The 3-dB bandwidth of the low-pass signal e^{-t} u(t), where u(t) is the unit step
function, is given by

**A. ** 1/2π Hz

**B. **

**C. ** ∞

**D. ** 1 Hz

**Answer : ****Option A**

**Explaination / Solution: **

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The result of the convolution is

**A. ** x ( t + t_{0})

**B. ** x ( t - t_{0})

**C. ** x ( -t + t_{0})

**D. ** x ( -t - t_{0})

**Answer : ****Option D**

**Explaination / Solution: **

From the convolution property,

From the convolution property,

Now, we replace t by -t to obtain

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Let the Laplace transform of a function F(t) which exists for t > 0 be F_{1}(s) and
the Laplace transform of its delayed version be the
complex conjugate of F1(s) with the Laplace variable set as s=σ + jw. If G(s) = , then the inverse Laplace transform of G(s) is

**A. **

**B. **

**C. ** An ideal step function u(t)

**D. **

**Answer : ****Option B**

**Explaination / Solution: **

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Consider a linear system whose state space representation is x(t) = Ax(t). If the initial state vector of the system is then the system response is If the itial state vector of the system changes to the system response becomes

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option A**

**Explaination / Solution: **

The eigenvalue and eigenvector pairs (λ_{i}v_{i})for the system are

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Consider a causal LTI system characterized by differential equation The response of the system to the input where u(t) denotes the unit step
function, is

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option D**

**Explaination / Solution: **

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A discrete time signal x[n] = sin (π^{2}n) n being an integer, is

**A. ** periodic with period π

**B. ** periodic with period π^{2}

**C. ** periodic with period π/2

**D. ** not periodic

**Answer : ****Option D**

**Explaination / Solution: **

In the given options (A), (B) and (C), we have the periods respectively as

In the given options (A), (B) and (C), we have the periods respectively as

N1 = π

N2 = π^{2}

N3 = π/3

None of the above period is an integer. Since, a discrete time signal has its period
an integer. So, all the three options are incorrect. Hence, we are left with the
option (D). i.e. the discrete time signal x[n] = sin (π^{2}n) is not periodic.

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Consider a linear time invariant system x = Ax, with initial condition x(0) at t = 0. Suppose α and β are eigenvectors of (2 x 2) matrix A corresponding to distinct eigenvalues λ_{1} and λ_{2} respectively.
Then the response x(t) of the system due to initial condition x(0) = α is

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option A**

**Explaination / Solution: **

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The state variable description of an LTI system is given by**A. **

**B. **

**C. **

**D. **

**Answer : ****Option D**

**Explaination / Solution: **

where y is the output and u is the input. The system is controllable for

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For a periodic signal the fundamental frequency in rad/s
**A. ** 100

**B. ** 300

**C. ** 500

**D. ** 1500

**Answer : ****Option A**

**Explaination / Solution: **

Given, the signal

Given, the signal

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The period of the signal is
**A. ** 0.4πs

**B. ** 0.8πs

**C. ** 1.25s

**D. ** 2.5s

**Answer : ****Option D**

**Explaination / Solution: **

No Explaination.

No Explaination.

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