin (10\pi t)} \over {\pi t}}} \right)\cos (40\pi t)$$

The output of the system is

A
$$2\sin (10\pi t) + 5cos(15\pi t)$$
B
$$5\cos (15\pi t) + 7sin(42\pi t)$$
C
$$7\sin (42\pi t) + 4cos(45\pi t)$$
D
$$2\sin (10\pi t) + 4cos(45\pi t)$$
2
GATE EE 2022
MCQ (Single Correct Answer)
+1
-0.33

Consider the system as shown below:

GATE EE 2022 Signals and Systems - Linear Time Invariant Systems Question 1 English

where y(t) = x(et). The system is

A
linear and causal.
B
linear and non-causal.
C
non-linear and causal.
D
non-linear and non-causal.
3
GATE EE 2022
MCQ (Single Correct Answer)
+1
-0.33

The discrete time Fourier series representation of a signal x[n] with period N is written as $$x[n] = \sum\nolimits_{k = 0}^{N - 1} {{a_k}{e^{j(2kn\pi /N)}}} $$. A discrete time periodic signal with period N = 3, has the non-zero Fourier series coefficients : a$$-$$3 = 2 and a4 = 1. The signal is

A
$$2 + 2{e^{ - \left( {j{{2\pi } \over 6}n} \right)}}\cos \left( {{{2\pi } \over 6}n} \right)$$
B
$$1 + 2{e^{\left( {j{{2\pi } \over 6}n} \right)}}\cos \left( {{{2\pi } \over 6}n} \right)$$
C
$$1 + 2{e^{\left( {j{{2\pi } \over 3}n} \right)}}\cos \left( {{{2\pi } \over 6}n} \right)$$
D
$$2 + 2{e^{\left( {j{{2\pi } \over 6}n} \right)}}\cos \left( {{{2\pi } \over 6}n} \right)$$
4
GATE EE 2022
MCQ (Single Correct Answer)
+1
-0.33

As you grow older, an injury to your __________ may take longer to ___________.

A
heel / heel
B
heal / heel
C
heal / heal
D
heel / heal
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